diff --git a/README.md b/README.md index d38f19f..0278df4 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,38 @@ -# audio +# Создание снимков аудио файлов через октавное CQT - преобразование -Октавное вейвлет-преобразование для создания эталонных слепков сравнения аудио шумов \ No newline at end of file +Создание частотного-массива (слепка) исходного файла для создания эталонных шаблонов шумов. + +## Библиотеки + +``` +import Pkg; Pkg.add("DSP") +import Pkg; Pkg.add("SignalAnalysis") +import Pkg; Pkg.add("FFTW") +import Pkg; Pkg.add("Plots") +import Pkg; Pkg.add("CSV") +import Pkg; Pkg.add("Tables") +import Pkg; Pkg.add("DataFrames") +import Pkg; Pkg.add("WAV") + +``` + +## Использование + +``` +julia zaudio.jl test.wav + +``` + +## Шаги + +1. Читаем WAV файл + +2. Нормализуем уровень средним + +3. Разбиваем на кадры + +4. Кадры с низкой энергией отбрасываем + +5. Осуществляем CQT - преобразование + +6. Сохраняем в datasets diff --git a/analise.jl b/analise.jl new file mode 100644 index 0000000..b1f22d1 --- /dev/null +++ b/analise.jl @@ -0,0 +1,68 @@ +using Statistics +using Plots +using Tables +using CSV +using DataFrames + + +# Папка с датасетами + +data_dir = "datasets/" + +# Чтение файла данных + +function read() + if !isempty(ARGS) + try + data = CSV.read(data_dir*ARGS[1], DataFrame, skipto=2) + ret = [] + map(eachrow(data)) do col + push!(ret,std(col)) + end + return ret + catch e + println("Ошибка чтения wav-файла: "*e) + end + else + println("Не указан входной файл") + exit() + end +end + +# Скользящее среднее + +function m_average(arr::Vector{Any}, n::Number)::Vector{Any} + so_far = sum(arr[1:n]) + out = zero(arr[n:end]) + out[1] = so_far + for (i, (start, stop)) in enumerate(zip(arr, arr[n+1:end])) + so_far += stop - start + out[i+1] = so_far + end + return out +end + + + +audio_data = read() + +println(typeof(audio_data)) + +println(size(audio_data)) + +println(ndims(audio_data)) + +println(audio_data[1:41]) + +audio_data = m_average(audio_data,20) + +numbers = size(mel_spectrogram) + +minimum_mel = 2595 * log10(1 + (freq / window_length) / 700) +maximum_mel = 2595 * log10(1 + (freq / 2) / 700) +mel_scale = range(minimum_mel, stop = maximum_mel, length = numbers) +hertz_scale = 700 .* (10 .^ (mel_scale / 2595) .- 1) + +plot_object = plot(audio_data, xticks = convert(Array{Int}, round.(hertz_scale[1:8:numbers]))) +plot!(title = "Sound form", size = (990, 600)) +savefig(plot_object, data_dir*ARGS[1]*"-"*"analize.png") diff --git a/audio.jl b/audio.jl new file mode 100644 index 0000000..cb0af4a --- /dev/null +++ b/audio.jl @@ -0,0 +1,265 @@ +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots +using Tables +using CSV +using DSP +using SignalAnalysis +using DataFrames +using LinearAlgebra +using Logging + +global file_frame = "" + +global savedata = false #Сохранять ли при обработке спектограммы + +detect = true #Флаг необходимости сравнения с эталонами + +# Настройки CQT преобразования + +octave_resolution = 24 +minimum_frequency = 55 +maximum_frequency = 9520 +time_resolution = 25 + +# Размеры кадра в сек + +window_duration = 0.04; + +# Уровень энергии для порогового фильтра + +energy_level = 50 + +# Количество кадров для сглаживания скользящей средней слепка аудио-данных + +m_offset = 20 + +function err(mes) + redirect_stdio(stderr="audio.log") do + logger = ConsoleLogger(stderr) + @error mes + with_logger(logger) do + println(mes) + end + end + exit(2) +end + +# Загрузка сохраненного файла данных очищенных окон с преобразованием в среднеквадратичное отклонение по частотным полосам + +function load(filename)::Vector{Any} + if !isempty(filename) + try + data = CSV.read(filename, DataFrame, skipto=2) + return data[!, :Column1] + catch e + println("Ошибка чтения csv-файла") + end + else + err("Не указан входной файл") + end +end + +function sets()::Dict{String, Vector{Float64}} + datasets = Dict{String, Vector{Float64}}() + for file in readdir("datasets") + datasets[replace(file,".csv" => "")] = load("datasets/"*file) + end + return datasets +end + +# Сравнение частотного снимка с сохраненными эталонами + +function determ(data) + for (name,frame) in sets() + if cor(data[70:end], frame[70:end]) < 0.99 #Если корреляция по Пирсону по ВЧ низкая, то сигнал невалидный + continue + end + dataLF = normalize(data[1:70]) + frame = normalize(frame[1:70]) + if sum(broadcast(abs, dataLF-frame)) < 0.2 #Если сумма асболютных отклнений по НЧ низкая, то фрейм совпадает + return name + end + end + return +end + +# Скользящее среднее + +function m_average(arr::Vector{Float64}, n::Number)::Vector{Any} + so_far = sum(arr[1:n]) + out = zero(arr[n:end]) + out[1] = so_far + for (i, (start, stop)) in enumerate(zip(arr, arr[n+1:end])) + so_far += stop - start + out[i+1] = so_far + end + return out +end + +# Нормализация уровня + +function normalizeWAV(audio_input::Matrix{Float64},freq::Number) + return mean(audio_input, dims=2), freq +end + +# Разбитие на окна + +function windows(freq::Number) + local window_length = nextpow(2, ceil(Int, window_duration*freq)) + local window_function = zaf.hamming(window_length, "periodic") # оконная аналитическая функция + return window_length, convert(Int, window_length/2), window_function +end + +# Фильтрация окон по уровню минимальной энергии звука в каждом окне + +function filter(audio_input::Matrix{Float64},window_length::Number)::Matrix{Float64} + output_signal = zeros(1,1) + number_samples = length(audio_input) + padding_length = floor(Int, window_length / 2) + number_times = + ceil( + Int, + ((number_samples + 2 * padding_length) - window_length) / + step_length, + ) + 1 + local i = 0 + for j = 1:(number_times-10) # 10 последних кадров отбарсываем + frame = audio_input[i+1:i+window_length] + if energy(frame) > energy_level + output_signal = [output_signal;frame] + end + i = i + step_length + + end + return output_signal +end + +# Преобразование Фурье + +function stft(audio::Matrix{Float64},freq::Number) + local window_length,step_length,window_function = windows(freq) + return zaf.stft(audio, window_function, step_length), window_length, step_length, window_function +end + +# Спектограмма разложения ряда Фурье + +function spectrogram(audio::Matrix{Float64},freq::Number)::Matrix{Float64} + local audio_stft, window_length = stft(audio,freq) + local audio_spectrogram = abs.(audio_stft[2:convert(Int, window_length/2)+1, :]) # Отбрасываем постоянную составляющую + local number_samples = length(audio_input) + local xtick_step = 1 + local ytick_step = 1000 + local plot_object = zaf.specshow(audio_spectrogram, number_samples, freq, xtick_step, ytick_step) + heatmap!(title = "Spectrogram (dB)", size = (990, 600)) + savefig(plot_object, file_frame*".spectr.png") + CSV.write(file_frame*".spectr.csv", Tables.table(audio_spectrogram)) + return audio_spectrogram +end + +# CQT-октавное вевлет-преобразование + +function cqt(audio::Matrix{Float64},freq::Number)::Matrix{Float64} + local cqt_kernel = zaf.cqtkernel(freq, octave_resolution, minimum_frequency, maximum_frequency) + cqt_spectrogram = zaf.cqtspectrogram(audio, freq, time_resolution, cqt_kernel) + if savedata + CSV.write(file_frame*".cqt.csv", Tables.table(cqt_spectrogram)) + local xtick_step = 1 + local plot_object = zaf.cqtspecshow(cqt_spectrogram, time_resolution, octave_resolution, minimum_frequency, xtick_step) + heatmap!(title = "CQT spectrogram (dB)", size = (990, 600)) + savefig(plot_object, file_frame*".cqt.png") + end + return cqt_spectrogram +end + +# Преобразование вевлет-спектрограммы в спектр среднего значения по октавам со сглаживанием + +function raft(spectr::Matrix{Float64})::Vector{Any} + freqs, frames = size(spectr) + raft_data = zeros(freqs) + for i in 1:freqs + raft_data[i] = mean(spectr[i, :]) + end + return m_average(raft_data,m_offset) +end + +# Cохранение образа записи + +function save(audio_data::Vector{Any},freq::Number)::Vector{Any} + CSV.write(file_frame*".csv", Tables.table(audio_data)) + numbers = length(audio_data) + xtick_locations = [0:octave_resolution:numbers;] + xtick_labels = convert( + Array{Int}, + minimum_frequency * 2 .^ (xtick_locations / octave_resolution), + ) + plot_object = plot(audio_data, xticks = (xtick_locations, xtick_labels)) + plot!(title = "Sound form", size = (990, 600)) + savefig(plot_object, file_frame*".png") + return audio_data +end + + +# Считываем данные из WAV файла и нормализуем их, частота дискретизации получается из заголовка WAV-файла + +if !isempty(ARGS) + global file_frame = replace(ARGS[1],".wav" => "") + if length(ARGS)>1 && ARGS[2] == "-s" + savedata = true + end + if length(ARGS)>1 && ARGS[2] == "-d" + println("Режим формирования нового эталонного датасета") + if ARGS[3] isa String + savedata = true + global file_frame = "datasets/"*ARGS[3] + detect = false + else + err("Не указано название датасета") + end + end +else + err("Не указан входной файл") +end + +audio_input, freq = wavread(ARGS[1]) + +audio_input, freq = normalizeWAV(audio_input, freq) + +# Исходя из частоты дискретизации получаем длину кадров и шаг между ними + +window_length,step_length,window_function = windows(freq) + +# Фильтруем кадры, отбрасывая кадры с низкой энергией + +audio = filter(audio_input,window_length) + +frames, freqs = size(audio) + +if frames<5 + err("Недостаточная энергия сигнала: "*ARGS[1]) +end + +# Осущетсвляем CQT-преобразование и сохранение спектограммы и массива данных + +cqt_spectrogram = cqt(audio,freq) + +# Преобразуем спектограмму в с спектр среднеквадратичных отклонений + +raft_data = raft(cqt_spectrogram) + +# Cохраняем результат + +if savedata + #spectrogram(audio_input,freq) + save(raft_data,freq) +end + +# Сравниваем с эталонами и выводим результат в stdout + +if detect + println(determ(raft_data)) +end + + diff --git a/datasets/cleaner.wav-analise.csv b/datasets/cleaner.wav-analise.csv new file 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diff --git a/datasets/voice.wav-cqt.png b/datasets/voice.wav-cqt.png new file mode 100644 index 0000000..42e79a2 Binary files /dev/null and b/datasets/voice.wav-cqt.png differ diff --git a/datasets/voice.wav-spectr.png b/datasets/voice.wav-spectr.png new file mode 100644 index 0000000..13bb4da Binary files /dev/null and b/datasets/voice.wav-spectr.png differ diff --git a/docs/analiticheskiy-obzor-i-klassifikatsiya-metodov-vydeleniya-priznakov-akusticheskogo-signala-v-rechevyh-sistemah.pdf b/docs/analiticheskiy-obzor-i-klassifikatsiya-metodov-vydeleniya-priznakov-akusticheskogo-signala-v-rechevyh-sistemah.pdf new file mode 100644 index 0000000..6955f57 Binary files /dev/null and b/docs/analiticheskiy-obzor-i-klassifikatsiya-metodov-vydeleniya-priznakov-akusticheskogo-signala-v-rechevyh-sistemah.pdf differ diff --git a/files/cleaner.wav b/files/cleaner.wav new file mode 100644 index 0000000..2b497ec Binary files /dev/null and b/files/cleaner.wav differ diff --git a/files/door1.wav b/files/door1.wav new file mode 100644 index 0000000..f44f4dc Binary files /dev/null and b/files/door1.wav differ diff --git a/files/record.sh b/files/record.sh new file mode 100644 index 0000000..ed18233 --- /dev/null +++ b/files/record.sh @@ -0,0 +1,44 @@ +#!/bin/bash + +declare -i timeout=65 # default timeout in seconds. + +Kill='/bin/kill' +split_line='-------------------------------------------------------------------------------' + +success_msg='status OK' + +ext_prg="arecord "$1 +( ${ext_prg} ) +cPID=$! +sleep 5 +((timeout-=5)) + +status=0 +if [[ ${timeout} -gt 0 ]]; then + while [[ $( ps | grep -o -G "^${cPID}"; ) -eq ${cPID} && ${status} -eq 0 ]]; do + status=$((timeout-- ? 0 : 1)); sleep 1 + done +fi + +if [[ ${status} -eq 1 ]]; then + eval '${Kill} -9 ${cPID}' &>/dev/null; + echo "${split_line}" + echo `basename $0`": Timeout occured, record saved." + echo "Process(${cPID}): ${ext_prg}" + echo "was killed because of timeout." + echo "${split_line}" + exit 1 +else + echo "${split_line}" + echo -en "Process(${cPID}): ${ext_prg}\nterminate by itself successfully.\n" + rc=$(cat ${ftmp} | awk "/${success_msg}/"'{print $2}') + if [[ -z "${rc}" ]]; then + echo "${ext_prg}: ERR: no success code returned!!!" + exit 1 + else + echo "${ext_prg}: return success code!!!" + fi + echo "${split_line}" +fi + +exit 0 diff --git a/files/test.wav b/files/test.wav new file mode 100644 index 0000000..4b62ff5 Binary files /dev/null and b/files/test.wav differ diff --git a/files/voice.wav b/files/voice.wav new file mode 100644 index 0000000..6860b12 Binary files /dev/null and b/files/voice.wav differ diff --git a/zaf.jl b/zaf.jl new file mode 100644 index 0000000..9358d2c --- /dev/null +++ b/zaf.jl @@ -0,0 +1,1532 @@ +""" +This Julia module implements a number of functions for audio signal analysis. + +# Functions: + stft - Compute the short-time Fourier transform (STFT). + istft - Compute the inverse STFT. + melfilterbank - Compute the mel filterbank. + melspectrogram - Compute the mel spectrogram using a mel filterbank. + mfcc - Compute the mel-frequency cepstral coefficients (MFCCs) using a mel filterbank. + cqtkernel - Compute the constant-Q transform (CQT) kernel. + cqtspectrogram - Compute the CQT spectrogram using a CQT kernel. + cqtchromagram - Compute the CQT chromagram using a CQT kernel. + dct - Compute the discrete cosine transform (DCT) using the fast Fourier transform (FFT). + dst - Compute the discrete sine transform (DST) using the FFT. + mdct - Compute the modified discrete cosine transform (MDCT) using the FFT. + imdct - Compute the inverse MDCT using the FFT. + +# Other: + hamming - Compute the Hamming window. + sigplot - Plot a signal in seconds. + specshow - Display an spectrogram in dB, seconds, and Hz. + melspecshow - Display a mel spectrogram in dB, seconds, and Hz. + mfccshow - Display MFCCs in seconds. + cqtspecshow - Display a CQT spectrogram in dB, seconds, and Hz. + cqtchromshow - Display a CQT chromagram in seconds. + +# Author: + Zafar Rafii + zafarrafii@gmail.com + http://zafarrafii.com + https://github.com/zafarrafii + https://www.linkedin.com/in/zafarrafii/ + 05/11/20 +""" +module zaf + +using FFTW, SparseArrays, Plots + +export stft, istft, melfilterbank, melspectrogram, mfcc, cqtkernel, +cqtspectrogram, cqtchromagram, dct, dst, mdct, imdct + + +""" + audio_stft = stft(audio_signal, window_function, step_length) + +Compute the short-time Fourier transform (STFT). + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `window_function::Float`: the window function (window_length,). +- `step_length::Integer`: the step length in samples. +- `audio_stft::Complex`: the audio STFT (window_length, number_frames). + +# Example: Compute the spectrogram from an audio file. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Set the window duration in seconds (audio is stationary around 40 milliseconds) +window_duration = 0.04; + +# Derive the window length in samples (use powers of 2 for faster FFT and constant overlap-add (COLA)) +window_length = nextpow(2, ceil(Int, window_duration*sampling_frequency)) + +# Compute the window function (periodic Hamming window for COLA) +window_function = zaf.hamming(window_length, "periodic") + +# Set the step length in samples (half of the window length for COLA) +step_length = convert(Int, window_length/2) + +# Compute the STFT +audio_stft = zaf.stft(audio_signal, window_function, step_length) + +# Derive the magnitude spectrogram (without the DC component and the mirrored frequencies) +audio_spectrogram = abs.(audio_stft[2:convert(Int, window_length/2)+1, :]) + +# Magnitude spectrogram (without the DC component and the mirrored frequencies) +audio_spectrogram = abs.(audio_stft[2:convert(Int, window_length/2)+1, :]) + +# Display the spectrogram in dB, seconds, and Hz +number_samples = length(audio_signal) +xtick_step = 1 +ytick_step = 1000 +plot_object = zaf.specshow(audio_spectrogram, number_samples, sampling_frequency, xtick_step, ytick_step) +heatmap!(title = "Spectrogram (dB)", size = (990, 600)) +``` +""" +function stft(audio_signal, window_function, step_length) + + # Get the number of samples and the window length in samples + number_samples = length(audio_signal) + window_length = length(window_function) + + # Derive the zero-padding length at the start and at the end of the signal to center the windows + padding_length = floor(Int, window_length / 2) + + # Compute the number of time frames given the zero-padding at the start and at the end of the signal + number_times = + ceil( + Int, + ((number_samples + 2 * padding_length) - window_length) / + step_length, + ) + 1 + + # Zero-pad the start and the end of the signal to center the windows + audio_signal = [ + zeros(padding_length) + audio_signal + zeros( + ( + number_times * step_length + (window_length - step_length) - + padding_length + ) - number_samples, + ) + ] + + # Initialize the STFT + audio_stft = zeros(window_length, number_times) + + # Loop over the time frames + i = 0 + for j = 1:number_times + + # Window the signal + audio_stft[:, j] = audio_signal[i+1:i+window_length] .* window_function + i = i + step_length + + end + + # Compute the Fourier transform of the frames using the FFT + audio_stft = fft(audio_stft, 1) + +end + +""" + audio_istft = istft(audio_signal, window_function, step_length) + +Compute the inverse short-time Fourier transform (STFT). + +# Arguments: +- `audio_stft::Complex`: the audio STFT (window_length, number_frames). +- `window_function::Float`: the window function (window_length,). +- `step_length::Integer`: the step length in samples. +- `audio_signal::Float`: the audio signal (number_samples,). + +# Example: Estimate the center and sides signals of a stereo audio file. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Plots + +# Read the (stereo) audio signal with its sampling frequency in Hz +audio_signal, sampling_frequency = wavread("audio_file.wav") + +# Set the parameters for the STFT +window_length = nextpow(2, ceil(Int, 0.04*sampling_frequency)) +window_function = zaf.hamming(window_length, "periodic") +step_length = convert(Int, window_length/2) + +# Compute the STFTs for the left and right channels +audio_stft1 = zaf.stft(audio_signal[:,1], window_function, step_length) +audio_stft2 = zaf.stft(audio_signal[:,2], window_function, step_length) + +# Derive the magnitude spectrograms (with DC component) for the left and right channels +audio_spectrogram1 = abs.(audio_stft1[1:convert(Int, window_length/2)+1, :]) +audio_spectrogram2 = abs.(audio_stft2[1:convert(Int, window_length/2)+1, :]) + +# Estimate the time-frequency masks for the left and right channels for the center +center_mask1 = min.(audio_spectrogram1, audio_spectrogram2)./audio_spectrogram1 +center_mask2 = min.(audio_spectrogram1, audio_spectrogram2)./audio_spectrogram2 + +# Derive the STFTs for the left and right channels for the center (with mirrored frequencies) +center_stft1 = [center_mask1; center_mask1[convert(Int, window_length/2):-1:2,:]] .* audio_stft1 +center_stft2 = [center_mask2; center_mask2[convert(Int, window_length/2):-1:2,:]] .* audio_stft2 + +# Synthesize the signals for the left and right channels for the center +center_signal1 = zaf.istft(center_stft1, window_function, step_length) +center_signal2 = zaf.istft(center_stft2, window_function, step_length) + +# Derive the final stereo center and sides signals +center_signal = [center_signal1 center_signal2]; +center_signal = center_signal[1:size(audio_signal, 1), :] +sides_signal = audio_signal-center_signal; + +# Write the center and sides signals +wavwrite(center_signal, "center_signal.wav", Fs=sampling_frequency) +wavwrite(sides_signal, "sides_signal.wav", Fs=sampling_frequency) + +# Display the original, center, and sides signals in seconds +xtick_step = 1 +plot_object1 = zaf.sigplot(audio_signal, sampling_frequency, xtick_step) +plot!(ylims = (-1, 1), title = "Original signal") +plot_object2 = zaf.sigplot(center_signal, sampling_frequency, xtick_step) +plot!(ylims = (-1, 1), title = "Center signal") +plot_object3 = zaf.sigplot(sides_signal, sampling_frequency, xtick_step) +plot!(ylims = (-1, 1), title = "Sides signal") +plot(plot_object1, plot_object2, plot_object3, layout = (3, 1), size = (990, 600)) +``` +""" +function istft(audio_stft, window_function, step_length) + + # Get the window length in samples and the number of time frames + window_length, number_times = size(audio_stft) + + # Compute the number of samples for the signal + number_samples = number_times * step_length + (window_length - step_length) + + # Initialize the signal + audio_signal = zeros(number_samples) + + # Compute the inverse Fourier transform of the frames and real part to ensure real values + audio_stft = real(ifft(audio_stft, 1)) + + # Loop over the time frames + i = 0 + for j = 1:number_times + + # Perform a constant overlap-add (COLA) of the signal + # (with proper window function and step length) + audio_signal[i+1:i+window_length] = + audio_signal[i+1:i+window_length] + audio_stft[:, j] + i = i + step_length + + end + + # Remove the zero-padding at the start and at the end of the signal + audio_signal = + audio_signal[window_length-step_length+1:number_samples-(window_length-step_length)] + + # Normalize the signal by the gain introduced by the COLA (if any) + audio_signal = + audio_signal / sum(window_function[1:step_length:window_length]) + +end + +""" +mel_filterbank = melfilterbank(sampling_frequency, window_length, number_filters) + + Compute the mel filterbank. + +# Arguments: +- `sampling_frequency::Float`: the sampling frequency in Hz. +- `window_length::Integer`: the window length for the Fourier analysis in samples. +- `number_filters::Integer`: the number of mel filters. +- `mel_filterbank::Float`: the mel filterbank (sparse) (number_mels, number_frequencies). + +# Example: Compute and display the mel filterbank. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using Plots + +# Compute the mel filterbank using some parameters +sampling_frequency = 44100 +window_length = nextpow(2, ceil(Int, 0.04*sampling_frequency)) +number_mels = 128 +mel_filterbank = zaf.melfilterbank(sampling_frequency, window_length, number_mels) + +# Display the mel filterbank +heatmap(Array(mel_filterbank), fillcolor = :jet, legend = false, fmt = :png, size = (990, 300), + title = "Mel filterbank", xlabel = "Frequency index", ylabel = "Mel index") +``` +""" +function melfilterbank( + sampling_frequency, + window_length, + number_filters, +) + + # Compute the minimum and maximum mels + minimum_mel = 2595 * log10(1 + (sampling_frequency / window_length) / 700) + maximum_mel = 2595 * log10(1 + (sampling_frequency / 2) / 700) + + # Derive the width of the half-overlapping filters in the mel scale (constant) + filter_width = + 2 * (maximum_mel - minimum_mel) / (number_filters + 1) + + # Compute the start and end indices of the filters in the mel scale (linearly spaced) + filter_indices = [minimum_mel:filter_width/2:maximum_mel;] + + # Derive the indices of the filters in the linear frequency scale (log spaced) + filter_indices = + round.( + Int, + 700 * (10 .^ (filter_indices / 2595) .- 1) * window_length / + sampling_frequency, + ) + + # Initialize the mel filterbank + mel_filterbank = zeros(number_filters, convert(Int, window_length / 2)) + + # Loop over the filters + for i = 1:number_filters + + # Compute the left and right sides of the triangular filters + # (this is more accurate than creating triangular filters directly) + mel_filterbank[i, filter_indices[i]:filter_indices[i+1]] = range( + 0, + stop = 1, + length = filter_indices[i+1] - filter_indices[i] + 1, + ) + mel_filterbank[i, filter_indices[i+1]:filter_indices[i+2]] = range( + 1, + stop = 0, + length = filter_indices[i+2] - filter_indices[i+1] + 1, + ) + + end + + # Make the mel filterbank sparse + mel_filterbank = sparse(mel_filterbank) + +end + +""" +melspectrogram(audio_signal, window_function, step_length, mel_filterbank) + + Compute the mel spectrogram using a mel filterbank. + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `window_function::Float`: the window function (window_length,). +- `step_length::Integer`: the step length in samples. +- `mel_filterbank::Float`: the mel filterbank (number_mels, number_frequencies). +- `mel_spectrogram::Float`: the mel spectrogram (number_mels, number_times). + +# Example: Compute and display the mel spectrogram. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Set the parameters for the Fourier analysis +window_length = nextpow(2, ceil(Int, 0.04*sampling_frequency)) +window_function = zaf.hamming(window_length, "periodic") +step_length = convert(Int, window_length/2) + +# Compute the mel filterbank +number_mels = 128 +mel_filterbank = zaf.melfilterbank(sampling_frequency, window_length, number_mels) + +# Compute the mel spectrogram using the filterbank +mel_spectrogram = zaf.melspectrogram(audio_signal, window_function, step_length, mel_filterbank) + +# Display the mel spectrogram in dB, seconds, and Hz +number_samples = length(audio_signal) +xtick_step = 1 +plot_object = zaf.melspecshow(mel_spectrogram, number_samples, sampling_frequency, window_length, xtick_step) +heatmap!(title = "Mel spectrogram (dB)", size = (990, 600)) +``` +""" +function melspectrogram( + audio_signal, + window_function, + step_length, + mel_filterbank, +) + + # Compute the magnitude spectrogram (without the DC component and the mirrored frequencies) + audio_stft = zaf.stft(audio_signal, window_function, step_length) + audio_spectrogram = abs.(audio_stft[2:convert(Int, length(window_function)/2)+1, :]) + + # Compute the mel spectrogram by using the filterbank + mel_spectrogram = mel_filterbank * audio_spectrogram + +end + +""" +audio_mfcc = mfcc(audio_signal, window_function, step_length, mel_filterbank, number_coefficients) + + Compute the mel-frequency cepstral coefficients (MFCCs). + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `window_function::Float`: the window function (window_length,). +- `step_length::Integer`: the step length in samples. +- `mel_filterbank::Float`: the mel filterbank (number_mels, number_frequencies). +- `number_coefficients::Integer`: the number of coefficients (without the 0th coefficient). +- `audio_mfcc::Float`: the audio MFCCs (number_coefficients, number_times). + +# Example: Compute and display the MFCCs, delta MFCCs, and delta-detla MFCCs. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Set the parameters for the Fourier analysis +window_length = nextpow(2, ceil(Int, 0.04*sampling_frequency)) +window_function = zaf.hamming(window_length, "periodic") +step_length = convert(Int, window_length/2) + +# Compute the mel filterbank +number_mels = 40 +mel_filterbank = zaf.melfilterbank(sampling_frequency, window_length, number_mels) + +# Compute the MFCCs using the filterbank +number_coefficients = 20 +audio_mfcc = zaf.mfcc(audio_signal, window_function, step_length, mel_filterbank, number_coefficients) + +# Compute the delta and delta-delta MFCCs +audio_dmfcc = diff(audio_mfcc, dims=2) +audio_ddmfcc = diff(audio_dmfcc, dims=2) + +# Display the MFCCs, delta MFCCs, and delta-delta MFCCs in seconds +xtick_step = 1 +number_samples = length(audio_signal) +plot_object1 = zaf.mfccshow(audio_mfcc, number_samples, sampling_frequency, xtick_step); plot!(title = "MFCCs") +plot_object2 = zaf.mfccshow(audio_dmfcc, number_samples, sampling_frequency, xtick_step); plot!(title = "Delta MFCCs") +plot_object3 = zaf.mfccshow(audio_ddmfcc, number_samples, sampling_frequency, xtick_step); plot!(title = "Delta MFCCs") +plot(plot_object1, plot_object2, plot_object3, layout = (3, 1), size = (990, 600)) +``` +""" +function mfcc( + audio_signal, + window_function, + step_length, + mel_filterbank, + number_coefficients, +) + + # Compute the power spectrogram (without the DC component and the mirrored frequencies) + audio_stft = zaf.stft(audio_signal, window_function, step_length) + audio_spectrogram = 2 .^ abs.(audio_stft[2:convert(Int, length(window_function)/2)+1, :]) + + # Compute the discrete cosine transform of the log magnitude spectrogram + # mapped onto the mel scale using the filter bank + audio_mfcc = FFTW.dct(log.(mel_filterbank * audio_spectrogram .+ eps()), 1) + + # Keep only the first coefficients (without the 0th) + audio_mfcc = audio_mfcc[2:number_coefficients+1, :] + +end + +""" + cqt_kernel = cqtkernel(sampling_frequency, frequency_resolution, minimum_frequency, maximum_frequency) + +Compute the constant-Q transform (CQT) kernel. + +# Arguments: +- `sampling_frequency::Float` the sampling frequency in Hz. +- `frequency_resolution::Integer` the frequency resolution in number of frequency channels per semitone. +- `minimum_frequency::Float`: the minimum frequency in Hz. +- `maximum_frequency::Float`: the maximum frequency in Hz. +- `cqt_kernel::Complex`: the CQT kernel (sparse) (number_frequencies, fft_length). + +# Example: Compute and display the CQT kernel. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using Plots + +# Set the parameters for the CQT kernel +sampling_frequency = 44100 +octave_resolution = 24 +minimum_frequency = 55 +maximum_frequency = sampling_frequency/2 + +# Compute the CQT kernel +cqt_kernel = zaf.cqtkernel(sampling_frequency, octave_resolution, minimum_frequency, maximum_frequency) + +# Display the magnitude CQT kernel +heatmap(abs.(Array(cqt_kernel)), fillcolor = :jet, legend = false, fmt = :png, size = (990, 300), + title = "Magnitude CQT kernel", xlabel = "FFT index", ylabel = "CQT index") +``` +""" +function cqtkernel( + sampling_frequency, + octave_resolution, + minimum_frequency, + maximum_frequency, +) + + # Compute the constant ratio of frequency to resolution (= fk/(fk+1-fk)) + quality_factor = 1 / (2^(1 / octave_resolution) - 1) + + # Compute the number of frequency channels for the CQT + number_frequencies = round( + Int, + octave_resolution * log2(maximum_frequency / minimum_frequency), + ) + + # Compute the window length for the FFT (= longest window for the minimum frequency) + fft_length = nextpow( + 2, + ceil(Int, quality_factor * sampling_frequency / minimum_frequency), + ) + + # Initialize the (complex) CQT kernel + cqt_kernel = zeros(ComplexF64, number_frequencies, fft_length) + + # Loop over the frequency channels + for i = 1:number_frequencies + + # Derive the frequency value in Hz + frequency_value = minimum_frequency * 2^((i - 1) / octave_resolution) + + # Compute the window length in samples + # (nearest odd value to center the temporal kernel on 0) + window_length = + 2 * round( + Int, + quality_factor * sampling_frequency / frequency_value / 2, + ) + 1 + + # Compute the temporal kernel for the current frequency (odd and symmetric) + temporal_kernel = + hamming(window_length, "symmetric") .* + exp.( + 2 * + pi * + im * + quality_factor * + (-(window_length - 1)/2:(window_length-1)/2) / window_length, + ) / window_length + + # Derive the pad width to center the temporal kernels + pad_width = convert(Int, (fft_length - window_length + 1) / 2) + + # Save the current temporal kernel at the center + # (the zero-padded temporal kernels are not perfectly symmetric anymore because of the even length here) + cqt_kernel[i, pad_width+1:pad_width+window_length] = temporal_kernel + + end + + # Derive the spectral kernels by taking the FFT of the temporal kernels + # (the spectral kernels are almost real because the temporal kernels are almost symmetric) + cqt_kernel = fft(cqt_kernel, 2) + + # Make the CQT kernel sparser by zeroing magnitudes below a threshold + cqt_kernel[abs.(cqt_kernel).<0.01] .= 0 + + # Make the CQT kernel sparse + cqt_kernel = sparse(cqt_kernel) + + # Get the final CQT kernel by using Parseval's theorem + cqt_kernel = conj.(cqt_kernel) / fft_length + +end + +""" + audio_spectrogram = cqtspectrogram(audio_signal, sampling_frequency, time_resolution, cqt_kernel) + +Compute the constant-Q transform (CQT) spectrogram using a kernel. + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `sample_rate::Float`: the sample rate in Hz. +- `time_resolution::Float`: the number of time frames per second. +- `cqt_kernel::Complex`: the CQT kernel (number_frequencies, fft_length). +- `cqt_spectrogram::Float`: the CQT spectrogram (number_frequencies, number_times). + +# Example: Compute and display the CQT spectrogram. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Compute the CQT kernel +octave_resolution = 24 +minimum_frequency = 55 +maximum_frequency = 3520 +cqt_kernel = zaf.cqtkernel(sampling_frequency, octave_resolution, minimum_frequency, maximum_frequency) + +# Compute the CQT spectrogram using the kernel +time_resolution = 25 +audio_spectrogram = zaf.cqtspectrogram(audio_signal, sampling_frequency, time_resolution, cqt_kernel) + +# Display the CQT spectrogram in dB, seconds, and Hz +xtick_step = 1 +plot_object = zaf.cqtspecshow(cqt_spectrogram, time_resolution, octave_resolution, minimum_frequency, xtick_step) +heatmap!(title = "CQT spectrogram (dB)", size = (990, 600)) +``` +""" +function cqtspectrogram( + audio_signal, + sampling_frequency, + time_resolution, + cqt_kernel, +) + + # Derive the number of time samples per time frame + step_length = round(Int, sampling_frequency / time_resolution) + + # Compute the number of time frames + number_times = floor(Int, length(audio_signal) / step_length) + + # Get the number of frequency channels and the FFT length + number_frequencies, fft_length = size(cqt_kernel) + + # Zero-pad the signal to center the CQT + audio_signal = [ + zeros(ceil(Int, (fft_length - step_length) / 2)) + audio_signal + zeros(floor(Int, (fft_length - step_length) / 2)) + ] + + # Initialize the spectrogram + audio_spectrogram = zeros(number_frequencies, number_times) + + # Loop over the time frames + i = 0 + for j = 1:number_times + + # Compute the magnitude CQT using the kernel + audio_spectrogram[:, j] = + abs.(cqt_kernel * fft(audio_signal[i+1:i+fft_length])) + i = i + step_length + + end + + # Return the output explicitly + return audio_spectrogram + +end + +""" + cqt_chromagram = cqtchromagram(audio_signal, sampling_frequency, time_resolution, octave_resolution, cqt_kernel) + +Compute the constant-Q transform (CQT) chromagram using a kernel. + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `sampling_frequency::Float`: the sample rate in Hz. +- `time_resolution::Float`: the number of time frames per second. +- `octave_resolution::Integer`: the number of frequency channels per octave. +- `cqt_kernel::Complex`: the CQT kernel (number_frequencies, fft_length). +- `cqt_chromagram::Float`: the CQT chromagram (number_chromas, number_times). + +# Example: Compute and display the CQT chromagram. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Compute the CQT kernel +octave_resolution = 24 +minimum_frequency = 55 +maximum_frequency = 3520 +cqt_kernel = zaf.cqtkernel(sampling_frequency, octave_resolution, minimum_frequency, maximum_frequency) + +# Compute the CQT chromagram using the kernel +time_resolution = 25 +cqt_chromagram = zaf.cqtchromagram(audio_signal, sampling_frequency, time_resolution, octave_resolution, cqt_kernel) + +# Display the CQT chromagram in seconds +xtick_step = 1 +plot_object = zaf.cqtchromshow(cqt_chromagram, time_resolution, xtick_step) +heatmap!(title = "CQT chromagram", size = (990, 300)) +``` +""" +function cqtchromagram( + audio_signal, + sampling_frequency, + time_resolution, + octave_resolution, + cqt_kernel, +) + + # Compute the CQT spectrogram + cqt_spectrogram = cqtspectrogram( + audio_signal, + sampling_frequency, + time_resolution, + cqt_kernel, + ) + + # Get the number of frequency channels and time frames + number_frequencies, number_times = size(cqt_spectrogram) + + # Initialize the chromagram + cqt_chromagram = zeros(octave_resolution, number_times) + + # Loop over the chroma channels + for i = 1:octave_resolution + + # Sum the energy of the frequency channels for every chroma + cqt_chromagram[i, :] = sum( + cqt_spectrogram[i:octave_resolution:number_frequencies, :], + dims = 1, + ) + + end + + # Return the output explicitly + return cqt_chromagram + +end + +""" +audio_dct = dct(audio_signal, dct_type) + + Compute the discrete cosine transform (DCT) using the fast Fourier transform (FFT). + +# Arguments: +- `audio_signal::Float`: the audio signal (window_length,). +- dct_type::Integer`: the DCT type (1, 2, 3, or 4). +- audio_dct::Float`: the audio DCT (number_frequencies,). + +# Example: Compute the 4 different DCTs and compare them to FFTW's DCTs. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using FFTW +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Get an audio segment for a given window length +window_length = 1024 +audio_segment = audio_signal[1:window_length] + +# Compute the DCT-I, II, III, and IV +audio_dct1 = zaf.dct(audio_segment, 1) +audio_dct2 = zaf.dct(audio_segment, 2) +audio_dct3 = zaf.dct(audio_segment, 3) +audio_dct4 = zaf.dct(audio_segment, 4) + +# Compute FFTW's DCT-I, II, III, and IV (orthogonalized) +audio_segment2 = copy(audio_segment) +audio_segment2[[1, end]] = audio_segment2[[1, end]]*sqrt(2) +fftw_dct1 = FFTW.r2r(audio_segment2, FFTW.REDFT00) +fftw_dct1[[1, window_length]] = fftw_dct1[[1, window_length]]/sqrt(2) +fftw_dct1 = fftw_dct1/2 * sqrt(2/(window_length - 1)) + +fftw_dct2 = FFTW.r2r(audio_segment, FFTW.REDFT10) +fftw_dct2[1] = fftw_dct2[1]/sqrt(2) +fftw_dct2 = fftw_dct2/2 * sqrt(2/window_length) + +audio_segment2 = copy(audio_segment) +audio_segment2[1] = audio_segment2[1]*sqrt(2) +fftw_dct3 = FFTW.r2r(audio_segment2, FFTW.REDFT01) +fftw_dct3 = fftw_dct3/2 * sqrt(2/window_length) + +fftw_dct4 = FFTW.r2r(audio_segment, FFTW.REDFT11) +fftw_dct4 = fftw_dct4/2 * sqrt(2/window_length) + +# Plot the DCT-I, II, III, and IV, FFTW's versions, and their differences (using yformatter because of precision issue in ticks) +dct1_plot = plot(audio_dct1, title = "DCT-I") +dct2_plot = plot(audio_dct2, title = "DCT-II") +dct3_plot = plot(audio_dct3, title = "DCT-III") +dct4_plot = plot(audio_dct4, title = "DCT-IV") +dct1_plot2 = plot(fftw_dct1, title = "FFTW's DCT-I") +dct2_plot2 = plot(fftw_dct2, title = "FFTW's DCT-II") +dct3_plot2 = plot(fftw_dct3, title = "FFTW's DCT-III") +dct4_plot2 = plot(fftw_dct4, title = "FFTW's DCT-IV") +diff1_plot = plot(audio_dct1-fftw_dct1, title = "DCT-I - FFTW's DCT-I") +diff2_plot = plot(audio_dct2-fftw_dct2, title = "DCT-II - FFTW's DCT-II", yformatter = y->string(convert(Int, round(y/1e-16)),"x10⁻¹⁶")) +diff3_plot = plot(audio_dct3-fftw_dct3, title = "DCT-III - FFTW's DCT-III", yformatter = y->string(convert(Int, round(y/1e-16)),"x10⁻¹⁶")) +diff4_plot = plot(audio_dct4-fftw_dct4, title = "DCT-IV - FFTW's DCT-IV", yformatter = y->string(convert(Int, round(y/1e-16)),"x10⁻¹⁶")) +plot(dct1_plot, dct2_plot, dct3_plot, dct4_plot, dct1_plot2, dct2_plot2, dct3_plot2, dct4_plot2, + diff1_plot, diff2_plot, diff3_plot, diff4_plot, xlims = (0, window_length), legend = false, titlefont = 10, + layout = (3,4), size = (990, 600), fmt = :png) +``` +""" +function dct(audio_signal, dct_type) + + # Check if the DCT type is I, II, III, or IV + if dct_type == 1 + + # Get the number of samples + window_length = length(audio_signal) + + # Pre-process the signal to make the DCT-I matrix orthogonal + # (copy the signal to avoid modifying it outside of the function) + audio_signal = copy(audio_signal) + audio_signal[[1, end]] = audio_signal[[1, end]] * sqrt(2) + + # Compute the DCT-I using the FFT + audio_dct = [audio_signal; audio_signal[end-1:-1:2]] + audio_dct = fft(audio_dct, 1) + audio_dct = real(audio_dct[1:window_length]) / 2 + + # Post-process the results to make the DCT-I matrix orthogonal + audio_dct[[1, end]] = audio_dct[[1, end]] / sqrt(2) + audio_dct = audio_dct * sqrt(2 / (window_length - 1)) + + elseif dct_type == 2 + + # Get the number of samples + window_length = length(audio_signal) + + # Compute the DCT-II using the FFT + audio_dct = zeros(4 * window_length) + audio_dct[2:2:2*window_length] = audio_signal + audio_dct[2*window_length+2:2:4*window_length] = audio_signal[end:-1:1] + audio_dct = fft(audio_dct, 1) + audio_dct = real(audio_dct[1:window_length]) / 2 + + # Post-process the results to make the DCT-II matrix orthogonal + audio_dct[1] = audio_dct[1] / sqrt(2) + audio_dct = audio_dct * sqrt(2 / window_length) + + elseif dct_type == 3 + + # Get the number of samples + window_length = length(audio_signal) + + # Pre-process the signal to make the DCT-III matrix orthogonal + # (copy the signal to avoid modifying it outside of the function) + audio_signal = copy(audio_signal) + audio_signal[1] = audio_signal[1] * sqrt(2) + + # Compute the DCT-III using the FFT + audio_dct = zeros(4 * window_length) + audio_dct[1:window_length] = audio_signal + audio_dct[window_length+2:2*window_length+1] = -audio_signal[end:-1:1] + audio_dct[2*window_length+2:3*window_length] = -audio_signal[2:end] + audio_dct[3*window_length+2:4*window_length] = audio_signal[end:-1:2] + audio_dct = fft(audio_dct, 1) + audio_dct = real(audio_dct[2:2:2*window_length]) / 4 + + # Post-process the results to make the DCT-III matrix orthogonal + audio_dct = audio_dct * sqrt(2 / window_length) + + elseif dct_type == 4 + + # Get the number of samples + window_length = length(audio_signal) + + # Compute the DCT-IV using the FFT + audio_dct = zeros(8 * window_length) + audio_dct[2:2:2*window_length] = audio_signal + audio_dct[2*window_length+2:2:4*window_length] = -audio_signal[end:-1:1] + audio_dct[4*window_length+2:2:6*window_length] = -audio_signal + audio_dct[6*window_length+2:2:8*window_length] = audio_signal[end:-1:1] + audio_dct = fft(audio_dct, 1) + audio_dct = real(audio_dct[2:2:2*window_length]) / 4 + + # Post-process the results to make the DCT-IV matrix orthogonal + audio_dct = audio_dct * sqrt(2 / window_length) + + end + +end + +""" +audio_dst = dst(audio_signal, dst_type) + + Compute the discrete sine transform (DST) using the fast Fourier transform (FFT). + +# Arguments: +- `audio_signal::Float`: the audio signal (window_length,). +- `dst_type::Integer`: the DST type (1, 2, 3, or 4). +- `audio_dst::Float`: the audio DST (number_frequencies,) + +# Example: Compute the 4 different DSTs and compare them to their respective inverses. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Get an audio segment for a given window length +window_length = 1024 +audio_segment = audio_signal[1:window_length] + +# Compute the DST-I, II, III, and IV +audio_dst1 = zaf.dst(audio_segment, 1) +audio_dst2 = zaf.dst(audio_segment, 2) +audio_dst3 = zaf.dst(audio_segment, 3) +audio_dst4 = zaf.dst(audio_segment, 4) + +# Compute their respective inverses, i.e., DST-I, II, III, and IV +audio_idst1 = zaf.dst(audio_dst1, 1) +audio_idst2 = zaf.dst(audio_dst2, 3) +audio_idst3 = zaf.dst(audio_dst3, 2) +audio_idst4 = zaf.dst(audio_dst4, 4) + +# Plot the DST-I, II, III, and IV, their respective inverses, and their differences with the original audio segment +dst1_plot = plot(audio_dst1, title = "DST-I") +dst2_plot = plot(audio_dst2, title = "DST-II") +dst3_plot = plot(audio_dst3, title = "DST-III") +dst4_plot = plot(audio_dst4, title = "DST-IV") +idst1_plot2 = plot(audio_idst1, title = "Inverse DST-I (DST-I)") +idst2_plot2 = plot(audio_idst2, title = "Inverse DST-II (DST-III)") +idst3_plot2 = plot(audio_idst3, title = "Inverse DST-III (DST-II)") +idst4_plot2 = plot(audio_idst4, title = "Inverse DST-IV (DST-IV)") +diff1_plot = plot(audio_idst1-audio_segment, title = "Inverse DST-I - audio segment") +diff2_plot = plot(audio_idst2-audio_segment, title = "Inverse DST-II - audio segment") +diff3_plot = plot(audio_idst3-audio_segment, title = "Inverse DST-III - audio segment") +diff4_plot = plot(audio_idst4-audio_segment, title = "Inverse DST-IV - audio segment") +plot(dst1_plot, dst2_plot, dst3_plot, dst4_plot, idst1_plot2, idst2_plot2, idst3_plot2, idst4_plot2, + diff1_plot, diff2_plot, diff3_plot, diff4_plot, xlims = (0, window_length), legend = false, titlefont = 10, + layout = (3,4), size = (990, 600), fmt = :png) +``` +""" +function dst(audio_signal, dst_type) + + # Check if the DST type is I, II, III, or IV + if dst_type == 1 + + # Get the number of samples + window_length = length(audio_signal) + + # Compute the DST-I using the FFT + audio_dst = zeros(2 * window_length + 2) + audio_dst[2:window_length+1] = audio_signal + audio_dst[window_length+3:end] = -audio_signal[end:-1:1] + audio_dst = fft(audio_dst, 1) + audio_dst = -imag(audio_dst[2:window_length+1]) / 2 + + # Post-process the results to make the DST-I matrix orthogonal + audio_dst = audio_dst * sqrt(2 / (window_length + 1)) + + elseif dst_type == 2 + + # Get the number of samples + window_length = length(audio_signal) + + # Compute the DST-II using the FFT + audio_dst = zeros(4 * window_length) + audio_dst[2:2:2*window_length] = audio_signal + audio_dst[2*window_length+2:2:4*window_length] = -audio_signal[end:-1:1] + audio_dst = fft(audio_dst, 1) + audio_dst = -imag(audio_dst[2:window_length+1]) / 2 + + # Post-process the results to make the DST-II matrix orthogonal + audio_dst[end] = audio_dst[end] / sqrt(2) + audio_dst = audio_dst * sqrt(2 / window_length) + + elseif dst_type == 3 + + # Get the number of samples + window_length = length(audio_signal) + + # Pre-process the signal to make the DST-III matrix orthogonal + # (copy the signal to avoid modifying it outside of the function) + audio_signal = copy(audio_signal) + audio_signal[end] = audio_signal[end] * sqrt(2) + + # Compute the DST-III using the FFT + audio_dst = zeros(4 * window_length) + audio_dst[2:window_length+1] = audio_signal + audio_dst[window_length+2:2*window_length] = audio_signal[end-1:-1:1] + audio_dst[2*window_length+2:3*window_length+1] = -audio_signal + audio_dst[3*window_length+2:4*window_length] = -audio_signal[end-1:-1:1] + audio_dst = fft(audio_dst, 1) + audio_dst = -imag(audio_dst[2:2:2*window_length]) / 4 + + # Post-processing to make the DST-III matrix orthogonal + audio_dst = audio_dst * sqrt(2 / window_length) + + elseif dst_type == 4 + + # Get the number of samples + window_length = length(audio_signal) + + # Compute the DST-IV using the FFT + audio_dst = zeros(8 * window_length) + audio_dst[2:2:2*window_length] = audio_signal + audio_dst[2*window_length+2:2:4*window_length] = audio_signal[end:-1:1] + audio_dst[4*window_length+2:2:6*window_length] = -audio_signal + audio_dst[6*window_length+2:2:8*window_length] = -audio_signal[end:-1:1] + audio_dst = fft(audio_dst, 1) + audio_dst = -imag(audio_dst[2:2:2*window_length]) / 4 + + # Post-process the results to make the DST-IV matrix orthogonal + audio_dst = audio_dst * sqrt(2 / window_length) + + end + +end + +""" +audio_mdct = mdct(audio_signal, window_function) + + Compute the modified discrete cosine transform (MDCT) using the fast Fourier transform (FFT). + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples,). +- `window_function::Float`: the window function (window_length,). +- `audio_mdct::Float`: the audio MDCT (number_frequencies, number_times). + +# Example: Compute and display the MDCT as used in the AC-3 audio coding format. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Add and use the DSP package to get the kaiser window function +using Pkg +Pkg.add("DSP") +using DSP + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Compute the Kaiser-Bessel-derived (KBD) window as used in the AC-3 audio coding format +window_length = 512 +alpha_value = 5 +window_function = kaiser(convert(Int, window_length/2)+1, alpha_value*pi) +window_function2 = cumsum(window_function[1:convert(Int, window_length/2)]) +window_function = sqrt.([window_function2; window_function2[convert(Int, window_length/2):-1:1]]./sum(window_function)) + +# Compute the MDCT +audio_mdct = zaf.mdct(audio_signal, window_function) + +# Display the MDCT in dB, seconds, and Hz +xtick_step = 1 +ytick_step = 1000 +plot_object = zaf.specshow(abs.(audio_mdct), length(audio_signal), sampling_frequency, xtick_step, ytick_step) +heatmap!(title = "MDCT (dB)", size = (990, 600)) +``` +""" +function mdct(audio_signal, window_function) + + # Get the number of samples and the window length in samples + number_samples = length(audio_signal) + window_length = length(window_function) + + # Derive the step length and the number of frequencies (for clarity) + step_length = convert(Int, window_length / 2) + number_frequencies = convert(Int, window_length / 2) + + # Derive the number of time frames + number_times = ceil(Int, number_samples / step_length) + 1 + + # Zero-pad the start and the end of the signal to center the windows + audio_signal = [ + zeros(step_length) + audio_signal + zeros((number_times + 1) * step_length - number_samples) + ] + + # Initialize the MDCT + audio_mdct = zeros(number_frequencies, number_times) + + # Prepare the pre-processing and post-processing arrays + preprocessing_array = exp.(-im * pi / window_length * (0:window_length-1)) + postprocessing_array = + exp.( + -im * pi / window_length * + (window_length / 2 + 1) * + (0.5:window_length/2-0.5), + ) + + # Loop over the time frames + # (do the pre and post-processing, and take the FFT in the loop to avoid storing twice longer frames) + i = 0 + for j = 1:number_times + + # Window the signal + audio_segment = audio_signal[i+1:i+window_length] .* window_function + i = i + step_length + + # Compute the Fourier transform of the windowed segment using the FFT after pre-processing + audio_segment = fft(audio_segment .* preprocessing_array) + + # Truncate to the first half before post-processing (and take the real to ensure real values) + audio_mdct[:, j] = + real(audio_segment[1:number_frequencies] .* postprocessing_array) + + end + + # Return the output explicitly as it is not clear here what the last value is + return audio_mdct + +end + +""" +audio_signal = imdct(audio_mdct, window_function) + + Compute the inverse modified discrete cosine transform (MDCT) using the fast Fourier transform (FFT). + +# Arguments: +- `audio_mdct::Float`: the audio MDCT (number_frequencies, number_times). +- `window_function::Float`: the window function (window_length,). +- `audio_signal::Float`: the audio signal (number_samples,). + +# Example: Verify that the MDCT is perfectly invertible. +``` +# Load the needed modules +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots + +# Read the audio signal with its sampling frequency in Hz, and average it over its channels +audio_signal, sampling_frequency = wavread("audio_file.wav") +audio_signal = mean(audio_signal, dims=2) + +# Compute the MDCT with a slope function as used in the Vorbis audio coding format +window_length = 2048 +window_function = sin.(pi/2*(sin.(pi/window_length*(0.5:window_length-0.5)).^2)) +audio_mdct = zaf.mdct(audio_signal, window_function) + +# Compute the inverse MDCT +audio_signal2 = zaf.imdct(audio_mdct, window_function) +audio_signal2 = audio_signal2[1:length(audio_signal)] + +# Compute the differences between the original signal and the resynthesized one +audio_differences = audio_signal-audio_signal2 +y_max = maximum(abs.(audio_differences)) + +# Display the original and resynthesized signals, and their differences in seconds +xtick_step = 1 +plot_object1 = zaf.sigplot(audio_signal, sampling_frequency, xtick_step) +plot!(ylims = (-1, 1), title = "Original signal") +plot_object2 = zaf.sigplot(audio_signal2, sampling_frequency, xtick_step) +plot!(ylims = (-1, 1), title = "Resyntesized signal") +plot_object3 = zaf.sigplot(audio_differences, sampling_frequency, xtick_step) +plot!(ylims = (-y_max, y_max), title = "Original - resyntesized signal") +plot(plot_object1, plot_object2, plot_object3, layout = (3, 1), size = (990, 600)) +``` +""" +function imdct(audio_mdct, window_function) + + # Get the number of frequency channels and time frames + number_frequencies, number_times = size(audio_mdct) + + # Derive the window length and the step length in samples (for clarity) + window_length = 2 * number_frequencies + step_length = number_frequencies + + # Derive the number of samples for the signal + number_samples = step_length * (number_times + 1) + + # Initialize the audio signal + audio_signal = zeros(number_samples) + + # Prepare the pre-processing and post-processing arrays + preprocessing_array = + exp.( + -im * pi / (2 * number_frequencies) * + (number_frequencies + 1) * + (0:number_frequencies-1), + ) + postprocessing_array = + exp.( + -im * pi / (2 * number_frequencies) * ( + 0.5+number_frequencies/2:2*number_frequencies+number_frequencies/2-0.5 + ), + ) / number_frequencies + + # Compute the Fourier transform of the frames using the FFT after pre-processing + # (zero-pad to get twice the length) + audio_mdct = fft( + [ + audio_mdct .* preprocessing_array + zeros(number_frequencies, number_times) + ], + 1, + ) + + # Apply the window function to the frames after post-processing + # (take the real to ensure real values) + audio_mdct = 2 * real(audio_mdct .* postprocessing_array) .* window_function + + # Loop over the time frames + i = 0 + for j = 1:number_times + + # Recover the signal with the time-domain aliasing cancellation (TDAC) principle + audio_signal[i+1:i+window_length] = + audio_signal[i+1:i+window_length] + audio_mdct[:, j] + i = i + step_length + + end + + # Remove the zero-padding at the start and at the end of the signal + audio_signal = audio_signal[step_length+1:end-step_length] + +end + +""" + window_function = hamming(window_length, window_sampling="symmetric") + +Compute the Hamming window. + +# Arguments: +- `window_length::Integer`: the window length in samples. +- `window_sampling::Char="symmetric"`: the window sampling method ("symmetric" or "periodic"). +- `window_function::Float`: the window function (window_length,). +""" +function hamming(window_length, window_sampling = "symmetric") + + # Compute the Hamming window, symmetric for filter design and periodic for spectral analysis + if window_sampling == "symmetric" + window_function = + 0.54 .- + 0.46 * cos.(2 * pi * (0:window_length-1) / (window_length - 1)) + elseif window_sampling == "periodic" + window_function = + 0.54 .- 0.46 * cos.(2 * pi * (0:window_length-1) / window_length) + end + +end + +""" + plot_object = zaf.sigplot(audio_signal, sampling_frequency, xtick_step=1) + +Plot a signal in seconds. + +# Arguments: +- `audio_signal::Float`: the audio signal (number_samples, number_channels). +- `sampling_frequency::Float`: the sampling frequency from the original signal in Hz. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `plot_object:Plots:` the plot object. +""" +function sigplot(audio_signal, sampling_frequency, xtick_step = 1) + + # Get the number of samples + number_samples = size(audio_signal, 1) + + # Prepare the tick locations and labels for the x-axis + xtick_locations = [ + xtick_step*sampling_frequency:xtick_step*sampling_frequency:number_samples; + ] + xtick_labels = convert( + Array{Int}, + [xtick_step:xtick_step:number_samples/sampling_frequency;], + ) + + # Plot the signal in seconds + plot_object = plot( + audio_signal, + legend = false, + fmt = :png, + xlims = (0, number_samples), + xticks = (xtick_locations, xtick_labels), + xlabel = "Time (s)", + ) + +end + +""" + plot_object = zaf.specshow(audio_spectrogram, number_samples, sampling_frequency, xtick_step=1, ytick_step=1000) + +Display a spectrogram in dB, seconds, and Hz. + +# Arguments: +- `audio_spectrogram::Float`: the audio spectrogram (without DC and mirrored frequencies) (number_frequencies, number_times). +- `number_samples::Integer`: the number of samples from the original signal. +- `sampling_frequency::Float`: the sampling frequency from the original signal in Hz. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `ytick_step::Integer=1000`: the step for the y-axis ticks in Hz (default: 1000 Hz). +- `plot_object:Plots:` the plot object. +""" +function specshow( + audio_spectrogram, + number_samples, + sampling_frequency, + xtick_step = 1, + ytick_step = 1000, +) + + # Get the number of frequency channels and time frames + number_frequencies, number_times = size(audio_spectrogram) + + # Derive the number of Hertz and seconds + number_hertz = sampling_frequency / 2 + number_seconds = number_samples / sampling_frequency + + # Derive the number of time frames per second and the number of frequency channels per Hz + time_resolution = number_times / number_seconds + frequency_resolution = number_frequencies / number_hertz + + # Prepare the tick locations and labels for the x-axis + xtick_locations = + [xtick_step*time_resolution:xtick_step*time_resolution:number_times;] + xtick_labels = convert(Array{Int}, [xtick_step:xtick_step:number_seconds;]) + + # Prepare the tick locations and labels for the y-axis + ytick_locations = [ + ytick_step*frequency_resolution:ytick_step*frequency_resolution:number_frequencies; + ] + ytick_labels = convert(Array{Int}, [ytick_step:ytick_step:number_hertz;]) + + # Display the spectrogram in dB, seconds, and Hz + plot_object = heatmap( + 20 * log10.(audio_spectrogram), + fillcolor = :jet, + legend = false, + fmt = :png, + xticks = (xtick_locations, xtick_labels), + yticks = (ytick_locations, ytick_labels), + xlabel = "Time (s)", + ylabel = "Frequency (Hz)", + ) + +end + +""" + plot_object = zaf.melspecshow(mel_spectrogram, number_samples, sampling_frequency, window_length, xtick_step=1) + +Display a mel spectrogram in dB, seconds, and Hz. + +# Arguments: +- `mel_spectrogram::Float`: the mel spectrogram (number_mels, number_times). +- `number_samples::Integer`: the number of samples from the original signal. +- `sampling_frequency::Float`: the sampling frequency from the original signal in Hz. +- `window_length::Integer`: the window length from the Fourier analysis in number of samples. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `plot_object:Plots:` the plot object. +""" +function melspecshow( + mel_spectrogram, + number_samples, + sampling_frequency, + window_length, + xtick_step = 1, +) + + # Get the number of mels and time frames + number_mels, number_times = size(mel_spectrogram) + + # Derive the number of seconds and the number of time frames per second + number_seconds = number_samples / sampling_frequency + time_resolution = number_times / number_seconds + + # Derive the minimum and maximum mel + minimum_mel = 2595 * log10(1 + (sampling_frequency / window_length) / 700) + maximum_mel = 2595 * log10(1 + (sampling_frequency / 2) / 700) + + # Compute the mel scale (linearly spaced) + mel_scale = range(minimum_mel, stop = maximum_mel, length = number_mels) + + # Derive the Hertz scale (log spaced) + hertz_scale = 700 .* (10 .^ (mel_scale / 2595) .- 1) + + # Prepare the tick locations and labels for the x-axis + xtick_locations = + [xtick_step*time_resolution:xtick_step*time_resolution:number_times;] + xtick_labels = convert(Array{Int}, [xtick_step:xtick_step:number_seconds;]) + + # Prepare the tick locations and labels for the y-axis + ytick_locations = [1:8:number_mels;] + ytick_labels = convert(Array{Int}, round.(hertz_scale[1:8:number_mels])) + + # Display the mel spectrogram in dB, seconds, and Hz + plot_object = heatmap( + 20 * log10.(mel_spectrogram), + fillcolor = :jet, + legend = false, + fmt = :png, + xticks = (xtick_locations, xtick_labels), + yticks = (ytick_locations, ytick_labels), + xlabel = "Time (s)", + ylabel = "Frequency (Hz)", + ) + +end + +""" + plot_object = zaf.mfccshow(audio_mfcc, number_samples, sampling_frequency, xtick_step=1) + +Display MFCCs in seconds. + +# Arguments: +- `audio_mfcc::Float`: the audio MFCC (number_coefficients, number_times). +- `number_samples::Integer`: the number of samples from the original signal. +- `sampling_frequency::Integer`: the sampling frequency from the original signal in Hz. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `plot_object:Plots:` the plot object. +""" +function mfccshow(audio_mfcc, number_samples, sampling_frequency, xtick_step = 1) + + # Get the number of time frames + number_times = size(audio_mfcc, 2) + + # Derive the number of seconds and the number of time frames per second + number_seconds = number_samples / sampling_frequency + time_resolution = number_times / number_seconds + + # Prepare the tick locations and labels for the x-axis + xtick_locations = + [xtick_step*time_resolution:xtick_step*time_resolution:number_times;] + xtick_labels = convert( + Array{Int}, + [xtick_step:xtick_step:number_times/time_resolution;], + ) + + # Display the MFCCs in seconds + plot_object = heatmap( + audio_mfcc, + fillcolor = :jet, + legend = false, + fmt = :png, + xticks = (xtick_locations, xtick_labels), + xlabel = "Time (s)", + ylabel = "Coefficients", + ) + +end + +""" + plot_object = zaf.cqtspecshow(cqt_spectrogram, time_resolution, frequency_resolution, minimum_frequency, xtick_step=1) + +Display a CQT spectrogram in dB and seconds, and Hz. + +# Arguments: +- `cqt_spectrogram::Float`: the CQT spectrogram (number_frequencies, number_times). +- `time_resolution::Integer`: number of time frames per second. +- `octave_resolution::Integer`: number of frequency channels per octave. +- `minimum_frequency::Float`: the minimum frequency in Hz. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `plot_object:Plots:` the plot object. +""" +function cqtspecshow( + cqt_spectrogram, + time_resolution, + octave_resolution, + minimum_frequency, + xtick_step = 1, +) + + # Get the number of frequency channels and time frames + number_frequencies, number_times = size(cqt_spectrogram) + + # Prepare the tick locations and labels for the x-axis + xtick_locations = + [xtick_step*time_resolution:xtick_step*time_resolution:number_times;] + xtick_labels = convert( + Array{Int}, + [xtick_step:xtick_step:number_times/time_resolution;], + ) + + # Prepare the tick locations and labels for the y-axis + ytick_locations = [0:octave_resolution:number_frequencies;] + ytick_labels = convert( + Array{Int}, + minimum_frequency * 2 .^ (ytick_locations / octave_resolution), + ) + + # Display the CQT spectrogram in dB, seconds, and Hz + plot_object = heatmap( + 20 * log10.(cqt_spectrogram), + fillcolor = :jet, + legend = false, + fmt = :png, + xticks = (xtick_locations, xtick_labels), + yticks = (ytick_locations, ytick_labels), + xlabel = "Time (s)", + ylabel = "Frequency (Hz)", + ) + +end + +""" + plot_object = zaf.cqtchromshow(cqt_chromagram, time_resolution, xtick_step=1) + +Display a CQT chromagram in seconds. + +# Arguments: +- `cqt_chromagram::Float`: the CQT chromagram (number_chromas, number_times). +- `time_resolution::Integer`: the number of time frames per second. +- `xtick_step::Integer=1`: the step for the x-axis ticks in seconds (default: 1 second). +- `plot_object:Plots:` the plot object. +""" +function cqtchromshow(cqt_chromagram, time_resolution, xtick_step = 1) + + # Get the number of time frames + number_times = size(cqt_chromagram, 2) + + # Prepare the tick locations and labels for the x-axis + xtick_locations = + [xtick_step*time_resolution:xtick_step*time_resolution:number_times;] + xtick_labels = convert( + Array{Int}, + [xtick_step:xtick_step:number_times/time_resolution;], + ) + + # Display the CQT chromagram in seconds + plot_object = heatmap( + cqt_chromagram, + fillcolor = :jet, + legend = false, + fmt = :png, + xticks = (xtick_locations, xtick_labels), + xlabel = "Time (s)", + ylabel = "Chroma", + ) + +end + +end diff --git a/zaudio.jl b/zaudio.jl new file mode 100644 index 0000000..20f407d --- /dev/null +++ b/zaudio.jl @@ -0,0 +1,219 @@ +include("./zaf.jl") +using .zaf +using WAV +using Statistics +using Plots +using Tables +using CSV +using DSP +using SignalAnalysis +using DataFrames + +# Папка сохранения полученных датасетов + +data_dir = "datasets/" + +# Папка исходных аудио-файлов + +files_dir = "files/" + +# Настройки CQT преобразования + +octave_resolution = 24 +minimum_frequency = 55 +maximum_frequency = 9520 +time_resolution = 25 + +# Размеры кадра в сек + +window_duration = 0.04; + +# Уровень энергии для порогового фильтра + +energy_level = 50 + +# Количество кадров для сглаживания скользящей средней слепка аудио-данных + +m_offset = 20 + +# Чтение WAV-файла + +function read() + if !isempty(ARGS) + try + return wavread(files_dir*ARGS[1]) + catch e + println("Ошибка чтения wav-файла") + end + else + println("Не указан входной файл") + exit() + end +end + +# Загрузка сохраненного файла данных очищенных окон с преобразованием в среднеквадратичное отклонение по частотным полосам + +function load(filename)::Vector{Any} + if !isempty(filename) + try + data = CSV.read(filename, DataFrame, skipto=2) + return data[!, :Column1] + catch e + println("Ошибка чтения csv-файла") + end + else + println("Не указан входной файл") + exit() + end +end + +# Скользящее среднее + +function m_average(arr::Vector{Float64}, n::Number)::Vector{Any} + so_far = sum(arr[1:n]) + out = zero(arr[n:end]) + out[1] = so_far + for (i, (start, stop)) in enumerate(zip(arr, arr[n+1:end])) + so_far += stop - start + out[i+1] = so_far + end + return out +end + +# Нормализация уровня + +function normalize(audio_input::Matrix{Float64},freq::Number) + return mean(audio_input, dims=2), freq +end + +# Разбитие на окна + +function windows(freq::Number) + local window_length = nextpow(2, ceil(Int, window_duration*freq)) + local window_function = zaf.hamming(window_length, "periodic") # оконная аналитическая функция + return window_length, convert(Int, window_length/2), window_function +end + +# Фильтрация окон по уровню минимальной энергии звука в каждом окне + +function filter(audio_input::Matrix{Float64},window_length::Number)::Matrix{Float64} + output_signal = zeros(1,1) + number_samples = length(audio_input) + padding_length = floor(Int, window_length / 2) + number_times = + ceil( + Int, + ((number_samples + 2 * padding_length) - window_length) / + step_length, + ) + 1 + local i = 0 + for j = 1:(number_times-10) # 10 последних кадров отбарсываем + frame = audio_input[i+1:i+window_length] + if energy(frame) > energy_level + output_signal = [output_signal;frame] + end + i = i + step_length + + end + return output_signal +end + +# Преобразование Фурье + +function stft(audio::Matrix{Float64},freq::Number) + local window_length,step_length,window_function = windows(freq) + return zaf.stft(audio, window_function, step_length), window_length, step_length, window_function +end + +# Спектограмма разложения ряда Фурье + +function spectrogram(audio::Matrix{Float64},freq::Number)::Matrix{Float64} + local audio_stft, window_length = stft(audio,freq) + local audio_spectrogram = abs.(audio_stft[2:convert(Int, window_length/2)+1, :]) # Отбрасываем постоянную составляющую + local number_samples = length(audio_input) + local xtick_step = 1 + local ytick_step = 1000 + local plot_object = zaf.specshow(audio_spectrogram, number_samples, freq, xtick_step, ytick_step) + heatmap!(title = "Spectrogram (dB)", size = (990, 600)) + savefig(plot_object, data_dir*ARGS[1]*"-"*"spectr.png") + #CSV.write(data_dir*ARGS[1]*"-"*"spectr.csv", Tables.table(audio_spectrogram)) + return audio_spectrogram +end + +# CQT-октавное вевлет-преобразование + +function cqt(audio::Matrix{Float64},freq::Number)::Matrix{Float64} + local cqt_kernel = zaf.cqtkernel(freq, octave_resolution, minimum_frequency, maximum_frequency) + cqt_spectrogram = zaf.cqtspectrogram(audio, freq, time_resolution, cqt_kernel) + CSV.write(data_dir*ARGS[1]*"-"*"cqt.csv", Tables.table(cqt_spectrogram)) + local xtick_step = 1 + local plot_object = zaf.cqtspecshow(cqt_spectrogram, time_resolution, octave_resolution, minimum_frequency, xtick_step) + heatmap!(title = "CQT spectrogram (dB)", size = (990, 600)) + savefig(plot_object, data_dir*ARGS[1]*"-"*"cqt.png") + return cqt_spectrogram +end + +# Преобразование вевлет-спектрограммы в спектр среднего значения по октавам со сглаживанием + +function raft(spectr::Matrix{Float64})::Vector{Any} + freqs, frames = size(spectr) + raft_data = zeros(freqs) + for i in 1:freqs + raft_data[i] = mean(spectr[i, :]) + end + return m_average(raft_data,m_offset) +end + +# Cохранение образа записи + +function save(audio_data::Vector{Any},freq::Number)::Vector{Any} + CSV.write(data_dir*ARGS[1]*"-"*"analise.csv", Tables.table(audio_data)) + numbers = length(audio_data) + xtick_locations = [0:octave_resolution:numbers;] + xtick_labels = convert( + Array{Int}, + minimum_frequency * 2 .^ (xtick_locations / octave_resolution), + ) + plot_object = plot(audio_data, xticks = (xtick_locations, xtick_labels)) + plot!(title = "Sound form", size = (990, 600)) + savefig(plot_object, data_dir*ARGS[1]*"-"*"analise.png") + return audio_data +end + + +# Считываем данные из WAV файла и нормализуем их, частота дискретизации получается из заголовка WAV-файла + +audio_input, freq = read() + +audio_input, freq = normalize(audio_input, freq) + +# Исходя из частоты дискретизации получаем длину кадров и шаг между ними + +window_length,step_length,window_function = windows(freq) + +# Сохраняем спектограмму исходного сигнала + +spectrogram(audio_input,freq) + +# Фильтруем кадры, отбрасывая кадры с низкой энергией + +audio = filter(audio_input,window_length) + +frames, freqs = size(audio) + +if frames<5 + println("Файл не прошел фильтр суммарной энергии сигнала") + exit() +end + +# Осущетсвляем CQT-преобразование и сохранение спектограммы и массива данных + +cqt_spectrogram = cqt(audio,freq) + +# Преобразуем спектограмму в с спектр среднеквадратичных отклонений + +raft_data = raft(cqt_spectrogram) + +# Cохраняем результат + +save(raft_data,freq)