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Zaf-Python

Zafar's Audio Functions in Python for audio signal analysis.

Files:

See also:

  • Zaf-Matlab: Zafar's Audio Functions in Matlab for audio signal analysis.
  • Zaf-Julia: Zafar's Audio Functions in Julia for audio signal analysis.

zaf.py

This Python module implements a number of functions for audio signal analysis.

Simply copy the file zaf.py in your working directory and you are good to go. Make sure you have Python 3, NumPy, and SciPy installed.

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:

  • wavread - Read a WAVE file (using SciPy).
  • wavwrite - Write a WAVE file (using SciPy).
  • sigplot - Plot a signal in seconds.
  • specshow - Display a 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.

stft

Compute the short-time Fourier transform (STFT).

audio_stft = zaf.stft(audio_signal, window_function, step_length)
    
Inputs:
    audio_signal: audio signal (number_samples,)
    window_function: window function (window_length,)
    step_length: step length in samples
Output:
    audio_stft: audio STFT (window_length, number_frames)

Example: Compute and display the spectrogram from an audio file.

# Import the needed modules
import numpy as np
import scipy.signal
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# 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 = pow(2, int(np.ceil(np.log2(window_duration*sampling_frequency))))

# Compute the window function (use SciPy's periodic Hamming window for COLA as NumPy's Hamming window is symmetric)
window_function = scipy.signal.hamming(window_length, sym=False)

# Set the step length in samples (half of the window length for COLA)
step_length = 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 = np.absolute(audio_stft[1:int(window_length/2)+1, :])

# Display the spectrogram in dB, seconds, and Hz
number_samples = len(audio_signal)
plt.figure(figsize=(14, 7))
zaf.specshow(audio_spectrogram, number_samples, sampling_frequency, xtick_step=1, ytick_step=1000)
plt.title("Spectrogram (dB)")
plt.tight_layout()
plt.show()

istft

Compute the inverse short-time Fourier transform (STFT).

audio_signal = zaf.istft(audio_stft, window_function, step_length)

Inputs:
    audio_stft: audio STFT (window_length, number_frames)
    window_function: window function (window_length,)
    step_length: step length in samples
Output:
    audio_signal: audio signal (number_samples,)

Example: Estimate the center and the sides from a stereo audio file.

# Import the needed modules
import numpy as np
import scipy.signal
import zaf
import matplotlib.pyplot as plt

# Read the (stereo) audio signal with its sampling frequency in Hz
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")

# Set the parameters for the STFT
window_length = pow(2, int(np.ceil(np.log2(0.04*sampling_frequency))))
window_function = scipy.signal.hamming(window_length, sym=False)
step_length = int(window_length/2)

# Compute the STFTs for the left and right channels
audio_stft1 = zaf.stft(audio_signal[:, 0], window_function, step_length)
audio_stft2 = zaf.stft(audio_signal[:, 1], window_function, step_length)

# Derive the magnitude spectrograms (with DC component) for the left and right channels
number_frequencies = int(window_length/2)+1
audio_spectrogram1 = abs(audio_stft1[0:number_frequencies, :])
audio_spectrogram2 = abs(audio_stft2[0:number_frequencies, :])

# Estimate the time-frequency masks for the left and right channels for the center
center_mask1 = np.minimum(audio_spectrogram1, audio_spectrogram2)/audio_spectrogram1
center_mask2 = np.minimum(audio_spectrogram1, audio_spectrogram2)/audio_spectrogram2

# Derive the STFTs for the left and right channels for the center (with mirrored frequencies)
center_stft1 = np.multiply(np.concatenate((center_mask1, center_mask1[-2:0:-1, :])), audio_stft1)
center_stft2 = np.multiply(np.concatenate((center_mask2, center_mask2[-2:0:-1, :])), 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 = np.stack((center_signal1, center_signal2), axis=1)
center_signal = center_signal[0:np.shape(audio_signal)[0], :]
sides_signal = audio_signal-center_signal

# Write the center and sides signals
zaf.wavwrite(center_signal, sampling_frequency, "center_file.wav")
zaf.wavwrite(sides_signal, sampling_frequency, "sides_file.wav")

# Display the original, center, and sides signals in seconds
xtick_step = 1
plt.figure(figsize=(14, 7))
plt.subplot(3, 1, 1), zaf.sigplot(audio_signal, sampling_frequency, xtick_step)
plt.ylim(-1, 1), plt.title("Original signal")
plt.subplot(3, 1, 2), zaf.sigplot(center_signal, sampling_frequency, xtick_step)
plt.ylim(-1, 1), plt.title("Center signal")
plt.subplot(3, 1, 3), zaf.sigplot(sides_signal, sampling_frequency, xtick_step)
plt.ylim(-1, 1), plt.title("Sides signal")
plt.tight_layout()
plt.show()

melfilterbank

Compute the mel filterbank.

mel_filterbank = zaf.melfilterbank(sampling_frequency, window_length, number_mels)

Inputs:
    sampling_frequency: sampling frequency in Hz
    window_length: window length for the Fourier analysis in samples
    number_mels: number of mel filters
    
Output:
    mel_filterbank: mel filterbank (sparse) (number_mels, number_frequencies)

Example: Compute and display the mel filterbank.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Compute the mel filterbank using some parameters
sampling_frequency = 44100
window_length = pow(2, int(np.ceil(np.log2(0.04 * sampling_frequency))))
number_mels = 128
mel_filterbank = zaf.melfilterbank(sampling_frequency, window_length, number_mels)

# Display the mel filterbank
plt.figure(figsize=(14, 5))
plt.imshow(mel_filterbank.toarray(), aspect="auto", cmap="jet", origin="lower")
plt.title("Mel filterbank")
plt.xlabel("Frequency index")
plt.ylabel("Mel index")
plt.tight_layout()
plt.show()

melspectrogram

Compute the mel spectrogram using a mel filterbank.

mel_filterbank = zaf.melspectrogram(audio_signal, window_function, step_length, mel_filterbank)

Inputs:
    audio_signal: audio signal (number_samples,)
    window_function: window function (window_length,)
    step_length: step length in samples
    mel_filterbank: mel filterbank (number_mels, number_frequencies)
Output:
    mel_spectrogram: mel spectrogram (number_mels, number_times)

Example: Compute and display the mel spectrogram.

# Import the needed modules
import numpy as np
import scipy.signal
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Set the parameters for the Fourier analysis
window_length = pow(2, int(np.ceil(np.log2(0.04*sampling_frequency))))
window_function = scipy.signal.hamming(window_length, sym=False)
step_length = 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 = len(audio_signal)
plt.figure(figsize=(14, 5))
zaf.melspecshow(mel_spectrogram, number_samples, sampling_frequency, window_length, xtick_step=1)
plt.title("Mel spectrogram (dB)")
plt.tight_layout()
plt.show()

mfcc

Compute the mel-frequency cepstral coefficients (MFCCs) using a mel filterbank.

audio_mfcc = zaf.mfcc(audio_signal, sample_frequency, number_filters, number_coefficients)

Inputs:
    audio_signal: audio signal (number_samples,)
    sampling_frequency: sampling frequency in Hz
    number_filters: number of filters
    number_coefficients: number of coefficients (without the 0th coefficient)
Output:
    audio_mfcc: audio MFCCs (number_times, number_coefficients)

Example: Compute and display the MFCCs, delta MFCCs, and delta-delta MFCCs.

# Import the needed modules
import numpy as np
import scipy.signal
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Set the parameters for the Fourier analysis
window_length = pow(2, int(np.ceil(np.log2(0.04*sampling_frequency))))
window_function = scipy.signal.hamming(window_length, sym=False)
step_length = 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 = np.diff(audio_mfcc, n=1, axis=1)
audio_ddmfcc = np.diff(audio_dmfcc, n=1, axis=1)

# Display the MFCCs, delta MFCCs, and delta-delta MFCCs in seconds
number_samples = len(audio_signal)
xtick_step = 1
plt.figure(figsize=(14, 7))
plt.subplot(3, 1, 1)
zaf.mfccshow(audio_mfcc, number_samples, sampling_frequency, xtick_step), plt.title("MFCCs")
plt.subplot(3, 1, 2)
zaf.mfccshow(audio_dmfcc, number_samples, sampling_frequency, xtick_step), plt.title("Delta MFCCs")
plt.subplot(3, 1, 3)
zaf.mfccshow(audio_ddmfcc, number_samples, sampling_frequency, xtick_step), plt.title("Delta-delta MFCCs")
plt.tight_layout()
plt.show()

cqtkernel

Compute the constant-Q transform (CQT) kernel.

cqt_kernel = zaf.cqtkernel(sampling_frequency, octave_resolution, minimum_frequency, maximum_frequency)

Inputs:
    sampling_frequency: sampling frequency in Hz
    octave_resolution: number of frequency channels per octave
    minimum_frequency: minimum frequency in Hz
    maximum_frequency: maximum frequency in Hz
Output:
    cqt_kernel: CQT kernel (sparse) (number_frequencies, fft_length)

Example: Compute and display the CQT kernel.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# 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
plt.figure(figsize=(14, 5))
plt.imshow(np.absolute(cqt_kernel).toarray(), aspect="auto", cmap="jet", origin="lower")
plt.title("Magnitude CQT kernel")
plt.xlabel("FFT index")
plt.ylabel("CQT index")
plt.tight_layout()
plt.show()

cqtspectrogram

Compute the constant-Q transform (CQT) spectrogram using a CQT kernel.

cqt_spectrogram = zaf.cqtspectrogram(audio_signal, sample_frequency, time_resolution, cqt_kernel)

Inputs:
    audio_signal: audio signal (number_samples,)
    sampling_frequency: sampling frequency in Hz
    time_resolution: number of time frames per second
    cqt_kernel: CQT kernel (number_frequencies, fft_length)
Output:
    cqt_spectrogram: CQT spectrogram (number_frequencies, number_times)

Example: Compute and display the CQT spectrogram.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# 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
cqt_spectrogram = zaf.cqtspectrogram(audio_signal, sampling_frequency, time_resolution, cqt_kernel)

# Display the CQT spectrogram in dB, seconds, and Hz
plt.figure(figsize=(14, 5))
zaf.cqtspecshow(cqt_spectrogram, time_resolution, octave_resolution, minimum_frequency, xtick_step=1)
plt.title("CQT spectrogram (dB)")
plt.tight_layout()
plt.show()

cqtchromagram

Compute the constant-Q transform (CQT) chromagram using a CQT kernel.

cqt_chromagram = zaf.cqtchromagram(audio_signal, sampling_frequency, time_resolution, octave_resolution, cqt_kernel)

Inputs:
    audio_signal: audio signal (number_samples,)
    sampling_frequency: sampling frequency in Hz
    time_resolution: number of time frames per second
    octave_resolution: number of frequency channels per octave
    cqt_kernel: CQT kernel (number_frequencies, fft_length)
Output:
    cqt_chromagram: CQT chromagram (number_chromas, number_times)

Example: Compute and display the CQT chromagram.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# 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
plt.figure(figsize=(14, 3))
zaf.cqtchromshow(cqt_chromagram, time_resolution, xtick_step=1)
plt.title("CQT chromagram")
plt.tight_layout()
plt.show()

dct

Compute the discrete cosine transform (DCT) using the fast Fourier transform (FFT).

audio_dct = zaf.dct(audio_signal, dct_type)

Inputs:
    audio_signal: audio signal (window_length,)
    dct_type: dct type (1, 2, 3, or 4)
Output:
    audio_dct: audio DCT (number_frequencies,)

Example: Compute the 4 different DCTs and compare them to SciPy's DCTs.

# Import the needed modules
import numpy as np
import zaf
import scipy.fftpack
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Get an audio segment for a given window length
window_length = 1024
audio_segment = audio_signal[0: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 SciPy's DCT-I, II, III, and IV (orthogonalized)
scipy_dct1 = scipy.fftpack.dct(audio_segment, type=1, norm="ortho")
scipy_dct2 = scipy.fftpack.dct(audio_segment, type=2, norm="ortho")
scipy_dct3 = scipy.fftpack.dct(audio_segment, type=3, norm="ortho")
scipy_dct4 = scipy.fftpack.dct(audio_segment, type=4, norm="ortho")

# Plot the DCT-I, II, III, and IV, SciPy's versions, and their differences
plt.figure(figsize=(14, 7))
plt.subplot(3, 4, 1), plt.plot(audio_dct1), plt.autoscale(tight=True), plt.title("DCT-I")
plt.subplot(3, 4, 2), plt.plot(audio_dct2), plt.autoscale(tight=True), plt.title("DCT-II")
plt.subplot(3, 4, 3), plt.plot(audio_dct3), plt.autoscale(tight=True), plt.title("DCT-III")
plt.subplot(3, 4, 4), plt.plot(audio_dct4), plt.autoscale(tight=True), plt.title("DCT-IV")
plt.subplot(3, 4, 5), plt.plot(scipy_dct1), plt.autoscale(tight=True), plt.title("SciPy's DCT-I")
plt.subplot(3, 4, 6), plt.plot(scipy_dct2), plt.autoscale(tight=True), plt.title("SciPy's DCT-II")
plt.subplot(3, 4, 7), plt.plot(scipy_dct3), plt.autoscale(tight=True), plt.title("SciPy's DCT-III")
plt.subplot(3, 4, 8), plt.plot(scipy_dct4), plt.autoscale(tight=True), plt.title("SciPy's DCT-IV")
plt.subplot(3, 4, 9), plt.plot(audio_dct1-scipy_dct1), plt.autoscale(tight=True), plt.title("DCT-I - SciPy's DCT-I")
plt.subplot(3, 4, 10), plt.plot(audio_dct2-scipy_dct2), plt.autoscale(tight=True), plt.title("DCT-II - SciPy's DCT-II")
plt.subplot(3, 4, 11), plt.plot(audio_dct3-scipy_dct3), plt.autoscale(tight=True), plt.title("DCT-III - SciPy's DCT-III")
plt.subplot(3, 4, 12), plt.plot(audio_dct3-scipy_dct3), plt.autoscale(tight=True), plt.title("DCT-IV - SciPy's DCT-IV")
plt.tight_layout()
plt.show()

dst

Compute the discrete sine transform (DST) using the fast Fourier transform (FFT).

audio_dst = zaf.dst(audio_signal, dst_type)

Inputs:
    audio_signal: audio signal (window_length,)
    dst_type: DST type (1, 2, 3, or 4)
Output:
    audio_dst: audio DST (number_frequencies,)

Example: Compute the 4 different DSTs and compare their respective inverses with the original audio.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Get an audio segment for a given window length
window_length = 1024
audio_segment = audio_signal[0: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
plt.figure(figsize=(14, 7))
plt.subplot(3, 4, 1), plt.plot(audio_dst1), plt.autoscale(tight=True), plt.title("DCT-I")
plt.subplot(3, 4, 2), plt.plot(audio_dst2), plt.autoscale(tight=True), plt.title("DST-II")
plt.subplot(3, 4, 3), plt.plot(audio_dst3), plt.autoscale(tight=True), plt.title("DST-III")
plt.subplot(3, 4, 4), plt.plot(audio_dst4), plt.autoscale(tight=True), plt.title("DST-IV")
plt.subplot(3, 4, 5), plt.plot(audio_idst1), plt.autoscale(tight=True), plt.title("Inverse DST-I (DST-I)")
plt.subplot(3, 4, 6), plt.plot(audio_idst2), plt.autoscale(tight=True), plt.title("Inverse DST-II (DST-III)")
plt.subplot(3, 4, 7), plt.plot(audio_idst3), plt.autoscale(tight=True), plt.title("Inverse DST-III (DST-II)")
plt.subplot(3, 4, 8), plt.plot(audio_idst4), plt.autoscale(tight=True), plt.title("Inverse DST-IV (DST-IV)")
plt.subplot(3, 4, 9), plt.plot(audio_idst1-audio_segment), plt.autoscale(tight=True)
plt.title("Inverse DST-I - audio segment")
plt.subplot(3, 4, 10), plt.plot(audio_idst2-audio_segment), plt.autoscale(tight=True)
plt.title("Inverse DST-II - audio segment")
plt.subplot(3, 4, 11), plt.plot(audio_idst3-audio_segment), plt.autoscale(tight=True)
plt.title("Inverse DST-III - audio segment")
plt.subplot(3, 4, 12), plt.plot(audio_idst4-audio_segment), plt.autoscale(tight=True)
plt.title("Inverse DST-IV - audio segment")
plt.tight_layout()
plt.show()

mdct

Compute the modified discrete cosine transform (MDCT) using the fast Fourier transform (FFT).

audio_mdct = zaf.mdct(audio_signal, window_function)

Inputs:
    audio_signal: audio signal (number_samples,)
    window_function: window function (window_length,)
Output:
    audio_mdct: audio MDCT (number_frequencies, number_times)

Example: Compute and display the MDCT as used in the AC-3 audio coding format.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Compute the Kaiser-Bessel-derived (KBD) window as used in the AC-3 audio coding format
window_length = 512
alpha_value = 5
window_function = np.kaiser(int(window_length/2)+1, alpha_value*np.pi)
window_function2 = np.cumsum(window_function[1:int(window_length/2)])
window_function = np.sqrt(np.concatenate((window_function2, window_function2[int(window_length/2)::-1]))
                          /np.sum(window_function))

# Compute the MDCT
audio_mdct = zaf.mdct(audio_signal, window_function)

# Display the MDCT in dB, seconds, and Hz
number_samples = len(audio_signal)
plt.figure(figsize=(14, 7))
zaf.specshow(np.absolute(audio_mdct), number_samples, sampling_frequency, xtick_step=1, ytick_step=1000)
plt.title("MDCT (dB)")
plt.tight_layout()
plt.show()

imdct

Compute the inverse modified discrete cosine transform (MDCT) using the fast Fourier transform (FFT).

audio_signal = zaf.imdct(audio_mdct, window_function)

Inputs:
    audio_mdct: audio MDCT (number_frequencies, number_times)
    window_function: window function (window_length,)
Output:
    audio_signal: audio signal (number_samples,)

Example: Verify that the MDCT is perfectly invertible.

# Import the needed modules
import numpy as np
import zaf
import matplotlib.pyplot as plt

# Read the audio signal (normalized) with its sampling frequency in Hz, and average it over its channels
audio_signal, sampling_frequency = zaf.wavread("audio_file.wav")
audio_signal = np.mean(audio_signal, 1)

# Compute the MDCT with a slope function as used in the Vorbis audio coding format
window_length = 2048
window_function = np.sin(np.pi/2*pow(np.sin(np.pi/window_length*np.arange(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[0:len(audio_signal)]

# Compute the differences between the original signal and the resynthesized one
audio_differences = audio_signal-audio_signal2
y_max = np.max(np.absolute(audio_differences))

# Display the original and resynthesized signals, and their differences in seconds
xtick_step = 1
plt.figure(figsize=(14, 7))
plt.subplot(3, 1, 1), zaf.sigplot(audio_signal, sampling_frequency, xtick_step)
plt.ylim(-1, 1), plt.title("Original signal")
plt.subplot(3, 1, 2), zaf.sigplot(audio_signal2, sampling_frequency, xtick_step)
plt.ylim(-1, 1), plt.title("Resyntesized signal")
plt.subplot(3, 1, 3), zaf.sigplot(audio_differences, sampling_frequency, xtick_step)
plt.ylim(-y_max, y_max), plt.title("Original - resyntesized signal")
plt.tight_layout()
plt.show()

examples.ipynb

This Jupyter notebook shows some examples for the different functions of the Python module zaf.

See Jupyter notebook viewer.

audio_file.wav

23 second audio excerpt from the song Que Pena Tanto Faz performed by Tamy.

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