import numpy as np
[docs]def frame(data, window_length, hop_length):
"""Convert array into a sequence of successive possibly overlapping frames.
An n-dimensional array of shape (num_samples, ...) is converted into an
(n+1)-D array of shape (num_frames, window_length, ...), where each frame
starts hop_length points after the preceding one.
This is accomplished using stride_tricks, so the original data is not
copied. However, there is no zero-padding, so any incomplete frames at the
end are not included.
data: np.array of dimension N >= 1.
window_length: Number of samples in each frame.
hop_length: Advance (in samples) between each window.
(N+1)-D np.array with as many rows as there are complete frames that can be
num_samples = data.shape
num_frames = 1 + int(np.floor((num_samples - window_length) / hop_length))
shape = (num_frames, window_length) + data.shape[1:]
strides = (data.strides * hop_length,) + data.strides
return np.lib.stride_tricks.as_strided(data, shape=shape, strides=strides)
"""Calculate a "periodic" Hann window.
The classic Hann window is defined as a raised cosine that starts and
ends on zero, and where every value appears twice, except the middle
point for an odd-length window. Matlab calls this a "symmetric" window
and np.hanning() returns it. However, for Fourier analysis, this
actually represents just over one cycle of a period N-1 cosine, and
thus is not compactly expressed on a length-N Fourier basis. Instead,
it's better to use a raised cosine that ends just before the final
zero value - i.e. a complete cycle of a period-N cosine. Matlab
calls this a "periodic" window. This routine calculates it.
window_length: The number of points in the returned window.
A 1D np.array containing the periodic hann window.
return 0.5 - (0.5 * np.cos(2 * np.pi / window_length *
[docs]def stft_magnitude(signal, fft_length,
"""Calculate the short-time Fourier transform magnitude.
signal: 1D np.array of the input time-domain signal.
fft_length: Size of the FFT to apply.
hop_length: Advance (in samples) between each frame passed to FFT.
window_length: Length of each block of samples to pass to FFT.
2D np.array where each row contains the magnitudes of the fft_length/2+1
unique values of the FFT for the corresponding frame of input samples.
frames = frame(signal, window_length, hop_length)
# Apply frame window to each frame. We use a periodic Hann (cosine of period
# window_length) instead of the symmetric Hann of np.hanning (period
window = periodic_hann(window_length)
windowed_frames = frames * window
return np.abs(np.fft.rfft(windowed_frames, int(fft_length)))
# Mel spectrum constants and functions.
_MEL_BREAK_FREQUENCY_HERTZ = 700.0
_MEL_HIGH_FREQUENCY_Q = 1127.0
"""Convert frequencies to mel scale using HTK formula.
frequencies_hertz: Scalar or np.array of frequencies in hertz.
Object of same size as frequencies_hertz containing corresponding values
on the mel scale.
return _MEL_HIGH_FREQUENCY_Q * np.log(
1.0 + (frequencies_hertz / _MEL_BREAK_FREQUENCY_HERTZ))
"""Return a matrix that can post-multiply spectrogram rows to make mel.
Returns a np.array matrix A that can be used to post-multiply a matrix S of
spectrogram values (STFT magnitudes) arranged as frames x bins to generate a
"mel spectrogram" M of frames x num_mel_bins. M = S A.
The classic HTK algorithm exploits the complementarity of adjacent mel bands
to multiply each FFT bin by only one mel weight, then add it, with positive
and negative signs, to the two adjacent mel bands to which that bin
contributes. Here, by expressing this operation as a matrix multiply, we go
from num_fft multiplies per frame (plus around 2*num_fft adds) to around
num_fft^2 multiplies and adds. However, because these are all presumably
accomplished in a single call to np.dot(), it's not clear which approach is
faster in Python. The matrix multiplication has the attraction of being more
general and flexible, and much easier to read.
num_mel_bins: How many bands in the resulting mel spectrum. This is
the number of columns in the output matrix.
num_spectrogram_bins: How many bins there are in the source spectrogram
data, which is understood to be fft_size/2 + 1, i.e. the spectrogram
only contains the nonredundant FFT bins.
audio_sample_rate: Samples per second of the audio at the input to the
spectrogram. We need this to figure out the actual frequencies for
each spectrogram bin, which dictates how they are mapped into mel.
lower_edge_hertz: Lower bound on the frequencies to be included in the mel
spectrum. This corresponds to the lower edge of the lowest triangular
upper_edge_hertz: The desired top edge of the highest frequency band.
An np.array with shape (num_spectrogram_bins, num_mel_bins).
ValueError: if frequency edges are incorrectly ordered or out of range.
nyquist_hertz = audio_sample_rate / 2.
if lower_edge_hertz < 0.0:
raise ValueError("lower_edge_hertz %.1f must be >= 0" % lower_edge_hertz)
if lower_edge_hertz >= upper_edge_hertz:
raise ValueError("lower_edge_hertz %.1f >= upper_edge_hertz %.1f" %
if upper_edge_hertz > nyquist_hertz:
raise ValueError("upper_edge_hertz %.1f is greater than Nyquist %.1f" %
spectrogram_bins_hertz = np.linspace(0.0, nyquist_hertz, num_spectrogram_bins)
spectrogram_bins_mel = hertz_to_mel(spectrogram_bins_hertz)
# The i'th mel band (starting from i=1) has center frequency
# band_edges_mel[i], lower edge band_edges_mel[i-1], and higher edge
# band_edges_mel[i+1]. Thus, we need num_mel_bins + 2 values in
# the band_edges_mel arrays.
band_edges_mel = np.linspace(hertz_to_mel(lower_edge_hertz),
hertz_to_mel(upper_edge_hertz), num_mel_bins + 2)
# Matrix to post-multiply feature arrays whose rows are num_spectrogram_bins
# of spectrogram values.
mel_weights_matrix = np.empty((num_spectrogram_bins, num_mel_bins))
for i in range(num_mel_bins):
lower_edge_mel, center_mel, upper_edge_mel = band_edges_mel[i:i + 3]
# Calculate lower and upper slopes for every spectrogram bin.
# Line segments are linear in the *mel* domain, not hertz.
lower_slope = ((spectrogram_bins_mel - lower_edge_mel) /
(center_mel - lower_edge_mel))
upper_slope = ((upper_edge_mel - spectrogram_bins_mel) /
(upper_edge_mel - center_mel))
# .. then intersect them with each other and zero.
mel_weights_matrix[:, i] = np.maximum(0.0, np.minimum(lower_slope,
# HTK excludes the spectrogram DC bin; make sure it always gets a zero
mel_weights_matrix[0, :] = 0.0
"""Convert waveform to a log magnitude mel-frequency spectrogram.
data: 1D np.array of waveform data.
audio_sample_rate: The sampling rate of data.
log_offset: Add this to values when taking log to avoid -Infs.
window_length_secs: Duration of each window to analyze.
hop_length_secs: Advance between successive analysis windows.
**kwargs: Additional arguments to pass to spectrogram_to_mel_matrix.
2D np.array of (num_frames, num_mel_bins) consisting of log mel filterbank
magnitudes for successive frames.
window_length_samples = int(round(audio_sample_rate * window_length_secs))
hop_length_samples = int(round(audio_sample_rate * hop_length_secs))
fft_length = 2 ** int(np.ceil(np.log(window_length_samples) / np.log(2.0)))
spectrogram = stft_magnitude(
mel_spectrogram = np.dot(spectrogram, spectrogram_to_mel_matrix(
return np.log(mel_spectrogram + log_offset)