def stft(time_signal, time_dim=None, size=1024, shift=256,
window=signal.blackman, fading=True, window_length=None):
"""
Calculates the short time Fourier transformation of a multi channel multi
speaker time signal. It is able to add additional zeros for fade-in and
fade out and should yield an STFT signal which allows perfect
reconstruction.
:param time_signal: multi channel time signal.
:param time_dim: Scalar dim of time.
Default: None means the biggest dimension
:param size: Scalar FFT-size.
:param shift: Scalar FFT-shift. Typically shift is a fraction of size.
:param window: Window function handle.
:param fading: Pads the signal with zeros for better reconstruction.
:param window_length: Sometimes one desires to use a shorter window than
the fft size. In that case, the window is padded with zeros.
The default is to use the fft-size as a window size.
:return: Single channel complex STFT signal
with dimensions frames times size/2+1.
"""
if time_dim is None:
time_dim = np.argmax(time_signal.shape)
# Pad with zeros to have enough samples for the window function to fade.
if fading:
pad = [(0, 0)] * time_signal.ndim
pad[time_dim] = [size - shift, size - shift]
time_signal = np.pad(time_signal, pad, mode='constant')
# Pad with trailing zeros, to have an integral number of frames.
frames = _samples_to_stft_frames(time_signal.shape[time_dim], size, shift)
samples = _stft_frames_to_samples(frames, size, shift)
pad = [(0, 0)] * time_signal.ndim
pad[time_dim] = [0, samples - time_signal.shape[time_dim]]
time_signal = np.pad(time_signal, pad, mode='constant')
if window_length is None:
window = window(size)
else:
window = window(window_length)
window = np.pad(window, (0, size - window_length), mode='constant')
time_signal_seg = segment_axis(time_signal, size,
size - shift, axis=time_dim)
letters = string.ascii_lowercase
mapping = letters[:time_signal_seg.ndim] + ',' + letters[time_dim + 1] \
+ '->' + letters[:time_signal_seg.ndim]
return rfft(np.einsum(mapping, time_signal_seg, window),
axis=time_dim + 1)
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