Calculate the short-time Fourier transform magnitude.

  Args:
    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.

  Returns:
    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.

def stft_magnitude(signal, fft_length,
                   hop_length=None,
                   window_length=None):
  """Calculate the short-time Fourier transform magnitude.

  Args:
    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.

  Returns:
    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_length-1).
  window = periodic_hann(window_length)
  windowed_frames = frames * window
  return np.abs(np.fft.rfft(windowed_frames, int(fft_length)))