Synthetic phase for inverse transforms

Would it be useful to have inverse transforms istft, icqt #165 synthesize phase when the input is magnitude spectra? @dpwe’s repsonse to #424 provides an example of how to do this for inverting MFCCs by transferring the phase of the corresponding forward transform of white noise.

I’ve test-driven this on my icqt prototype, and it sounds pretty good; much better than a magnitude-only reconstruction.

It’s a bit of a nuisance to do this by hand since the parameters and duration need to be matched to the input signal. It would be easy to do this from within the inverse transform though, since that information is all present. I’m thinking an optional (defaulting to False) parameter.

Thoughts?

[jongwook]

I’m using this implementation of Griffin-Lim algorithm, and the restored audio sounds perceivably better than random/from-white-noise initialization of phases.

def griffinlim(spectrogram, n_iter = 100, window = 'hann', n_fft = 2048, hop_length = -1, verbose = False):
    if hop_length == -1:
        hop_length = n_fft // 4

    angles = np.exp(2j * np.pi * np.random.rand(*spectrogram.shape))

    t = tqdm(range(n_iter), ncols=100, mininterval=2.0, disable=not verbose)
    for i in t:
        full = np.abs(spectrogram).astype(np.complex) * angles
        inverse = librosa.istft(full, hop_length = hop_length, window = window)
        rebuilt = librosa.stft(inverse, n_fft = n_fft, hop_length = hop_length, window = window)
        angles = np.exp(1j * np.angle(rebuilt))

        if verbose:
            diff = np.abs(spectrogram) - np.abs(rebuilt)
            t.set_postfix(loss=np.linalg.norm(diff, 'fro'))

    full = np.abs(spectrogram).astype(np.complex) * angles
    inverse = librosa.istft(full, hop_length = hop_length, window = window)

    return inverse

Is it something to be avoided due to the slow speed? In that case, I think @Jonathan-LeRoux’s algorithm would be a nice addition, although I found it hard to write it efficiently only using Python.

[bmcfee]

Curious, what use cases are there when the phase from the forward transform can’t be kept around for doing the inverse?

The main one I have in mind is sonifying samples from a generative model of magnitude spectra.