WADA SNR Estimation of Speech Signals in Python

snr.py

import numpy as np

def wada_snr(wav):
    # Direct blind estimation of the SNR of a speech signal.
    #
    # Paper on WADA SNR:
    #   http://www.cs.cmu.edu/~robust/Papers/KimSternIS08.pdf
    #
    # This function was adapted from this matlab code:
    #   https://labrosa.ee.columbia.edu/projects/snreval/#9

    # init
    eps = 1e-10
    # next 2 lines define a fancy curve derived from a gamma distribution -- see paper
    db_vals = np.arange(-20, 101)
    g_vals = np.array([0.40974774, 0.40986926, 0.40998566, 0.40969089, 0.40986186, 0.40999006, 0.41027138, 0.41052627, 0.41101024, 0.41143264, 0.41231718, 0.41337272, 0.41526426, 0.4178192 , 0.42077252, 0.42452799, 0.42918886, 0.43510373, 0.44234195, 0.45161485, 0.46221153, 0.47491647, 0.48883809, 0.50509236, 0.52353709, 0.54372088, 0.56532427, 0.58847532, 0.61346212, 0.63954496, 0.66750818, 0.69583724, 0.72454762, 0.75414799, 0.78323148, 0.81240985, 0.84219775, 0.87166406, 0.90030504, 0.92880418, 0.95655449, 0.9835349 , 1.01047155, 1.0362095 , 1.06136425, 1.08579312, 1.1094819 , 1.13277995, 1.15472826, 1.17627308, 1.19703503, 1.21671694, 1.23535898, 1.25364313, 1.27103891, 1.28718029, 1.30302865, 1.31839527, 1.33294817, 1.34700935, 1.3605727 , 1.37345513, 1.38577122, 1.39733504, 1.40856397, 1.41959619, 1.42983624, 1.43958467, 1.44902176, 1.45804831, 1.46669568, 1.47486938, 1.48269965, 1.49034339, 1.49748214, 1.50435106, 1.51076426, 1.51698915, 1.5229097 , 1.528578  , 1.53389835, 1.5391211 , 1.5439065 , 1.54858517, 1.55310776, 1.55744391, 1.56164927, 1.56566348, 1.56938671, 1.57307767, 1.57654764, 1.57980083, 1.58304129, 1.58602496, 1.58880681, 1.59162477, 1.5941969 , 1.59693155, 1.599446  , 1.60185011, 1.60408668, 1.60627134, 1.60826199, 1.61004547, 1.61192472, 1.61369656, 1.61534074, 1.61688905, 1.61838916, 1.61985374, 1.62135878, 1.62268119, 1.62390423, 1.62513143, 1.62632463, 1.6274027 , 1.62842767, 1.62945532, 1.6303307 , 1.63128026, 1.63204102])

    # peak normalize, get magnitude, clip lower bound
    wav = np.array(wav)
    wav = wav / abs(wav).max()
    abs_wav = abs(wav)
    abs_wav[abs_wav < eps] = eps

    # calcuate statistics
    # E[|z|]
    v1 = max(eps, abs_wav.mean())
    # E[log|z|]
    v2 = np.log(abs_wav).mean()
    # log(E[|z|]) - E[log(|z|)]
    v3 = np.log(v1) - v2

    # table interpolation
    wav_snr_idx = None
    if any(g_vals < v3):
        wav_snr_idx = np.where(g_vals < v3)[0].max()
    # handle edge cases or interpolate
    if wav_snr_idx is None:
        wav_snr = db_vals[0]
    elif wav_snr_idx == len(db_vals) - 1:
        wav_snr = db_vals[-1]
    else:
        wav_snr = db_vals[wav_snr_idx] + \
            (v3-g_vals[wav_snr_idx]) / (g_vals[wav_snr_idx+1] - \
            g_vals[wav_snr_idx]) * (db_vals[wav_snr_idx+1] - db_vals[wav_snr_idx])

    # Calculate SNR
    dEng = sum(wav**2)
    dFactor = 10**(wav_snr / 10)
    dNoiseEng = dEng / (1 + dFactor) # Noise energy
    dSigEng = dEng * dFactor / (1 + dFactor) # Signal energy
    snr = 10 * np.log10(dSigEng / dNoiseEng)

    return snr

Hi, thanks for this implementation. Have you tested in practice how long needs to be the wav file so that the estimated statistics match the theoretical ones? (ie that the amplitudes of clean speech samples match the expected gamma distribution). I was wondering which of the 2 approaches (this one vs the snr estimated after VAD) is the most accurate?

Shorter clips can indeed bias your results with this method, but I haven't tested what the limits are. I would probably recommend the VAD method in the other gist, due to the somewhat frequent edge cases and higher complexity of this method. The VAD method requires some silence regions in the audio however, which is an edge-case of it's own. A combination of the two could work, although I suspect the SNR from each method won't match exactly which could cause issues. I'm afraid I don't have a satisfying answer 😅

Hello, thanks a lot for sharing this piece of code.
To be sure to understand, the 100dB would correspond to very noisy samples because of edge cases, but apart from these edge cases, samples that are e.g. >90dB and <99dB are very clean samples (high SNR)?

Could you confirm we can use this as MIT Licensed, like your VAD gist you're mentioning here?

I was able to get good results by dropping samples at -20dB and 100dB, but as this is a statistical method you may still find exceptions.

As for licensing, this is a re-implementation of the original matlab code, but the source code doesn't have a license that I could find. I reached out to the authors months ago and haven't heard back, so I'm not sure it can be used in a commercial setting 🤷. I would license it as MIT (or the least restrictive derivative license) if I could though.

Your last block of code is not needed, e.g.

snr = 10 * np.log10(dSigEng / dNoiseEng)
    = 10 * np.log10((dEng * dFactor / (1 + dFactor)) / (dEng / (1 + dFactor)))
    = 10 * np.log10(dFactor)
    = 10 * np.log10(10**(wav_snr / 10))
    = wav_snr

Hello, I have a short question :) I want to use this function to calculate the SNR for audio files generated with a TTS system. So far, I get a SNR value of 100 for every audio. I also tried it with a different audio file (one that definitely contains noise) and the SNR value was 21. So I don't think I did anything incorrectly with the function.
Would you still disregard the SNR values for the TTS sentences? Or do you think this could a possible result?
I'm very new to this field, so I just would like to be sure. Thank you! :)

Hello, I am trying to re-computing the value of g_vals above with 0.5 shape parameters. Are you able to share the code of computing g_vals? It is quite hard to implement the integral equation in the paper. Thank you so much!