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

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!