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!

This implementation gives different results to the original c++ implementation, which can be found here. I went through the original code and spotted the following differences:

• they subtract the mean from the audio data
• they compute the energy before the normalisation
• they don't interpolate the g function
• they compute the signal and noise energy on blocks of 100,000 samples, they accumulate the energies and compute the final SNR with those accumulated values

So, if you want to get the same results, check my fork