Signal to noise ratio for time series audio data

Question

I am writing some software to benchmark an audio noise filtering method using SNR as an evaluation metric. One software component generates noisey audio by taking a clean audio file and a noise source file and simply adding the components. The clean file is usually longer, so the noise source is looped and/or padded to fill out all the samples.

I then pass this through my noise filter, getting a less noisey signal at the output.

How can I calculate SNR from the resultant data? My current method is to compute the RMS for the cleaned up signal and divide by RMS of the noise source giving the average power ratio. Is this the correct method?

Code is provided below:

float SignalCleaner::ComputeRMS(AudioFile<float> signal){
    float total_square = 0.0f;
    float n = (float) signal.getNumSamplesPerChannel() * (float) signal.getNumChannels();
    for(int channel_idx = 0; channel_idx < signal.getNumChannels(); channel_idx++){
        for(int sample_idx = 0; sample_idx < signal.getNumSamplesPerChannel(); sample_idx++){
            total_square += std::pow(signal.samples[channel_idx][sample_idx], 2);
        }
    }

    return std::sqrt(total_square / n);
}

float SignalCleaner::ComputeSNR(AudioFile<float> signal, AudioFile<float> noise){
    float signal_rms = ComputeRMS(signal);
    float noise_rms = ComputeRMS(noise);
    return 20 * std::log(signal_rms/noise_rms);

}

float SignalCleaner::SNRPreFiltered() {
    return ComputeSNR(noisey_signal, noise_source);
}


float SignalCleaner::SNRPostFiltered() {
    return ComputeSNR(output, noise_source);
}

Thanks, happy to provide further clarification

Answer 1

The current method proposed by the OP is flawed as it doesn't account for the possibility of signal losses in the filtering. This would require some sort of normalization, but once normalized then both powers would be the same and the ratio would be 1.

An optimum approach for computing SNR when a clean reference waveform is provided is to use the normalized cross-correlation between the two waveforms. The relationship between SNR and cross-correlation is further detailed in this post.