Envelope reconstruction algorithm for audio processing

Question

I need to reconstruct the envelope of a sound.

Audio data are professionally-recorded natural sounds (speech, bird songs) with very little noise. I would prefer working in the time domain rather than in the frequency domain (I've seen some algorithms based on FFT transformations that looked overcomplicated for what I need). The algorithm will be implemented in an interpreted language so it needs to stay "light" in computation.

As a first approach, I considered using a peak detection algorithm, then doing a linear interpolation between the peaks. But isn't there some pitfalls with such a naive approach? Are there some standard ways of implementing envelope reconstruction in the time domain that would better suit my needs?

_{FWIW, I'm not familiar with digital signal processing vocabulary, so do not hesitate to reword my question if I misused some terms}

Answer 1

As I said in a comment, you can get the envelope of a signal by running it through a lowpass filter.

The steps required for this (usually) are

1. Go through all the samples (x(N) ) and check for negative samples. Convert them to positive values

2. Implement a lowpass filter (FIR) by creating a filter kernel of appropriate length M (h(M) ). Note that your FIR filter (sin(x)/x) should normally be multiplied by a window function (e.g Hamming, Blackman etc).

3. Convolve your signal with the filter kernel.

   for(int i=0;i<N;i++)
   
    for(int j=0;j<M;j++)
   
      y[i+j] = y[i+j]+x[i]*h(j); 
   

Note that the output (filtered) signal is usually right shifted by M samples. Also, M is often chosen to be odd in order to create a perfectly symmetrical filter although I'm sure not all implementations adhere to this.

Answer 2

I would recommend a streaming RMS detector. The standard approach for computing a streaming RMS detector is to square the input samples and then apply these to a 1st-order lowpass filter. If you want the output in dB, take 10*log10() of this quantity. If you want the output in volts, take the square root of this quantity. If Logs and square-roots are too heavy for your processor, there are low-mips ways to approximate them. Note that RMS detection offers a good compromise between a peak detector (which is often over-responsive to very narrow transients) and average (which is sometimes too slow). Also, the ear tends to approximate RMS dynamics in its perception of loudness.