Downsampling wav audio file

Question

I have to downsample a wav file from 44100Hz to 16000Hz without using any external Python libraries, so preferably wave and/or audioop. I tried jus

Answer 1

To downsample (also called decimate) your signal (it means to reduce the sampling rate), or upsample (increase the sampling rate) you need to interpolate between your data.

The idea is that you need to somehow draw a curve between your points, and then take values from this curve at the new sampling rate. This is because you want to know the value of the sound wave at some time that wasn't sampled, so you have to guess this value by one way or an other. The only case where subsampling would be easy is when you divide the sampling rate by an integer $k$. In this case, you just have to take buckets of $k$ samples and keep only the first one. But this won't answer your question. See the picture below where you have a curve sampled at two different scales.

You could do it by hand if you understand the principle, but I strongly recommend you to use a library. The reason is that interpolating the right way isn't easy or either obvious.

You could use a linear interpolation (connect points with a line) or a binomial interpolation (connect three points with a piece of polynom) or (sometimes the best for sound) use a Fourier transform and interpolate in the space of frequency. Since fourier transform isn't something you want to re-write by hand, if you want a good subsampling/supsampling, See the following picture for two curves of upsampling using a different algorithm from scipy. The "resampling" function use fourier transform.

I was indeed in the case I was loading a 44100Hz wave file and required a 48000Hz sampled data, so I wrote the few following lines to load my data:

    # Imports
    from scipy.io import wavfile
    import scipy.signal as sps

    # Your new sampling rate
    new_rate = 48000

    # Read file
    sampling_rate, data = wavfile.read(path)

    # Resample data
    number_of_samples = round(len(data) * float(new_rate) / sampling_rate)
    data = sps.resample(data, number_of_samples)

Notice you can also use the method decimate in the case you are only doing downsampling and want something faster than fourier.