Spectrogram calculation issue with power=1

🐛 Bug

https://github.com/pytorch/audio/blob/42a705d51eeea34242ec54e902a90728e0d10e72/torchaudio/functional.py#L209

While this is true when power=2, it is summing up real part and imaginary part when power=1.

[vincentqb]

I see, so librosa does spec_f = spec_f.power(2).sum(-1).sqrt().pow(power) or, using the new syntax, spec_f = complex_norm(spec_f, power=power). We should also check how Kaldi is doing it to make sure we wouldn’t break the compliance interface.

[vincentqb]

So, if power is specified, you’d return the power of the magnitude (aka absolute value) of the complex number via spec_f = spec_f.pow(2).sum(-1).sqrt().pow(power) ?

The code currently behaves very closely to L^p norms: (sum_i |x_i|^p)^{1/p} even for non-integers p >= 0. The difference with the code is the absence of absolute value and the p-th root. I would expect this to have been the original intention.

• For the case p=2, we recover the standard magnitude of a complex number, as you mentioned.
• For p=1, we get |x_0| + |x_1| as mentioned above – not what the code is doing
• For p=0, we get len((x,y)) – always 2 for complex numbers – what the code is doing
• For p=infinity, we get max(|x_i|) – not currently supported by the code.

Mixing normalization by the L^2 norm (when using normalized) with other power is a little strange.

• I would expect power to be use to to normalize by the p-th norm, when specified (and remove the normalized option if it does not interfere with other places).
• If we want the magnitude, or other p-th norm, I would simply have a separate function to compute them, which the user can explicitly invoke.

Thoughts?