Compute deltas

[vincentqb]

This PR adds a functional/transform/compliance to compute the deltas of MFCC features, see also here.

• The effect at the boundary follows Kaldi's convention of replicating the values (see here).
• To compute the deltas-deltas, simply compute the deltas on the deltas (though Kaldi has a order parameter to compute higher order deltas). The compliance interface loops over the order to computer higher order differences.
• This function simply returns the deltas. Kaldi instead appends them to the set of available features, see here

To do:

• Add a test comparing with Kaldi's add_deltas. (leaving off this PR)

CC @cpuhrsch @mravanelli

[zhangguanheng66]

if this depends on the jit mode, it's better to add a jit test to make sure that it works properly.

[vincentqb]

Do you have an example of what you have in mind?

[zhangguanheng66]

You just need to add a text case to ensure every operator is traceable.

[vincentqb]

There was already a test verifying that the shape of the output is correct. I added a test to verify that the output matches the functional, see here. Thanks for pointing out this link, but could you clarify what you would like to verify? If the module were not to compile, the test would not run at all.

[cpuhrsch]

Nit: This technically isn't limited to spectrograms right? I mean, we could just talk about regular Tensors as inputs.

Also, the edge behavior might be something the user could want to change in the future. Some people rather not replicate the deltas, but just drop those frames altogether.

[vincentqb]

Nit: This technically isn't limited to spectrograms right? I mean, we could just talk about regular Tensors as inputs.

fair enough, it's commonly used on spectrogram, but i could replace this by waveform, since there is a time-component, though it is not limited to waveform. the list of standardized words might not be useful here? :)

Also, the edge behavior might be something the user could want to change in the future. Some people rather not replicate the deltas, but just drop those frames altogether.

This is the behavior that kaldi does, and also does not make configurable :) I'll add the option to change that, by simply passing along the mode option for pad, and default to 'replicate'.