Implement Short-time Fourier transform and its inverse

[pxl-th]

• Implement Short-time Fourier transform (STFT) and its inverse (iSTFT), modelled after torch.stft and torch.istft respectively.
• Add window functions (hann, hamming).
• Add Mel-scale filterbanks.
• Add tests.
• Add test/Project.toml file and install GPU backends only when testing them.
  Currrently latest CUDA does not support LLVM 7, but AMDGPU uses only it. Without this fix, we can't install all packages needed for testing.
• Add spectrogram function spectrogram and conversion from power to decibel (power_to_db) units and vice versa (db_to_power).

Spectrogram Example:

julia> x, sr = load("jfk.flac")
julia> spec = spectrogram(reshape(Float32.(x), :);
    n_fft=1024, hop_length=128, window=hann_window(1024))
julia> spec_db = power_to_db(spec)
julia> Makie.heatmap(transpose(spec_db))

PR Checklist

• Tests are added
• Documentation, if applicable

[pxl-th]

I'm not sure if NNlib.jl is the right place for audio stuff. But I figured since torch has it, we can too, for convenience

[darsnack]

Looks pretty good to me. The only thing might be adding some basic gradient tests. The bulk of gradient testing is already in AbstractFFTs.

[darsnack]

Maybe a UnicodePlot with output would be nicer here (and fit other docstrings in NNlib)

[pxl-th]

See output for UnicodePlot for heatmap: https://fluxml.ai/NNlib.jl/previews/PR587/audio/#Spectrogram

Not sure how I feel about it. Maybe it is worth switching to Plots.jl?

[darsnack]

Yeah it's not ideal, but my inclination towards UnicodePlots is so that docstrings render completely in the REPL as well. I'm happy to use Makie or Plots instead though.

Let's solicit opinions from @mcabbott or @ToucheSir.

[pxl-th]

I've updated to use Makie plots, here's UnicodePlots for reference:

UnicodePlots	Makie

[pxl-th]

I've addressed comments. I think we also need higher level API in future, like Spectrogram (or MelSpectrogram), that will hold parameters like window, filter banks on the specified device and other parameters. They can be added in Flux.jl though

[pxl-th]

@darsnack, kind bump

[CarloLucibello]

Can we make this a weak dependence and move any function relying on FFTW under an extension?

[pxl-th]

Done