ltx-audio: use radix-2 fft to speed up compute_log_mel_spectrogram

[stduhpf]

Summary

This PR optimises one part of the LTX2.3 audio VAE by implementing Cooley-Tukey Radix-2 FFT algorithm to replace inlined DFT. Output sound quality is indistinguishable in my experience (as it should be).

(I also changed the intermediate mel_value to be float instead of double, this technically increases the footprint of this PR a bit, I don't think it affect performance or quality much either way, I kinda included it in this PR by mistake, but the code is a bit cleaner like that, so I'm leaving it in)

Related Issue / Discussion

Additional Information

Performace comparison, generating a 32x32 24fps video

• 121 frames (5s):

	compute_log_mel_spectrogram() time	speedup	Total audio decode time	Total speedup
DFT (master)	21.315s	1x	209.086s	1x
FFT (PR)	1.284s	16.6x	188.718s	1.1x

• 9 frames (0.33s):

	compute_log_mel_spectrogram() time	speedup	Total audio decode time	Total speedup
DFT (master)	1.566s	1x	4.577s	1x
FFT (PR)	119ms	13.2x	2.873s	1.6x

Checklist

• I have read and confirmed this PR follows the contribution guidelines.

[stduhpf]

Even with this change, the audio decoding remains very slow, especially for longer sequences. Maybe it would be worth investigating for using temporal tiling there too?

[leejet]

I plan to add the missing operator to ggml, which should make it much faster. If this work takes too long or there are issues with the implementation, I’ll consider merging this PR.