[maaku]

> I don't expect that the signal processing hardware is the bottleneck here.

Computational resources is always the bottleneck in bioinformatics, quantum chemistry, or any sort of high data volume analysis or simulation, and the FFT is a fundamental and commonly used transform in all fields.

At least for people who still use computers to, well, compute things, a faster FFT is a huge deal.

[moultano]

How many domains still use FFT specifically though as opposed to some other transform? Most of the signal processing papers of the last decade that I've read or read about have used either wavelets, FFT on a small window such that this isn't really applicable, or some arbitrary non-orthogonal basis.

[KingMob]

When I was doing EEG signal analysis in grad school, I used the FFT all the time. While there's some cool stuff involving wavelets and using interesting basis sets (matching pursuit looks cool), if you're primarily looking at power and frequency over time, the FFT is sufficient, and usually faster than the other algorithms. (And if you're looking at power/phase, the common Morlet wavelet choice is mathematically equivalent to an FT with a Gaussian taper.)

I'm not sure what you mean by "on a small window such that this isn't really applicable"; can you give an example? As long as you accept the inherent time-frequency resolution trade-offs, there's no obstacle to using FFT on a small window. It's called the short-time Fourier transform (STFT), and it's used everywhere; it's probably used more than analyzing an entire signal, since we frequently want to know how power and phase change over time in a signal, and a full-signal FT can't tell you that.

[moultano]

>I'm not sure what you mean by "on a small window such that this isn't really applicable"

FFT is very useful on a small window, but algorithms that improve the asymptotic efficiency are unlikely to be useful at that scale. With n=100 the asymptote doesn't matter. We'll still be using the FFT forever, I'm just skeptical that the frontiers of technology will be advanced by a faster FFT, since it seems like the coolest stuff is happening elsewhere. It's increasingly becoming the quick-and-dirty counterpart to the sophisticated-but-slow methods.

[rnadna]

FFTs are used in lots of ways. The R function convolve(), for example, uses FFTs for efficiency.

[javajosh]

>At least for people who still use computers to, well, compute things, a faster FFT is a huge deal.

This is a useless post except that I wanted to highlight that wonderful little bon mot. Well done.