How about identifying the three notes in a chord? On the music idea

Some ideas:

Given a pure sine wave, identify the frequency. (Basically FFT plus a bit of theory plus solving a quadratic. Important to include test cases at a frequency which isn't a trivial rational multiple of the sample frequency. This is about the simplest non-trivial FFT question).

Audio synthesis: generate pink noise. (Requires a test framework which verifies that the power spectrum vs frequency is within a stated error bound of 1/f. This should be trivial to implement with iFFT, but for golfing that may not be the best approach, especially if FFT library implementations are banned. For reproducibility of testing, should require it to be seeded).

Noise reduction. Given a sample of "silence" (which will have mains hum and white noise) and a sample of non-silence (e.g. someone reading a sentence or two), remove the noise from the second sample without removing signal. (Con: hard to verify objectively that the spec is met or to measure how well it's met).

Time stretch with pitch correction. (This is a much harder version of an existing challenge. The risk is that no-one would submit an answer. But it's a very cool problem to work on)

Hmm I like the sine wave frequency idea, it's accessible but as you say non-trivial. It seems like it could also work with just numbers via STDIN (if it doesn't end up getting picked)

@Sp3000 @PeterTaylor yep, the sine wave idea sounds quite nice.

Thinking about this a bit more, I think I'd rather go for something where the interpretation of the data as audio has some benefit (as Sp3000 mentioned, this challenge makes sense regardless of what the data actually is, so there's no point in involving audio files in the first place)

So I think I'd prefer either the idea of extracting a score from a simple melody, or something that also has audio has the output.

Beat analysis: identify the tempo of a sample of music.

@PeterTaylor didn't we already have that one?

I thought so, but I didn't find anything by searching for "beat analysis"