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Well, kind of. The FT on a real signal gives you a symmetric spectrum that is complex.

IDK seems kinda weird, there's a lot of handwavey stuff that I don't fully understand.

And I'm also wondering what the significance of the frequency domain is--can you generalize compressed sensing with other transforms as well?

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Definitely. JPEG2000 uses a wavelet transform instead of the DCT to achieve similar goals.

One way to think of it is your transforming to some other basis. You could do something similar with any vector base change where you go from a dense representation to a sparse one. Think of things like an eigen decomposition where most of the eigenvalues are small or zero and can be ignored

Yeah. do they like make up tailored wavelet transforms just to get it nice and sparse?

Or does it have to be sparse? I thought it just has to have a low L1 norm

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