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Questions tagged [sparse-fourier-transform]

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55 votes
4 answers

What is the sparse Fourier transform?

MIT has been making a bit of noise lately about a new algorithm that is touted as a faster Fourier transform that works on particular kinds of signals, for instance: "Faster Fourier transform ...
0 votes
1 answer

Discrete Fourier Transform with known periodic sparsity pattern or constraints

Consider a discrete signal $x$ of size $n$, and write $c$ its discrete Fourier transform. Unless I'm mistaken, the relations between the two look something like: \begin{split}c_k = \sum_{j=0}^{n-1} ...
2 votes
0 answers

Lomb-Scargle or Periodogram for non-uniformly sampled data

I have non-uniformly sampled data and I'm trying to look at its Power Spectral Density (PSD). For that, I looked at the Periodogram PSD estimate of an interpolated (with uniform sampling period) ...
3 votes
1 answer

Sparse signal FFT

Say I had a time domain signal $x[k]$ wich is sparse: $\log(N)^2$ nonzero samples and the fourier transform has only a very (very!) small number of high frequency components. Are there any techniques ...
1 vote
0 answers

Sparse Fourier Transform for Sparse Pulse Trains

So I have signals for the form: $$x_{k}(t) = \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ that I receive as a superposition: $$x(t) = \sum_{k=0}^{K} \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ ...