Sparse signal FFT

1. What is a sparse FFT?
2. What is sparse signal?
3. What is sparsity in signal processing?
4. What are the two types of FFT?

What is a sparse FFT?

Sparse fast Fourier transform (or sparse FFT) is a new technique which computes the Fourier transform in a compressed way, using only a subset of the input data. Sparse FFT computes the desired transform in sublinear time, which means in an amount of time that is smaller than the size of data.

What is sparse signal?

Sparse signals are characterized by a few nonzero coefficients in one of their transformation domains. This was the main premise in designing signal compression algorithms. Compressive sensing as a new approach employs the sparsity property as a precondition for signal recovery.

What is sparsity in signal processing?

A signal is considered sparse if most of its information is contained within a few non-zero samples. Consequently, a signal reconstruction algorithm has to find a sparse vector that best represents the measured signal. Many algorithms to solve this problem are based on l1-norm optimization.

What are the two types of FFT?

These are called the radix-2 and mixed-radix cases, respectively (and other variants such as the split-radix FFT have their own names as well).