What is the purpose of the sparse Fourier transform?
The sparse Fourier transform (SFT) is a kind of discrete Fourier transform (DFT) for handling big data signals. Specifically, it is used in GPS synchronization, spectrum sensing and analog-to-digital converters.: The fast Fourier transform (FFT) plays an indispensable role on many scientific domains, especially on signal processing.
Which is an application of the discrete Fourier transform?
The discrete Fourier transform (DFT) is one of the most important and widely used computational tasks. Its applications are broad and include signal processing, communications, and audio/image/video compression. Hence, fast algorithms for DFT are highly valuable.
Is the output of a DFT always sparse?
A general algorithm for computing the exact DFT must take time at least proportional to its output size n. In many applications, however, most of the Fourier coefficients of a signal are small or equal to zero, i.e., the output of the DFT is sparse.
Which is better, FFT or exactly k-sparse?
Both algorithms improve over FFT, for any k = o (n) . Moreover, if one assume that FFT is optimal, the algorithm for the exactly k -sparse case is optimal. Under the same assumption, the result for the general case is at most one loglog n factor away from the optimal runtime for the case of “large” sparsity k = n/log n.
Is there an algorithm for faster 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 named one of world’s most important emerging technologies “. The MIT Technology Review magazine says:
How to get sparse representation of input signal?
The “secret souse” of the method is how to get sparse representation of input signal in frequency domain. The previous algorithms used kind of brute force for location of dominant sparse coefficient.