Signal Approximation via the Gopher Fast Fourier Transform
Abstract
We consider the problem of quickly estimating the best κterm Fourier representation for a given frequencysparse bandlimited signal (i.e., function) f: [0,2π]→¢. In essence, this requires the identification of κ of the largest magnitude frequencies of \vf∈¢^{N}, and the estimation their Fourier coefficients. Randomized sublineartime Monte Carlo algorithms, which have a small probability of failing to output accurate answers for each input signal, have been developed for solving this problem [1, 2]. These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT) and empirically evaluated in [3]. In this paper we present and evaluate the first implementation, called the Gopher Fast Fourier Transform (GFFT), of the more recently developed sparse Fourier transform techniques from [4]. Our experiments indicate that different variants of GFFT generally outperform AAFFT with respect to runtime and sample usage.
 Publication:

Application of Mathematics in Technical and Natural Sciences
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3526650
 Bibcode:
 2010AIPC.1301..494B
 Keywords:

 Fourier analysis;
 Monte Carlo methods;
 magnetic resonance imaging;
 algorithm theory;
 functional analysis;
 02.30.Nw;
 02.70.Uu;
 87.61.Qr;
 07.05.Pj;
 02.30.Sa;
 Fourier analysis;
 Applications of Monte Carlo methods;
 Functional imaging;
 Image processing;
 Functional analysis