Title




Sparse interpolation, the FFT algorithm and FIR filters
 
Author




 
Abstract




In signal processing, the Fourier transform is a popular method to analyze the frequency content of a signal, as it decomposes the signal into a linear combination of complex exponentials with integer frequencies. A fast algorithm to compute the Fourier transform is based on a binary divide and conquer strategy. In computer algebra, sparse interpolation is wellknown and closely related to Pronys method of exponential fitting, which dates back to 1795. In this paper we develop a divide and conquer algorithm for sparse interpolation and show how it is a generalization of the FFT algorithm. In addition, when considering an analog as opposed to a discrete version of our divide and conquer algorithm, we can establish a connection with digital filter theory. 
 
Language




English
 
Source (journal)




Lecture notes in computer science.  Berlin, 1973, currens
 
Source (book)




CASC 2017: Computer Algebra in Scientific Computing
Proceedings 19th International Workshop, CASC 2017, September 1822, 2017, Beijing, China
 
Source (series)




Theoretical computer science and general issues ; 10490
 
Publication




Cham
:
Springer
,
2017
 
ISBN




9783319663197
 
Volume/pages




(2017)
, p. 2739
 
Full text (Publisher's DOI)




 
Full text (open access)




 
Full text (publisher's version  intranet only)




 
