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


ISSN




03029743
[print]
16113349
[online]


ISBN




9783319663197


DOI




10.1007/9783319663203_3


Volume/pages




(2017)
, p. 2739


Full text (Publisher's DOI)






Full text (open access)






Full text (publisher's version  intranet only)





