Sparse Interpolation, the FFT Algorithm and FIR Filters

被引：1

作者：

Briani, Matteo ^{[1
]}

Cuyt, Annie ^{[1
]}

Lee, Wen-shin ^{[1
]}

机构：

[1] Univ Antwerp, Dept Math & Comp Sci Wis Inf, Middelheimlaan 1, B-2020 Antwerp, Belgium

来源：

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2017 | 2017年 / 10490卷

关键词：

D O I：

10.1007/978-3-319-66320-3_3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 well-known and closely related to Prony's 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.

引用

页码：27 / 39

页数：13

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