Fourier analysis and signal processing by use of the Mobius inversion formula

Author

Reed, Irving S. ; Tufts, Donald W. ; Yu, Xiaoli ; Truong, T.K. ; Shih, Ming-Tang ; Yin, Xiaowei

Author_Institution

Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA

Volume

38

Issue

3

fYear

1990

fDate

3/1/1990 12:00:00 AM

Firstpage

458

Lastpage

470

Abstract

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Mobius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed

Keywords

Fourier analysis; computerised signal processing; fast Fourier transforms; DFT; FFT; Fourier analysis; Fourier transform method; Mobius inversion formula; computer simulation; digital signal processing; fast Fourier transform; Algorithm design and analysis; Arithmetic; Computer simulation; Convolution; Digital signal processing; Discrete Fourier transforms; Fourier transforms; Signal analysis; Signal processing; Signal processing algorithms;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.106864

Filename

106864