Inverse Z-transform by Mobius inversion and the error bounds of aliasing in sampling

Author

Hsu, Chin-Chi ; Reed, Irving S. ; Truong, T.K.

Author_Institution

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

Volume

42

Issue

10

fYear

1994

fDate

10/1/1994 12:00:00 AM

Firstpage

2823

Lastpage

2831

Abstract

A general algorithm based on two special Mobius inversion formulae is developed to compute the inverse Z-transform. This approach to Fourier analysis uses what is called the arithmetic Fourier transform (AFT). With the new AFT algorithm. One can compute the inverse Z-transform of an infinite two-sided sequence. It is compared with the conventional DFT approach. Both methods have aliasing errors due to sampling. The error bounds of the aliasing effects in the DFT and the new proposed method are established and compared. In general, the AFT algorithm is not so vulnerable to the aliasing errors in the high-frequency components as the DFT approach

Keywords

Fourier analysis; Fourier transforms; Z transforms; error analysis; inverse problems; signal processing; AFT; Fourier analysis; Mobius inversion; aliasing; arithmetic Fourier transform; error bounds; high-frequency components; infinite two-sided sequence; inverse Z-transform; sampling; Algorithm design and analysis; Arithmetic; Discrete Fourier transforms; Fourier series; Fourier transforms; Sampling methods;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.324746

Filename

324746