Signal extrapolation in the real Zak space

Author

Brodzik, Andrzej K.

Author_Institution

Mitre Corp., Bedford, MA, USA

Volume

50

Issue

8

fYear

2002

fDate

8/1/2002 12:00:00 AM

Firstpage

1957

Lastpage

1964

Abstract

A new formulation of the Gerchberg-Papoulis (1974, 1975) algorithm for extrapolation of bandlimited signals was introduced. The new formulation was obtained by translating the fundamental operations of the GP procedure, the truncation, and the Fourier transform into the language of the finite Zak (1967) transform. However, the Zak transform formulation of the GP algorithm assumes complex-valued signals, whereas the GP procedure is usually applied to real signals. We present a new and more efficient algorithm that acts directly on a real signal via the real Zak transform (RZT) relation between a signal and its Hartley transform, leading, in effect, to approximately a four-fold reduction in the computational complexity of the complex Zak space approach

Keywords

Fourier transforms; Hartley transforms; Z transforms; bandlimited signals; computational complexity; extrapolation; signal processing; Fourier transform; GP algorithm; Gerchberg-Papoulis algorithm; Hartley transform; bandlimited signals; complex-valued signals; computational complexity reduction; finite Zak transform; real Zak space; real Zak transform; signal extrapolation; Algorithm design and analysis; Availability; Computational complexity; Data engineering; Extrapolation; Fast Fourier transforms; Filtering algorithms; Fourier transforms; Signal analysis; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2002.800407

Filename

1018791