Gerchberg-Papoulis algorithm and the finite Zak transform

Andrzej K. Brodzik; Richard Tolimieri

doi:10.1117/12.408597

4 December 2000 Gerchberg-Papoulis algorithm and the finite Zak transform

Andrzej K. Brodzik, Richard Tolimieri

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408597
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We propose a new, time-frequency formulation of the Gerchberg-Papoulis algorithm for extrapolation of band- limited signals. The new formulation is obtained by translating the constituent operations of the Gerchberg- Papoulis procedure, the truncation and the Fourier transform, into the language of the finite Zak transform, a time-frequency tool intimately related to the Fourier transform. We will show that the use of the Zak transform results in a significant reduction of the computational complexity of the Gerchberg-Papoulis procedure and in an increased flexibility of the algorithm.

Citation Download Citation

Andrzej K. Brodzik and Richard Tolimieri "Gerchberg-Papoulis algorithm and the finite Zak transform", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408597

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