Gerchberg-Papoulis algorithm and the finite Zak transform
Andrzej K. Brodzik, Richard Tolimieri · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
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.