Signal extrapolation in the real Zak space

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.