Uncertainty Principle of the Special Affine Fourier Transform for Discrete Signals

Abstract

The special affine Fourier transform (SAFT) encompasses series of famous transforms, and it has been proved as an effective way to solve problems of signal processing and optics. The product of the spreads of a signal in time and SAFT domains is limited, and the lower bound is given by the uncertainty principle of the SAFT. Unfortunately, this uncertainty principle is only established on the analog signal instead of discrete signals, which are more common in practice. This paper aims to introduce a novel uncertainty principle of the SAFT for discrete signals. First, the definitions of time and SAFT-band durations in discrete signals are given. Then, a minimum of the product of time and SAFT-frequency spreads is determined. Some related properties are also discussed.