Generalized Linear Canonical Transform with Higher Order Phase

Abstract

In this paper, a linear transform that is a further generalization of the linear canonical transform (LCT) and the fractional Fourier transform is proposed. Instead of the chirp terms adopted by the LCT, we apply exponent functions with higher order phases before and after applying the scaled Fourier transform. With the proposed higher order phase linear canonical transform (HOPLCT), one can convert the time-frequency distribution with a bent shape, which is usually the case for vocal signals, into a rectangular shape. It can much reduce the bandwidth of a signal and is very helpful for signal sampling and filter design.