Repeated filtering in consecutive fractional fourier domains and its application to signal restoration

Abstract

Filtering in a single time domain or in a single frequency domain has recently been generalized to filtering in a single fractional Fourier domain. In this paper, we further generalize this to repeated filtering in consecutive fractinal Fourier domains. We then discuss the applications of the repeated filtering method to signal restoration through several examples. In all of the examples, we see that when our repeated filtering method is compared with single domain filtering methods, significant improvements in performance are obtained with only modest increases in processing time. We also compare our method with the optimum general linear estimation method and see that the use of our method may result in significant computational savings while still yielding acceptable performance.