The fractional Fourier domain analysis of two channel filter banks

Sub-band coders have been applied widely in the image processing and speech signal processing. Two-channel multirate digital filter banks are the basic components of the tree-structured sub-band coders. This paper proposes the perfect reconstruction condition of two channel multirate filter banks in the fractional Fourier domain (FRFD), based on the theorem for FRFD analysis of signal sampling rate conversion and fractional convolution theory. Then, this paper illustrates that it is possible to design two-channel FIR Quadrature Mirror Filter Banks (QMFB) and Conjugate Quadrature Mirror Filter Banks (CQMFB) through the prototype filters of FIR QMFB and CQMFB in Fourier domain. The proposed theorems in this study advance the generalization of filter banks in FRFD, which are the bases of the applications of FRFT in the practices, such as image processing, speech signal processing, etc. Finally, the effectiveness of the proposed methods is verified by the simulations.