Generalized design method of multirate filter banks in the fractional fourier domain

The fractional Fourier transform (FRFT) is of better time frequency analysis character than the traditional Fourier transform. The filtering in the optimal fractional Fourier domain (FRFD) can estimate some special cases of non-stationary signals and systems with minimum mean square error. The theorem for the multirate filter bank in the FRFD leads to the efficient structure of filtering in the FRFD and the multi-resolution analysis of signal in the FRFD. But the existing perfect reconstruction filter banks in the FRFD are of special form, which cannot satisfy some practices. This paper proposes the generalized design method for the perfect reconstruction filter banks in the FRFD based on the FRFD analysis of sampling rate conversion and the fractional convolution theorem, which are the basis of the applications of filter bank theory in the FRFD. At last, the simulations verify the generalized design method.