Realization of one-dimensional nonuniform-band maximally decimated filter banks using two-dimensional filters

In the design of nonuniform-band filter banks (NFB), each filter must be designed to satisfy the perfect reconstruction (PR) condition corresponding to division ratio for the system. A simple design method for nonuniform-band maximally decimated filter banks using two-dimensional (2-D) filter to realize two-channel system is presented here. A 2-D filter is designed using a McClellan transform and one axis is fixed to arbitrary frequency in a 2-D plane. Then the frequency response that turns out to be a cross sectional response of 2-D filter, 1-D variable filter that has fixed frequency as a parameter can be realized. Using 2-D filters with complementary power, the lowpass filter and high-pass filter always satisfies power complementarily. The 2-D filter has been designed so that the filter pair satisfies the perfect reconstruction condition and it is adopted as the group of the necessary filters for NFB. In this method, the PR condition is not satisfied strictly but system simplification is achieved. Design examples, amplitude responses of them, and simulation results of the reconstruction of the signal are shown.