Modulated 2 dimensional perfect reconstruction FIR filter banks with permissible passbands

In this paper, we present a design method of 2 dimensional (2-D) perfect reconstruction (PR) filter banks with permissible passbands by modulating a complex prototype 2-D FIR digital filter. At first, we design a 2-D complex digital filter with half of a passband obtained by a sampling matrix. Then, we show that the 2-D analysis filter banks can be realized by modulating this prototype 2-D complex digital filter and taking the real part of the output. It is demonstrated that the modulation in 2-D frequency plane is equivalent to one dimensional (1-D) discrete-Fourier-transform (DFT). We also derive a necessary and sufficient condition for the 2-D PR filter banks.