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Modulated 2 dimensional perfect reconstruction FIR filter banks with permissible passbands

In this paper, the author considers the theory of modulated 2 dimensional (2-D) perfect reconstruction (PR) filter banks with permissible passbands. At first, the author designs a 2-D complex digital filter with half passband obtained by the sampling matrix. Next, 2-D analysis filter banks are realized by modulating this prototype 2-D complex digital filter and by taking the real part of the output. It is also shown that the modulation in the 2-D frequency plane is equivalent to a 1-D DFT. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. Finally, some examples are shown.