Theory of cosine‐modulated two‐dimensional perfect reconstruction filter banks

This paper considers a cosine‐modulated, two‐dimensional (2‐D) perfect reconstruction (PR) filter banks theory. First, a 2‐D digital filter with half‐pass‐band obtained by the sampling matrix had to be designed. Next, 2‐D analysis filter banks are realized by cosine‐modulating this prototype 2‐D digital filter so that 2‐D analyzed signals become real. It is shown that the modulation in the 2‐D frequency plane is equivalent to 1‐D modulation. A necessary and sufficient condition for 2‐D perfect reconstruction filter banks is derived. If the polyphase filter pairs of the prototype filter doubly complement, the resulting 2‐D filter bank satisfies the condition of perfect reconstruction.