THEORY OF COSINE-MODULATED 2-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-passband 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 ID 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.