Cosine-modulated 2 dimensional FIR filter banks satisfying perfect reconstruction

Considers the theory of cosine-modulated 2 dimensional (2-D) perfect reconstruction (PR) filter banks. First, a 2-D digital filter design with half passband, obtained by the sampling matrix, is discussed. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter. It is shown that the modulation in the 2-D frequency plane is equivalent to the 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 have a double-complement, the resulting 2-D filter bank satisfies the condition of perfect reconstruction