Design and implementation of cosine-modulated 2 dimensional perfect reconstruction FIR filter banks

It is well known that FIR filter banks, satisfying the perfect reconstruction (PR) property, can be obtained by cosine modulation of linear-phase prototype FIR digital filter. In this paper, I show to be able to design 2-Dimensional (2-D) PR filter banks using cosine modulation as same as 1-D case. At first, I design a 2-D digital filter with half passband obtained by the sampling matrix. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter. It is shown that the modulation in 2-D frequency plane is equivalent to the 1-D modulation. An necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. Furthermore I formulate the design method as a quadratic-constrained least-square minimization problem.