Finite number of necessary and sufficient discrete condition in frequency domain for maximally decimated M-channel mirrored paraunitary linear phase FIR filter bank

The conventional necessary and sufficient condition defined in the frequency domain for maximally decimated M-channel mirrored paraunitary linear phase FIR filter banks consists of a finite number of quadratic functional equations. As a functional equation consists of an infinite number of discrete equations, the conventional condition consists of an infinite number of discrete quadratic equations. This results in a very difficult situation for the design of these filter banks. To address this difficulty, this paper derives a finite number of necessary and sufficient discrete quadratic equations defined in the frequency domain for maximally decimated M-channel mirrored paraunitary linear phase FIR filter banks. These conditions facilitate the design.