Lagrange multiplier approaches to the design of two-channel perfect-reconstruction linear-phase FIR filter banks

The authors present two approaches to the design of two-channel perfect-reconstruction linear-phase finite-impulse-response (FIR) filter banks. Both approaches analyze and design the impulse responses of the analysis filter bank directly. The synthesis filter bank is then obtained by simply changing the signs of odd-order coefficients in the analysis filter bank. The approach deals with unequal-length filter banks. By designing the lower length filters first, one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect-reconstruction constraint equations. The second approach generalizes the first, and covers the design for all parts of linear phase perfect reconstruction constraint equations