Design and Properties of Two-channel Fir Filter Banks Optimized by Using Peak-constrained Least Squares Optimization Criterion

This paper considers the design and properties of two-channel alias-free finite-impulse response (FIR) filter banks where the analysis filters are optimized by using the peak-constrained least squares (PCLS) optimization criterion. All the alias-free twochannel filter banks proposed in the literature are under consideration. For the proposed PCLS designs, the maximum of the stopband energies of the two analysis filters is minimized subject to the given peak (minimum) stopband attenuation, the given passband and transition band constraints, and the given allowable reconstruction error. Therefore, in addition to the perfectreconstruction filter banks, nearly perfect-reconstruction banks can be optimized in a controlled manner. It is shown, by means of several examples, that PCLS designs provide tradeoff solutions between the extreme designs where the stopbands of the analysis filters are optimized in the minimax or the least squares (LS) senses. The use of such tradeoff solutions is beneficial in some applications. For designing PCLS filter banks, an appropriate constrained optimization problem is stated and is solved by slightly modifying the efficient algorithm proposed earlier by the authors of this paper for designing two-channel filter banks in the LS sense.