Constrained eigenfilter design without specified transition bands

The design of a finite-impulse response (FIR) filter with constraints in the frequency domain and/or time domain is considered. We further consider the design specification without explicitly specified transition band bandedges. An iterative algorithm without transition band specification is proposed to design FIR filters with various design constraints. We suggest the possible design tradeoff between transition band bandwidth and the ripple size of the filter. The proposed algorithm can be used to design filters with an optimal tradeoff from the design specification. The eigenfilter formulation further allows the propose algorithm to incorporate time-domain constraints simultaneously. Various design examples are presented to illustrate the versatility of the digital filter obtained by the propose algorithm. Although we have not proven the convergence of the proposed algorithm, it is found to converge efficiently in all the simulations.