Constrained eigenfilter design without specified transition bands

The design of the FIR filter with constraints in the frequency domain and/or the time domain is considered. We further consider the design specification without an explicitly specified transition band. A constrained eigenfilter is proposed to design the FIR filter with various design constraints, and without a transition band specification. We have suggest the possible design tradeoff between transition band bandwidth and the ripple size of the filter. The proposed algorithm can design filters with optimal tradeoff between transition band bandwidth and the peak constrained ripple size. The eigenfilter formulation further allows the filter design specification to incorporate time domain constraints. Various design examples are presented to illustrate the versatility of the digital filter obtained by the proposed filter design method.