Design of FIR Digital Filters Without Transition-Band Fluctuations

This paper presents a new method for the design of finite-impulse-response (FIR) digital filters without transition-band fluctuations. We derive a fluctuation-free condition from gradient constraints on the magnitude of transition-band re-sponses. Incorporating the condition, we formulate a new peak-constrained least-squares (PCLS) design of FIR filters as an iterative quadratic programming (QP) problem. Each iteration of the algorithm uses a multiple-exchange technique for giving a QP problem with a small number of constraints. The new algorithm obtains PCLS filters free from transition-band fluctuations efficiently. Design examples are included to illustrate the proposed algorithm. 1