L1 error criterion based optimal FIR filters

Abstract

This paper presents an L1 optimization method for the design of Nth order finite impulse response (FIR), highpass (HP) and bandstop (BS) digital filters. For the calculation of optimal filter coefficients, L1 optimization criterion is adopted. It is seen that filters in L1 sense posses flat passband and stopband while retaining a transition band, which is comparable to existing filter design techniques. Simulation results affirm that the proposed L1 method outperforms over the existing filter design methods in terms of smaller passband and stopband ripples and sharp transitions.