An \(L_1\)-Method: Application to Digital Symmetric Type-II FIR Filter Design

In this paper, the design of digital symmetric type-II linear-phase FIR low-pass (LP) and band-pass (BP) filter is formulated using the \(L_1\) optimality criterion. In order to obtain better filter performance we compute the optimal filter coefficients using the \(L_1\)-norm based fitness function. The use of \(L_1\) technique in digital filter design applications has the advantages of a flatter passband and high stopband attenuation over other gradient-based filter optimization methods. This technique is applied to optimally design type-II FIR filters. Simulations and statistical analysis have been performed for the 25th order LP and BP filters. It is observed, that the \(L_1\)-based filter results is an improved design in comparison with the filters obtained using the equiripple, least-square and window techniques.

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