Two Novel Implementations of the Remez Multiple Exchange Algorithm for Optimum FIR Filter Design

One of the main advantages of the linear-phase FIR filters over their IIR counterparts is the fact that there exist efficient algorithms for optimizing the arbitrary-magnitude FIR filters in the minimax sense. In case of IIR filters, the design of arbitrary-magnitude filters is usually time-consuming and the convergence to the optimum solution is not always guaranteed. The most efficient method for designing optimum magnitude linear-phase FIR filters with arbitrary-magnitude specifications is the Remez algorithm and the most frequent method to implement this algorithm is the one originally proposed by Parks and McClellan. Initially, they came upwith the design of conventional low-pass linear phase FIR filters, whose impulse response is symmetric and the order is even [5]. Later on, along with Rabiner they extended the original design technique in [7] such that the generalized algorithm is applicable to the design of all the four linear-phase FIR filter types with arbitrary specifications. Due to the initial work of Parks and McClellan for the extended algorithm, this algorithm is famously known as the Parks-McClellan (PM) algorithm.