remezfirpm

remezfirpm is a function associated with the design of finite impulse response (FIR) filters using the Remez exchange algorithm, also known as the Parks–McClellan algorithm. It computes linear-phase FIR filters that best approximate a desired frequency response in the minimax sense by minimizing the maximum error across specified frequency bands.

Typically, remezfirpm takes as input the filter order (or length), a specification of frequency bands, the desired amplitude in each band, and a weight vector that emphasizes certain bands or transitions. The output is a coefficient vector that defines the filter’s impulse response. The method is capable of producing lowpass, highpass, bandpass, and bandstop filters depending on the band and target specifications. Frequencies are usually normalized to the Nyquist frequency, with 0 at DC and 1 at half the sampling rate.

Algorithmically, the Remez exchange process iteratively selects extremal frequencies where the approximation error is largest, then solves for filter coefficients that minimize the maximum error at those points. The result is an equiripple ripple-free error profile within the passbands and stopbands, subject to the symmetry constraints that yield linear-phase filters.

In practice, remezfirpm is available in MATLAB’s signal processing toolboxes as an interface to the Parks–McClellan design method; equivalents or wrappers exist under related names in other environments, such as firpm or remez. While powerful, the method requires careful specification of bands, weights, and order; ill-specified designs may fail to meet the intended tolerances or produce excessive ripple.