signalremez

signalremez refers to a family of design methods for creating finite impulse response FIR filters using the Remez exchange algorithm, commonly known as the Parks–McClellan method. This approach optimizes the filter so that its magnitude response closely matches a desired response across specified frequency bands, while minimizing the maximum error (Chebyshev criterion). It is particularly valued for producing linear-phase filters with sharp transition bands and controlled ripples in passbands and stopbands.

The input specification typically includes the filter order, the desired symmetry of the impulse response (even or odd), the frequency bands to be designed (defined in normalized frequency units, with 0 at DC and 1 at the Nyquist frequency), the desired amplitude in each band, and a weight function that prioritizes certain bands over others. The output is the set of filter coefficients that define the FIR impulse response, from which the frequency response can be computed.

Algorithmically, signalremez operates by iteratively selecting a set of extremal frequencies where the current error between the actual and desired response is largest. At each iteration, a linear system is solved to obtain the filter coefficients and the associated ripple amplitudes, and the set of extremal frequencies is updated. The process repeats until the error curve becomes nearly equiripple across all bands or a maximum number of iterations is reached.

Output characteristics include a linear-phase FIR filter whose frequency response approximates the target response with minimized maximum deviation. The design supports different symmetry types (commonly referred to as Type I–IV) to yield real-valued, symmetric or antisymmetric coefficients. In software libraries, Parks–McClellan designs are often exposed as a function named remez or signal.remez, with MATLAB offering a comparable function called firpm. The method is most effective for moderate filter lengths and well-specified band requirements.