digital filter design

Digital filter design is the craft of choosing the coefficients of an FIR or IIR filter so that it lets some frequencies through and blocks others, matching a specification you draw as a target shape: how flat the passband, how deep the stopband, how steep the transition, how much phase distortion is allowed. It is goal-driven engineering — you sketch the wall you want sound or data to hit, then a method computes the numbers that build it.

Several well-worn recipes exist. The window method takes the ideal 'brick-wall' filter, which would need infinitely many taps, and truncates it with a smooth window for a workable FIR. The Parks–McClellan (Remez) algorithm produces the optimal equiripple FIR for a given length. For IIR, designers often start from a known analog prototype (Butterworth, Chebyshev) and warp it into the digital domain with the bilinear transform. Each choice trades sharpness, ripple, delay, and computational cost.