FIR Filter

FIR Filter — A nonrecursive digital filter whose output is a weighted sum of a finite number of current and previous input samples.

An FIR (Finite Impulse Response) filter computes each output from a finite weighted set of current and previous input samples:

y[n] = Σ(k=0..M) h[k] x[n-k]

With no recursive feedback path, stability is usually easier to reason about than in an IIR implementation.

Phase and Coefficient Symmetry

Appropriate symmetric or antisymmetric coefficients can provide linear phase, which is valuable when phase relationships in audio or other signals should be preserved.

Compute Cost

More taps can produce a sharper transition band but require more multiply-accumulate work per output sample. For very long filters, FFT-based convolution can become more efficient than direct convolution.

SIMD and multithreading may accelerate the computation, but memory bandwidth and block size still determine practical speedup.

FIR versus IIR

FIR is not automatically superior. An IIR filter can achieve similar selectivity at a lower order, while FIR may offer simpler stability and linear-phase properties. The choice depends on phase, latency, numerical and compute requirements.

Related: Convolution, Window Function, Resampling.