FIR filter

An FIR filter builds each output sample as a weighted average of the most recent few input samples — and nothing else. Picture a sliding window of, say, 64 recent readings, each multiplied by a fixed coefficient (a 'tap') and summed: that running, tilted average is the filtered output. Because it never feeds its own output back in, its memory of any single input pulse is finite — hit it with one spike and after the window passes, the output returns to silence. Hence 'finite impulse response.'

The headline virtue is exact linear phase: an FIR with symmetric coefficients delays every frequency by the same amount, so the waveform's shape is preserved and never smeared — vital for audio, image, and data communications where phase distortion would garble the signal. The cost is order: to get a steep, selective cutoff you may need hundreds or thousands of taps, far more multiply-accumulate operations than an IIR filter doing a similar job.