How it works
FIR filter design using the window method starts from the ideal impulse response h_d[n] = sin(ωc·n)/(πn), which is infinite and non-causal. Multiplying by a finite window like Hamming (N = 51 taps, sidelobe attenuation of −43 dB) truncates and shifts the response to be causal. Kaiser window gives the best control: adjustable parameter β trades transition bandwidth for stopband attenuation. The frequency-sampling method places exact zeros of the desired response at N equally-spaced frequencies, then computes coefficients via IDFT — useful when the frequency response is specified at discrete points.
Key points to remember
FIR filters are always stable because they have no feedback — all poles sit at the origin. Linear phase is guaranteed when h[k] = h[N-1-k] (symmetric) or h[k] = −h[N-1-k] (anti-symmetric). Rectangular window gives the sharpest transition but −13 dB sidelobes and Gibbs ripple; Hanning gives −44 dB; Blackman gives −74 dB. More taps mean better frequency selectivity but higher computation: a 64-tap filter running at 8 kHz sample rate needs 64 multiply-accumulate operations every 125 µs. FIR filters cannot achieve the sharp roll-off of a Chebyshev IIR filter with the same number of taps.
Exam tip
Anna University DSP papers almost always ask you to design a low-pass FIR filter using the Hamming window — know the window coefficients formula w[n] = 0.54 − 0.46·cos(2πn/(N−1)) and the cutoff frequency relationship ωc = 2πfc/fs by heart.