Digital Filters

• FIR (finite impulse response): $y[n] = \sum_{k=0}^{M} b_k\, x[n-k]$. Always stable, can have exactly linear phase; needs more taps.
• IIR (infinite impulse response): uses feedback from past outputs. Very efficient, but can be unstable and has non-linear phase.

The simplest useful filter is the moving average (FIR) or the exponential moving average (IIR), widely used to smooth sensor readings:

filtered = filtered + alpha * (sample - filtered);   // 0 < alpha <= 1

Design tools: scipy.signal, MATLAB, or the bilinear transform from analog prototypes.