In digital signal processing, filters are commonly categorized as: 1. FIR (Finite Impulse Response) Filters: The output depends only on current and past input values. Impulse response settles to zero in a finite amount of time. Always stable and can have linear phase (no phase distortion). Easier to design for precise control of frequency response. Require more memory and processing power for sharp filtering. Example: 𝑦 [ 𝑛 ] = 𝑏 0 𝑥 [ 𝑛 ] + 𝑏 1 𝑥 [ 𝑛 − 1 ] + ⋯ + 𝑏 𝑁 𝑥 [ 𝑛 − 𝑁 ] y[n]=b 0 ​ x[n]+b 1 ​ x[n−1]+⋯+b N ​ x[n−N] 2. IIR (Infinite Impulse Response) Filters: The output depends on current and past input values AND past output values. Impulse response theoretically continues forever. More computationally efficient than FIR for similar performance. Can become unstable if not carefully designed. Typically have non-linear phase. Example: 𝑦 [ 𝑛 ] = 𝑏 0 𝑥 [ 𝑛 ] + 𝑏 1 𝑥 [ 𝑛 − 1 ] + ⋯ + 𝑎 1 𝑦 [ 𝑛 − 1 ] + 𝑎 2 𝑦 [ 𝑛 − 2 ] + … y[n]=b 0 ​ x[n]+b 1 ​ x[n−1]+⋯+a 1 ​ y[n−1]+a 2 ​ y[n−2]+…