FIR,IIR

Finite impulse response, or FIR, filters express each output sample as a weighted sum of the last N inputs, where N is the order of the filter. Since they do not use feedback, they are inherently stable. If the coefficients are symmetrical (the usual case), then such a filter is linear phase, so it delays signals of all frequencies equally. This is important in many applications. It is also straightforward to avoid overflow in an FIR filter. The main disadvantage is that they may require significantly more processing and memory resources than cleverly designed IIR variants. FIR filters are generally easier to design than IIR filters - the Remez exchange algorithm is one suitable method for designing quite good filters semi-automatically. (See Methodology.)

Infinite impulse response, or IIR, filters are the digital counterpart to analog filters. Such a filter contains internal state, and the output and the next internal state are determined by a linear combination of the previous inputs and outputs (in other words, they use feedback, which FIR filters normally do not). In theory, the impulse response of such a filter never dies out completely, hence the name IIR, though in practice, this is not true given the finite resolution of computer arithmetic. IIR filters normally require less computing resources than an FIR filter of similar performance. However, due to the feedback, high order IIR filters may have problems with instability, arithmetic overflow, and limit cycles, and require careful design to avoid such pitfalls. Additionally, since the phase shift is inherently a non-linear function of frequency, the time delay through such a filter is frequency-dependent, which can be a problem in many situations. 2nd order IIR filters are often called 'biquads' and a common implementation of higher order filters is to cascade biquads. A useful reference for computing biquad coefficients is the RBJ Audio EQ Cookbook.

p