Introduction to IIR and FIR Filters

Fir: Finite Impact Response filter. The input disappears and the output disappears.
IIR: Infinite Impact Response filter. Input disappears and output does not disappear.

The common point is that the output of the FIR difference equation has nothing to do with the previous output; the output of the IIR difference equation is related to the previous output, that is, the difference equation is progressive.

In terms of performance The pole of the filter transfer function can be located anywhere in the unit circle. Therefore, it can obtain high selectivity with a lower order and has fewer storage units, so it is economical and efficient. However, this efficiency is at the cost of non-linear phase. The better the selectivity, the more serious the phase nonlinear. On the contrary, fir The filter can obtain a strict linear phase. The pole of the filter transfer function is fixed at the origin, so it can only achieve high selectivity with a higher order. For the same filter design index, the fir The Order required by the filter can be greater than that of the IIR filter. 5 ~ high filter height ~ 10 As a result, the cost is high, and the signal delay is also large. If the same selectivity and linear requirements are applied The filter must be added to the full-pass network for phase correction, and the number and complexity of the filter must also be greatly increased.

In terms of structure The filter must adopt a recursive structure, and the pole position must be within the Unit Circle. Otherwise, the system will be unstable. In addition, in this structure, due to the rounding processing of the sequence during the operation, this finite-character length effect sometimes introduces parasitic oscillation. On the contrary, fir Filters mainly adopt non-recursive structures. No stability problem exists in theoretically or practically limited precision operations, and the operation error is small. In addition, fir The filter can adopt the fast paybyte transform algorithm, and the computation speed can be much faster under the condition of the same order.