# Digital Signal Processing/Infinite Input Filtering

Filtering a data input that is infinite in length can be a tricky task for any computer to manage, and DSP engineers have identified two techniques for breaking down an infinite input into manageable chunks for filtering.

## "Infinite Input"

infinite input response (IIR) filters are structures that use a feedback element to help filter data. An IIR filter has a transfer function of the form:

${\displaystyle G(z)={\frac {\prod (a_{n}-z^{-1})}{\prod (b_{m}-z^{-1})}}}$

The constants an are known as the zeros of the transfer function, and the bm terms are known as the poles of the transfer function. FIR filters, by comparison do not have poles.

IIR filters are named as such because the filter does not stop responding once the input has stopped, but instead the feedback element will continue to input values into the filter structure for processing after the input has stopped.

## IIR vs FIR Filters

FIR IIR
Stability Always BIBO Stable May not be stable
Efficiency Not efficient Very Efficient
Phase May have linear phase phase not linear

An FIR filter will have an order that is a significantly higher than the order of an equivalent IIR filter. This means that FIR filters need more complexity and more components then IIR filters to complete the same task. However, IIR filters have a potential for instability, which requires more analysis.