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:

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

The constants a_n are known as the zeros of the transfer function, and the b_m 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.