# Connexions

You are here: Home » Content » IIR Filtering: Introduction

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

# IIR Filtering: Introduction

Summary: Infinite impulse response (IIR) filters are an alternative to finite impulse response (FIR) filters. Often, an IIR implementaion can meet a given filter specification with less computation than an FIR implementation, but IIR filters induce nonlinear phase and are more sensitive to numerical problems.

Note: You are viewing an old version of this document. The latest version is available here.

## Introduction

Like finite impulse-response (FIR) filters, infinite impulse-response (IIR) filters are linear time-invariant (LTI) systems that can recreate a large range of different frequency responses. Compared to FIR filters, IIR filters have both advantages and disadvantages. On one hand, implementing an IIR filter with certain stopband-attenuation and transition-band requirements typically requires far fewer filter taps than an FIR filter meeting the same specifications. This leads to a significant reduction in the computational complexity required to achieve a given frequency response. However, the poles in the transfer function require feedback to implement an IIR system. In addition to inducing nonlinear phase in the filter (delaying different frequency input signals by different amounts), the feedback introduces complications in implementing IIR filters on a fixed-point processor. Some of these complications are explored in IIR Filtering: Filter-Coefficient Quanitization Exercise in MATLAB.

Later, in the processor exercise, you will explore the advantages and disadvantages of IIR filters by implementing and examining a fourth-order IIR system on a fixed-point DSP. The IIR filter should be implemented as a cascade of two second-order, Direct Form II sections. The data flow for a second-order, Direct-Form II section, or bi-quad, is shown in Figure 1. Note that in Direct Form II, the states (delayed samples) are neither the input nor the output samples, but are instead the intermediate values wn w n .

## Content actions

### Give feedback:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks