Lab 3: theory

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 frequencyresponses. Compared to FIR filters, IIR filters have both advantages and disadvantages. On one hand, implementing anIIR filter with certain stopband-attenuation and transition-band requirements typically requires far fewerfilter taps than an FIR filter meeting the same specifications. This leads to a significant reduction in thecomputational complexity required to achieve a given frequency response. However, the poles in the transfer function requirefeedback to implement an IIR system. In addition to inducing nonlinear phase in the filter (delaying different frequencyinput signals by different amounts), the feedback introduces complications in implementing IIR filters on a fixed-pointprocessor. 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 implementingand examining a fourth-order IIR system on a fixed-point DSP. The IIR filter should be implemented as a cascade of twosecond-order, Direct Form II sections. The data flow for a second-order, Direct-Form II section, or bi-quad , is shown in [link] . Note that in Direct Form II, the states (delayed samples) are neither the input nor theoutput samples, but are instead the intermediate values $w(n)$ .