IIR Filtering: Introduction 2.20 2001/06/01 2003/07/31 10:51:01.871 GMT-5 Swaroop Appadwedula appadwed@uiuc.edu Douglas L. Jones dl-jones@uiuc.edu Michael L. Kramer kramer@ifp.uiuc.edu Dima Moussa dmoussa@uiuc.edu Brian Wade bwade@uiuc.edu Jake Janevitz jake@janevitz.com Daniel Grobe Sachs sachs@uiuc.edu Matthew J. Berry mjberry@uiuc.edu Mark A. Haun markhaun@uiuc.edu Swaroop Appadwedula appadwed@uiuc.edu Douglas L. Jones dl-jones@uiuc.edu Daniel Grobe Sachs sachs@uiuc.edu Matthew J. Berry mjberry@uiuc.edu Mark D. Butala butala@uiuc.edu Ricardo Anthony Radaelli-Sanchez ricky@alumni.rice.edu Robert L. Morrison rlmorris@uiuc.edu difference equation infinite impulse response IIR LTI linear time-invariant direct form II zeros poles gain factor freqz impulse response notch filter butter quantize conv elliptic low-pass filter ellip block repeat counter feedback bi-quad nonlinear phase DSP 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.

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 . Note that in Direct Form II, the states (delayed samples) are neither the input nor the output samples, but are instead the intermediate values w n .

Second-order, Direct Form II section