IIR Filtering: Introductionm10025IIR Filtering: Introduction2.222001/06/012009/06/03 15:27:22.963 GMT-5DouglasL.JonesDouglas L. Jonesdl-jones@uiuc.eduSwaroopAppadwedulaSwaroop Appadwedulaappadwed@uiuc.eduMatthewJ.BerryMatthew Berrymjberry@uiuc.eduMarkA.HaunMark Haunmarkhaun@uiuc.eduJakeJanevitzJake Janovetzjake@janovetz.comMichaelL.KramerMichael Kramerkramer@ifp.uiuc.eduDimaMoussaDima Moussadmoussa@uiuc.eduDanielGrobeSachsDaniel Sachssachs@uiuc.eduBrianWadeBrian Wadebwade@uiuc.eduDouglasL.JonesDouglas L. Jonesdl-jones@uiuc.eduSwaroopAppadwedulaSwaroop Appadwedulaappadwed@uiuc.eduMatthewJ.BerryMatthew Berrymjberry@uiuc.eduDanielGrobeSachsDaniel Sachssachs@uiuc.eduMarkD.ButalaMark Butalabutala@uiuc.eduRicardoAnthonyRadaelli-SanchezRicardo Radaelli-Sanchezricky@alumni.rice.eduRobertL.MorrisonRobert Morrisonrlmorris@uiuc.eduDouglasL.JonesDouglas L. Jonesdl-jones@uiuc.eduSwaroopAppadwedulaSwaroop Appadwedulaappadwed@uiuc.eduMatthewJ.BerryMatthew Berrymjberry@uiuc.eduMarkA.HaunMark Haunmarkhaun@uiuc.eduJakeJanevitzJake Janovetzjake@janovetz.comMichaelL.KramerMichael Kramerkramer@ifp.uiuc.eduDimaMoussaDima Moussadmoussa@uiuc.eduDanielGrobeSachsDaniel Sachssachs@uiuc.eduBrianWadeBrian Wadebwade@uiuc.edubi-quadblock repeat counterbutterconvdifference equationdirect form IIDSPellipelliptic low-pass filterfeedbackfreqzgain factorIIRimpulse responseinfinite impulse responselinear time-invariantLTInonlinear phasenotch filterpolesquantizezerosScience and TechnologyInfinite 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.enIntroduction
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
wn.