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IIR Filtering

Module by: Ricardo Radaelli-Sanchez, Douglas L. Jones. E-mail the authors

Summary: In this module, we will explore infinite impulse response, or IIR, filters.

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Introduction

Like FIR filters, IIR filters are LTI (linear time-invariant) systems that can be used to 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 the corresponding FIR filter. This leadings to a significant reduction in the computational complexity required to achieve a given frequency response. However, the poles in the transfer function require that feedback be used to implement an IIR system. In addition to inducing nonlinear phase in the filter (delaying different frequency input signals by different amounts), the feedback can lead to complications implementing IIR filters on a fixed-point processor.

In this lab, you will explore the advantages and disadvantages of IIR filters by implementing and examining a fourth-order IIR system on the TI C54x fixed-point DSP. The IIR filter should be implemented the cascade of two second-order direct-form II sections. The data flow for a direct-form II second-order, or bi-quad, section is shown below. 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 .

Figure 1: Direct Form II second-order section
Figure 1 (iir_DFIInew.png)

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