Multicore DSP

16IIR filter implementation

CHAPTER MENU

1. 16.1 Introduction
2. 16.2 Design procedure
3. 16.3 Coefficients calculation
   1. 16.3.1 Pole–zero placement approach
   2. 16.3.2 Analogue‐to‐digital filter design
   3. 16.3.3 Bilinear transform (BZT) method
      1. 16.3.3.1 Practical example of the bilinear transform method
      2. 16.3.3.2 Coefficients calculation
      3. 16.3.3.3 Realisation structures
   4. 16.3.4 Impulse invariant method
      1. 16.3.4.1 Practical example of the impulse invariant method
4. 16.4 IIR filter implementation
5. 16.5 Laboratory experiment
6. 16.6 Conclusion
7. Reference

16.1 Introduction

Infinite impulse response (IIR) filters are the first choice when speed is paramount and the phase non‐linearity characteristic is acceptable. IIR filters are computationally more efficient than finite impulse response (FIR) filters since they require fewer coefficients due to the fact that they use feedback or poles. However, this feedback can result in the filter being unstable if the coefficients deviate from their true values. This can happen during coefficient scaling or quantisation. In this chapter, it will be shown that the design and implementation of IIR filters are different than those for FIR filters.

The general equations of an IIR filter can be expressed as follows:

where a_k and b_k are the filter coefficients.

This transfer function can be factorised to give

where:

• are the zeros.
• are the poles.

In terms of ...