Digital Signal Processing and Applications with the OMAP-L138 eXperimenter

Chapter 4

Infinite Impulse Response Filters

• Infinite impulse response (IIR) filter structures: direct form I, direct form II, cascade, and parallel
• Impulse invariant and bilinear transform methods of filter design
• Sinusoidal waveform generation using difference equations
• MATLAB filter design and analysis package
• Programming examples using C and ASM code

FIR filter discussed in Chapter 3 has no analog counterpart. In this chapter, we discuss the infinite impulse response filter that makes use of the vast knowledge already acquired with analog filters. The design procedure described in this chapter involves the conversion of an analog filter to an equivalent discrete filter. Either the impulse invariance or bilinear transformation (BLT) technique may be used. Both procedures convert the transfer function of an analog filter in the s-domain into an equivalent discrete-time transfer function in the z-domain.

4.1 INTRODUCTION

Consider a general input-output equation of the form

or, equivalently,

This recursive difference equation represents an IIR filter. The output y(n), at time n, depends not only on the current input x(n), at time n, and on past inputs x(n − 1), x(n − 2), …, x(n − M) but also on past outputs y(n − 1), y(n − 2), …, y(n − N).

If we assume all initial conditions ...