Digital Signal Processing and Applications with the OMAP-L138 eXperimenter

Chapter 3

Finite Impulse Response Filters

• Introduction to digital filters
• The z-transform
• Design and implementation of finite impulse response (FIR) filters
• Programming examples using C and ASM code

3.1 INTRODUCTION TO DIGITAL FILTERS

Filtering is fundamental to digital signal processing. Commonly it refers to processing a sequence of samples representing a time domain signal so as to alter its frequency domain characteristics, and often this consists of attenuating or filtering out selected frequency components. Digital filters are classified according to their structure as nonrecursive FIR filters or as recursive infinite impulse response (IIR) filters. This chapter is concerned with FIR filters. IIR filters are described in Chapter 4.

3.1.1 FIR Filter

A generic FIR filter is shown in block diagram form in Figure 3.1. The components of the filter are:

• (i) A delay line, or buffer, in which a number of previous input samples x(n – i) are stored. At each sampling instant, the contents of the delay line are updated such that samples are shifted one position (to the right in the diagram) and a new input sample x(n) is introduced at the start of the delay line.
• (ii) A number of blocks (multipliers) that multiply the samples stored in the delay line by a set of filter coefficients h(n).
• (iii) A summing junction that sums the multiplier outputs to form the current filter output sample y(n).

Figure 3.1 Block diagram representation of a generic FIR filter.

In Figure 3.1, the delay ...