A Simple Approach to Digital Signal Processing

4

Filtering

In this chapter we look at filtering, first through a brief review of analog filters, followed by a description of how we can perform the same functions in the digital domain. We shall also cover some of the software tools available that help us to design digital filters.

WHAT IS FILTERING?

We know from basic electronic theory that capacitors and inductors have impedances (X) that depend on frequency, as defined below:

where

and

When either component is combined with a resistor we can build frequency-dependent voltage dividers. For example, let's look at a circuit containing a resistor and a capacitor as shown in Figure 4.1. If we now apply Ohm's law to this circuit we can see that:

FIGURE 4.1. An analog filter with a capacitor and resistor (CR)

so that:

Also

so solving for ...