# 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 ...