Chapter 16 - Linear Filters

Abstract

The theory of linear filtering was a major concern of electrical engineers long before it became practical to use digital computers to process the rapid sequences that come from sampling continuous-time signals at high frequencies. This helps to explain why much of the theory of digital signal processing still makes reference to the theory of analogue filters. Digital filters fall into two classes which are known as the finite impulse-response (FIR) filters and the infinite impulse-response (IIR) filters. For linear filters, these classes correspond, respectively, to finite polynomial lag operators and rational lag operators. The effects of a linear filter upon the cyclical components which constitute a signal are twofold. First, the filtering is liable to alter the amplitude of any component. Second, the filter will translate the components along the time axis; and, for any component of a given frequency, there will be a corresponding displacement in terms of an alteration of the phase angle. Digital filters with a finite-duration impulse response have the advantage that they can achieve exactly linear phase effects.