The filtering of digitized data, if not the most fundamental, is certainly the oldest discipline in the field of digital signal processing. Digital filtering's origins go back 50 years. The growing availability of digital computers in the early 1950s led to efforts in the smoothing of discrete sampled data and the analysis of discrete data control systems. However it wasn't until the early to mid-1960s, around the time the Beatles came to America, that the analysis and development of digital equivalents of analog filters began in earnest. That's when digital signal processing experts realized that computers could go beyond the mere analysis of digitized signals into the domain of actually changing signal characteristics through filtering. Today, digital filtering is so widespread that the quantity of literature pertaining to it exceeds that of any other topic in digital signal processing. In this chapter, we introduce the fundamental attributes of digital filters, learn how to quantify their performance, and review the principles associated with the design of finite impulse response digital filters.
So let's get started by illustrating the concept of filtering a time-domain signal as shown in Figure 5-1.
Figure 5-1. Filters: (a) an analog filter with a noisy tone input and a reduced-noise tone output; (b) the digital equivalent of the analog filter.
In general, filtering is the processing of a time-domain signal resulting in some change in that signal's original spectral content. The change is usually the reduction, or filtering out, of some unwanted input spectral components; that is, filters allow certain frequencies to pass while attenuating other frequencies. Figure 5-1 shows both analog and digital versions of a filtering process. Where an analog filter operates on a continuous signal, a digital filter processes a sequence of discrete sample values. The digital filter in Figure 5-1(b), of course, can be a software program in a computer, a programmable hardware processor, or a dedicated integrated circuit. Traditional linear digital filters typically come in two flavors: finite impulse response (FIR) filters and infinite impulse response (IIR) filters. Because FIR filters are the simplest type of digital filter to analyze, we'll examine them in this chapter and cover IIR filters in Chapter 6.