OVERVIEW

Electrical engineers instinctively think of signals in terms of their frequency spectra and think of systems in terms of their frequency response. Even teenagers know about audible portion of audio signals having a bandwidth of about 20 kHz and the need for good-quality speakers to respond up to 20 kHz. This is basically thinking in frequency domain. In Chapters 4 and 5 we discussed extensively the frequency-domain representation of systems and their spectral response (system response to signals of various frequencies). In Chapters 6, 7, 8, and 9 we discuss spectral representation of signals, where signals are expressed as a sum of sinusoids or exponentials. Actually, we touched on this topic in Chapters 4 and 5. Recall that the Laplace transform of a continuous-time signal is its spectral representation in terms of exponentials (or sinusoids) of complex frequencies. Similarly the z-transform of a discrete-time signal is its spectral representation in terms of discrete-time exponentials. However, in the earlier chapters we were concerned mainly with system representation, and the spectral representation of signals was incidental to the system analysis. Spectral analysis of signals is an important topic in its own right, and now we turn to this subject.

In this chapter we show that a periodic signal can be represented as a sum of sinusoids (or exponentials) of various frequencies. These results are extended to aperiodic signals in Chapter 7 and to discrete-time signals in Chapter 9. The fascinating subject of sampling of continuous-time signals is discussed in Chapter...