The study of communication systems involves:
In this study, the representation of signals and systems features prominently. More specifically, the Fourier transform plays a key role in this representation.
The Fourier transform provides the mathematical link between the time-domain representation (i.e., waveform) of a signal and its frequency-domain description (i.e., spectrum). Most importantly, we can go back and forth between these two descriptions of the signal with no loss of information. Indeed, we may invoke a similar transformation in the representation of linear systems. In this latter case, the time-domain and frequency-domain descriptions of a linear time-invariant system are defined in terms of its impulse response and frequency response, respectively.
In light of this background, it is in order that we begin a mathematical study of communication systems by presenting a review of Fourier analysis. This review, in turn, paves the way for the formulation of simplified representations of band-pass signals and systems to which we resort in subsequent chapters. We begin the study by developing the transition ...