Fundamentals of Statistical Signal Processing, Volume III

Chapter 3. Mathematical Modeling of Signals

3.1. Introduction

As previously mentioned, we will only consider real continuous-time lowpass signals that have been sampled at the Nyquist rate. Bandpass and complex signals are described in Chapter 12. In this chapter typical signal models are discussed while in Chapter 4 we complete the mathematical modeling by describing noise models. It should be noted as illustrated in Figure 3.1, that “One man’s signal is another man’s noise”. Thus, what we designate as a signal could equally well be considered noise. For example, the Doppler-shifted sinusoid introduced in Chapter 2 was used to model a signal. But a sinusoid could also be used to represent noise, in particular, a 60 Hz interference. Hence, our ...