Algorithms for Communications Systems and their Applications, 2nd Edition

Chapter 1Elements of signal theory

In this chapter, we recall some concepts on signal theory and random processes. For an in‐depth study, we recommend the companion book [1]. First, we introduce various forms of the Fourier transform. Next, we provide the complex representation of passband signals and their baseband equivalent. We will conclude with the study of random processes, with emphasis on the statistical estimation of first‐ and second‐order ergodic processes, i.e. periodogram, correlogram, auto‐regressive (AR), moving‐average (MA), and auto‐regressive moving average (ARMA) models.

1.1 Continuous‐time linear systems

A time‐invariant continuous‐time continuous‐amplitude linear system, also called analog filter, is represented in Figure 1.1, where and are the input and output signals, respectively, and denotes the filter impulse response.

Figure 1.1 Analog filter as a time‐invariant linear system with continuous domain.

The output at a certain instant , where denotes ...