Signals and systems Oppenheim Solutions chapter 1.2

You can find in that post the solution of the first chapter questions between 10 and 20.

The book is begin chapter 1 by introducing some of the elementary ideas related to the mathematical representation of signals and systems. In particular we discuss transformations (such as time shifts and scaling) of the independent variable of the signal. We also introduce some of the most important and basic continuous-time and discrete-time signals, namely real and complex exponentials and the continuous-time and discrete-time unit step and unit impulse.

Chapter 1 also introduces block diagram representation of interconnections of systems and discusses several basic system properties such as causality, linearity and time-invariance.

CONTINUOUS-TIME AND DISCRETE-TIME SIGNALS


Signals may describe a wide variety of physical phenomena. Although signals can be represented in many ways, in all cases the information in a signal is contained in a pattern of variations of some form.


Signals are represented mathematically as functions of one or more independent variables. For example, a speech signal can be represented mathematically by acoustic pressure as a function of time, and a picture can be represented by brightness as a function of two spatial variables. In this book, we focus our attention on signals involving a single independent variable. For convenience. we will generally refer to the independent variable as time, although it may not in fact represent time in specific applications. For example, in geophysics, signals representing variations with depth of physical quantities such as density, porosity, and electrical resistivity are used to study the structure of the earth. Also, knowledge of the variations of air pressure, temperature. and wind speed with altitude are extremely important in meteorological investigations.