Signal and Linear System Analysis

Author: Chief Editor: Zhu Zhonglin
Publisher:
Publishing Date: 2003-01-01
Features: Introduction This book is a revised edition of the trial teaching material "Signal and Linear System Analysis" published in 1982. The content of the book includes: Introduction, time-domain analysis and transform-domain (frequency domain and complex frequency domain) analysis of continuous-time signals and systems, system function and system characteristics, time-domain analysis and transform-domain (frequency domain and z-domain) analysis of discrete-time signals and systems, state-space analysis, and ten chapters. The book retains the system and features of the trial teaching material while integrating the teaching experience of the past decade, with updates to the content of each chapter. For the convenience of students, each chapter is accompanied by review questions and exercises, and answers to the exercises are provided at the end of the book. This book can be used as a textbook for undergraduate students in communication, control, information, and computer-related fields in universities, and can also serve as a reference for a wide range of science and technology professionals engaged in circuit design, communication engineering, control engineering, information engineering, and computer-related fields for self-study. Excerpt:
IV. Energy Signals and Power Signals According to the integrability of time functions, signals can be divided into energy signals and power signals. As we know, a signal can be regarded as a voltage or current that varies with time. Thus, if a signal \( f(t) \) passes through a 1-ohm resistor, the energy consumed by the signal within the time interval \(-T \leq t \leq T\) is called normalized energy, denoted as \( W \), and is given by Similarly, the average power of the signal within the above time interval is called normalized power, denoted as \( P \), and is given by For a given signal, if its normalized energy is finite and its normalized power is zero, i.e., \( 0 < W < \infty \) and \( P = 0 \), then the signal is called an energy signal; if the normalized power of the signal is finite and its normalized energy tends to infinity, i.e., \( 0 < P < \infty \) and \( W \to \infty \), then the signal is called a power signal. For example, the signal shown in Figure 1-2(b) is an energy signal; DC signals and periodic signals are power signals. Some signals are neither energy signals nor power signals, but it is impossible for a signal to be both an energy signal and a power signal. The above definitions also apply to discrete-time signals, where the normalized energy and normalized power of a signal are defined as follows. Let's illustrate this with examples.
[Example 1-1] Determine whether the following signals are energy signals or power signals.
[Solution] According to formulas (1-5) and (1-6), the normalized energy and power of the three signals are calculated as follows.
It can be seen that \( f_1(t) \) is an energy signal, \( f_2(t) \) is a power signal, and \( f_3(t) \) is neither an energy signal nor a power signal.
In summary, as the form and carrier of messages, signals generally manifest as voltages or currents that vary with time in the field of electronic technology and possess their inherent characteristics. What is called signal analysis primarily involves studying the methods of describing various signals and the basic characteristics of signals passing through devices. This forms the foundation for modern techniques such as filtering, sampling, detection, estimation, feature extraction, and waveform design. The following chapters of this book will delve into the basic concepts and methods of signal analysis in a step-by-step manner.
Review Questions 1. Explain the differences and connections between messages, information, and signals.
2. In signal analysis, how are signals classified? Explain the essential differences between each type of signal.
3. List several practical signals and indicate which type they belong to.