CH-1-Signals

# CH-1-Signals - book 1:44 page 1#1 C H A P T 1 E R Signals...

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“book” — 2012/2/17 — 1:44 — page 1 — #1 C H A P T E R 1 Signals Contents Overview, 2 1-1 Types of Signals, 3 1-2 Signal Transformations, 6 1-3 Waveform Properties, 9 1-4 Nonperiodic Waveforms, 11 1-5 Signal Power and Energy, 21 Chapter 1 Summary, 24 Problems, 25 Objectives Learn to: Perform transformations on signals. Use step, ramp, pulse, and exponential waveforms to model simple signals. Model impulse functions. Calculate power and energy contents of signals. Signals come in many forms: continuous, discrete, analog, digital, periodic, nonperiodic, with even or odd symmetry or no symmetry at all, and so on. Signals with special waveforms include ramps, exponentials, and impulses. This chapter introduces the vocabulary, the properties, and the transformations commonly associated with signals in preparation for exploring in future chapters how signals interact with systems .

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“book” — 2012/2/17 — 1:44 — page 2 — #2 2 CHAPTER 1 SIGNALS Overview This book is about how signals interact with systems. More precisely, it is about how a system transforms input signals ( excitations ) into output signals ( responses ) to perform a certain operation (or multiple operations). A system may be as simple as the voltage divider in Fig. 1-1, wherein the divider scales down input voltage υ i to output voltage υ o = [ R 2 /(R 1 + R 2 ) ] υ i , or as complex as a human body (Fig. 1-2). Actually, the human body is a system of systems ; it includes the respiratory, blood circulation, and nervous systems, among many others. Each can be modeled as a system with one or more input signals and one or more output signals. When a person’s fingertip touches a hot object (Fig. 1-3), a nerve ending in the finger senses the elevated temperature and sends a message (input signal) to the central nervous Circulatory system Nervous system Muscular/skeletal system Excretory system Reproductive system Respiratory system Digestive system Immune system Endocrine system Figure 1-2: The human body is a system of systems. R 1 R 2 + _ + _ υ o υ i Figure 1-1: A voltage divider is a simple system. system (CNS), consisting of the brain and spinal cord. Upon processing the input signal, the CNS (the system) generates severaloutputsignalsdirectedtovariousmusclesintheperson’s hand, ordering them to remove the finger away from the hot object.
“book” — 2012/2/17 — 1:44 — page 3 — #3 1-1 TYPES OF SIGNALS 3 Figure 1-3: Finger-CNS-muscle communication. By modeling signals and systems mathematically, we can use the system model to predict the output resulting from a specified input. We can also design systems to perform operations of interest. A few illustrative examples are depicted in Fig. 1-4. Signals and systems are either continuous or discrete. Both types are treated in this book, along with numerous examples of practical applications.

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