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Unformatted text preview: Chapter 2 Signals and Systems From Introduction to Communication Systems Copyright by Upamanyu Madhow, 2008-2011 A communication link involves several stages of signal manipulation: the transmitter transforms the message into a signal that can be sent over a communication channel; the channel distorts the signal and adds noise to it; and the receiver processes the noisy received signal to extract the message. Thus, communication systems design must be based on a sound understanding of signals, and the systems that shape them. In this chapter, we discuss concepts and terminology from signals and systems, with a focus on how we plan to apply them in our discussion of communication systems. Much of this chapter is a review of concepts with which the reader might already be familiar from prior exposure to signals and systems. However, special attention should be paid to the discussion of baseband and passband signals and systems (Sections 2.7 and 2.8): this material, which is crucial for our purpose, is typically not emphasized in a first course on signals and systems. Additional material on the geometric relationship between signals is covered in later chapters, when we discuss digital communication. Signal: A signal s ( t ) is a function of time (or some other independent variable, such as fre- quency, or spatial coordinates) which has an interesting physical interpretation. For example, it is generated by a transmitter, or processed by a receiver. While physically realizable signals such as those sent over a wire or over the air must take real values, we shall see that it is extremely useful (and physically meaningful) to consider a pair of real-valued signals, interpreted as the real and imaginary parts of a complex-valued signal. Thus, in general, we allow signals to take complex values. System: A system takes as input one or more signals, and produces as output one or more signals. We shall mainly be concerned with linear time invariant (LTI) systems, which provide good models for filters at the transmitter and receiver, as well as for the distortion induced by a variety of channels. Chapter plan: After a review of complex numbers and complex arithmetic in Section 2.1, we provide some examples of useful signals in Section 2.2. We then discuss LTI systems and convolu- tion in Section 2.3. This is followed by Fourier series (Section 2.4) and Fourier transform (Section 2.5). These sections (Sections 2.1 through Section 2.5) correspond to a review of material that is part of the assumed background for the core content of this textbook. However, even readers familiar with the material are encouraged to skim through it quickly in order to gain familiarity with the notation. This gets us to the point where we can classify signals and systems based 1 on the frequency band they occupy. Specifically, we discuss baseband and passband signals and systems in Sections 2.7 and 2.8. Messages are typically baseband, while signals sent over channels (especially radio channels) are typically passband. We discuss methods for going from baseband(especially radio channels) are typically passband....
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- Spring '11
- Fourier Series, UK, LTI system theory