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2. Fundamental Concepts in Signals & Systems 2.1 Introduction to the Chapter
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | In this chapter, we provide a concise summary of the fundamentals of signals and systems. We deal with both continuous and discrete linear time-invariant {LTI} systems. The basic definitions and the various mathematical tools are discussed. Issues such as infinite impulse response and delayed response are dealt with from an engineering perspective. A broad overview of LTI signal processing and control is also provided. Finally, the similarities and the differences between these two application domains are listed. We have tried to provide the very basic concepts in two different topics, signals & systems and controls that normally appear in at least two textbooks in a single chapter, and hence have to limit the scope of the presentation. The objective here is to discuss in general terms the reasons behind the widespread use of LTI models in signal processing and control, and the limitations that arise due to the use of such models. Further, we will use the line of thought and reasoning used here to introduce nonlinear dynamics. Though most of the readers will be familiar with most of the concepts provided, they will find the emphasis on "Engineering Concepts" new and worth reading 2.2 Representation of Signals Signals: A signal is an entity that carries information. Mathematically, it is represented as a dependent function of some independent variable. For example, a monaural audio system produces an acoustic signal (music) that changes as a function of time (independent variable). Thus, music signal, m(t), is an example of a one-dimensional (1D) signal. Similarly, a B/W TV receiver shows an image whose value (intensity) depends on the position on the screen (x, y coordinates) and time t. This signal is thus an example of a three-dimensional (3D) signal. We will consider only 1D signals in this book unless stated otherwise explicitly. x a (t) is called continuous or analog if its amplitude (which can theoretically be anything) is defined for all values of the independent variable t. A signal x dt (nT) (n integer and T some constant) is known as discrete if its amplitude can be anything but the signal is defined at only discrete instances of the independent variable. A signal x dl (nT) is known as digital if it is defined only at discrete instances of the independent variable and its amplitude is constrained to take one of Q pre-defined values (quantization levels). The difference in amplitude between two … |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ece.uc.edu/~pramamoo/CourseWork/BookNonLinearAndAdaptiveSysPDFfiles/Chapter2_SV_NoSec&Head_2c.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
