113_1_chapter01

113_1_chapter01 - Chapter 1 MOTIVATION Copyright c 1996 by...

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Chapter 1 MOTIVATION Copyright c ° 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be reproduced without written consent from the instructor: Prof. A. H. Sayed, Electrical Engineering Department, UCLA, CA 90095, sayed@ee.ucla.edu. In this initial chapter we explain what is meant by the title: Discrete-Time Signal Processing What is a signal? What is a discrete-time signal? And what is signal processing? Signals A signal is a function of one or more independent variables. The independent variable can be time, frequency, space coordinates, distance, or some other variable of interest. In this treatment, we shall focus almost exclusively on functions of a single variable and it will generally be the case that the independent variable is the time variable. Examples of Signals 1. x ( t ): the position of a cart at time t . Here t is the independent variable and it assumes real values. The signal is denoted by the letter x . 2. x ( i,j ): the intensity or brightness of the ( i,j )-th pixel in a two-dimensional image. Here ( i,j ) are the independent variables and they assume integer values. The signal is again denoted by the letter x . 3. x ( n ): the number of students attending a course at successive years. Here n is the independent variable and it assumes integer values. The signal is also denoted by the letter x . 4. w ( r ): the angular speed of a satellite in uniform circular motion around the earth at a radial distance r . Here r is the independent variable and it assumes positive real values. The signal is denoted by the letter w . 1
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2 Motivation Chapter 1 Classifcation oF Signals Signals can be classifed in many ways. For the purposes o± this treatment, we shall classi±y signals in two ways: 1. Continuous-time signals . In this case the independent variable assumes continuous real values. We shall generally denote a continuous-time signal by x ( t ), where t stands ±or the independent variable. An example o± a continuous-time signal is the the tem- perature variation in a room over a period o± time. 2.
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This note was uploaded on 11/07/2009 for the course EE 113 taught by Professor Walker during the Spring '08 term at UCLA.

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113_1_chapter01 - Chapter 1 MOTIVATION Copyright c 1996 by...

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