SP_I_P01_4p - Introduction to Signal Processing 1...

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Introduction to Signal Processing 1 Copyright © 2005-2009 – Hayder Radha I. Basic Signal and System Concepts A. Definition of a Signal Definition: A signal is a measure of some physical phenomenon, such as an electrical current, the temperature at an airport, etc. and it is a function of one or more variables. Introduction to Signal Processing 2 Copyright © 2005-2009 – Hayder Radha Most popular signals in electrical and computer engineering are functions of a single variable, which is usually time . A signal is usually a reference to the mathematical representation of the physical phenomenon under consideration. This physical phenomenon normally changes over time. Hence, we commonly express signals as functions of time: () x t , yt , ( ) it , vt ,…. Introduction to Signal Processing 3 Copyright © 2005-2009 – Hayder Radha Examples of Signals 1. Signals as functions of a single variable An example of a signal that is a function of a single variable is the voltage across an electric device such as a resistor, capacitor, or inductor: . Below is an example of a signal representing the voltage decay across a capacitance that is discharging its energy into a resistor starting at time zero: () ( ) exp , 0 t t =− . Introduction to Signal Processing 4 Copyright © 2005-2009 – Hayder Radha 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t
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Introduction to Signal Processing 5 Copyright © 2005-2009 – Hayder Radha 2. Signals as functions of two variables A prominent example of a signal that is expressed as a function of two variables is an image (picture) signal. The two variables usually represent two-dimensional spatial variable. Introduction to Signal Processing 6 Copyright © 2005-2009 – Hayder Radha x y Introduction to Signal Processing 7 Copyright © 2005-2009 – Hayder Radha 3. Signals as functions of three variables A video signal is an example of a function of three variables, two spatial variables and a time variable. In this course we will mainly focus on signals that are functions of a single variable. Introduction to Signal Processing 8 Copyright © 2005-2009 – Hayder Radha B. Signal Properties and Classification of Signals A signal can be categorized and classified using several key properties. Below we outline these properties that lead to different types of signals.
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Introduction to Signal Processing 9 Copyright © 2005-2009 – Hayder Radha 1. Continuous-Time and Discrete-Time Signals By considering a typical signal () x t that is a function of a single (time) variable t , one can classify a signal depending on the nature of this single variable (horizontal axis or domain ) under consideration. If the signal is a function of continuous time, then we have a continuous-time signal . In this case, the signal is defined over a continuum of time values. An example of a continuous-time signal is: Introduction to Signal Processing 1 0 Copyright © 2005-2009 – Hayder Radha () ( ) exp x tt =− . 0
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SP_I_P01_4p - Introduction to Signal Processing 1...

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