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LabAssignAlias - EE4150 (Spring 2001) LAB ASSIGNMENT #1...

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EE4150 (Spring 2001) LAB ASSIGNMENT #1 UNDERSTANDING ALIASING In the process of sampling one replaces a continuous time signal with a sequence of values obtained at “sampling times.” Mathematically, one has a continuous time signal x a ( t ), selects a sampling period T , and creates a discrete time signal x [ n ] x [ n ]= x a ( nT ) -∞ <n< (1) Remark 0.1 The case where the samples are obtained at unequal times is of little practical interest and will not be discussed If the discrete time signal replaces the continuous time signal, as is the case in digital signal processing, there may be a loss of information. It is not, in general, feasible to say what was the behavior of the continuous time signal “in between sampling times.” Whenever there is a loss of information due to the sampling, we say that aliasing has occurred. This project deals with the sampling continuous time signals and the possible loss of information that may arise. Discrete Time Signals as Continuous Time Signals Discrete time and continuous time signals are completely different mathematical objects. The former are functions of an integer variable n while the latter are functions of a real variable t .In order to be able to analyze them in a common frame it is necessary to create a continuous time model for discrete time signals. For every discrete time signal h [ n ], we associate the continuous time signal h * ( t )= X n = -∞ h [ n ] δ ( t - nT )( 2 ) where δ ( t ) represents the impulse function defined in continuous time. The concept is illustrated in Figure 1. Thus, we represent the discrete time signal as a train of impulse functions . The value of sampling period T is selected by the user accordingly with the characteristics of the sampled signal. However, technically, the same discrete signal may correspond to many continuous time signals.
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This note was uploaded on 02/26/2012 for the course EE 4150 taught by Professor Wu during the Fall '10 term at LSU.

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LabAssignAlias - EE4150 (Spring 2001) LAB ASSIGNMENT #1...

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