ImpulseResp - Impulse Function Response Linear Systems and...

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Impulse Function & Response Linear Systems and Signals Lecture 4 Dr. J. K. Aggarwal The University of Texas at Austin
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Impulse function The derivative of a function with a finite discontinuity is not defined at the point of discontinuity The concept of an impulse function enables us to define it.
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Consider the functions: Consider an approximation to each of these functions and find the derivative Each function is given by during transition Impulse Function …contd 0.5 0.5 t 0.5 1 t 1 0 u(t) t 0 at e t 0.5 () at e  1 t
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Impulse Function …contd Derivative: As f’(t), for the interval approaches , area under f’(t) between “approaches” unity. The limiting function defined by this pulse is called the impulse function . 0,    ,  () at ae  1 2 t 1 2 t
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Impulse Function : Definition The impulse function is defined by: ( ) 0 0 ( ) 1 tt t dt   () t A representation A visualization 1 2 0  t 0 t
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Other visualizations t 0 at e  t 1 0  2 2 2 1 2 t e  0 t 0 Thus, and () du t t dt t d    { 00 10 t t ut
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Graphical Representation An impulse of strength k is An impulse occurring at t=a is An impulse occurring at t=- a’ is t 0 1 () t ta a ' a ( ') ( kt
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Assume is continuous at t =0 , and takes the value , then If is continuous at t =T , If is continuous at t = -T',
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This note was uploaded on 02/08/2011 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas.

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ImpulseResp - Impulse Function Response Linear Systems and...

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