# Lect4 - FREQUENCY RESPONSE Consider a discrete time LTI system with a pure complex sinusoid of frequency ω as input as shown below y(n = e jω n

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FREQUENCY RESPONSE Consider a discrete time LTI system with a pure complex sinusoid of frequency ϖ as input, as shown below. The output is given by convolution -∞ = - -∞ = - = = k k j n j k k n j e k h e e k h n y w w w ) ( ) ( ) ( ) ( or, n j j e e H n y w w ) ( ) ( = . (4.1) Thus, the output of an LTI system to a complex sinusoidal input is again a complex sinusoidal input with exactly the same frequency as the input. The only effect of an LTI system on a complex sinusoidal input is to multiply the input by a complex number, ) ( w j e H . The function , ) ( w j e H , is called the frequency response of the system and it determines the amplitude and phase shifts introduced by the system in passing a complex sinusoid from input to output. Indeed, it is conventional to express ) ( w j e H in terms of its magnitude and phase as ) ( ) ( n h e n y n j = w H(z) n j e w

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) ( ) ( ) ( w j w w j j e A e H = (4.2) where ) ( ) ( w w j e H A = (4.3) and { } { } ) ( ) ( arg ) ( w w w
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## This note was uploaded on 10/18/2009 for the course EE ee332 taught by Professor Ee during the Spring '07 term at Istanbul Technical University.

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Lect4 - FREQUENCY RESPONSE Consider a discrete time LTI system with a pure complex sinusoid of frequency ω as input as shown below y(n = e jω n

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