113_1_Week07_print

113_1_Week07_print - 1 EE 113: Digital Signal Processing...

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1 EE 113: Digital Signal Processing Week 7 Frequency response (Chapter 3.8 – Mitra) All-pass and minimum-phase systems
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2 Why frequency response? ± DTFT of a sequence conveys important information about its frequency content ± DTFT of the impulse response sequence of a system conveys important information about the system
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3 Frequency content of a sequence We can approximate this integral expression by a finite sum: ! A generic input sequence x(n) can be regarded as a linear combination of exponential sequences ! DTFT of x(n) provides information about frequency content of x(n)
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4 Magnitude and Phase of the DTFT ± Examples on the board!! The DTFT of a sequence x(n) is a complex function of ω
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5 Example 2
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6 Example 3 More Examples: Example 3.17 and 3.18 - Mitra
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7 Sinusoids as Eigenfunctions ± IR h [ n ] completely describes LTI system: ± Complex sinusoid input i.e. ± Sinusoids are the eigenfunctions of LTI systems (only scaled, not ‘changed’) = hk [ ] xn k [ ] k x [ n ] h [ n ] y [ n ] = x [ n ] h [ n ] [ ] = e j ω 0 n yn [] = [ ] e j 0 n k ( ) k = e j 0 k e j 0 n k = He j 0 ( ) [ ] = j 0 ( ) e j 0 n +θ ω 0 ( ) ( ) H ( e j ) = | H ( e j ) | e j θ ( )
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8 System Response from H ( e j ω ) ± If x [ n ] is a complex sinusoid at 0 then the output of a system with IR h [ n ] is the same sinusoid scaled by | H ( e j ) | and phase-shifted by arg{ H ( e j )} = θ ( ) where H ( e j ) = DTFT{ h [ n ]} ± | H ( e j ) | magnitude response gain ± arg{ H ( e j )} phase resp. phase shift
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9 Why study DTFT? Frequency Response (FR) ± Knowing the scaling for every sinusoid fully describes the system behavior frequency response describes how a system affects each pure frequency
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10 Real sequences
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11 ± In practice signals are real e.g.
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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_Week07_print - 1 EE 113: Digital Signal Processing...

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