Chap 20 - SpectralContent ofDiscreteSignals...

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Spectral Content of Discrete Signals Lindner: Chapter 20
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Amplitude and Phase Spectra x ( n ) X ( Ω ) = x ( n ) e j Ω n n = −∞ : Let x(n) be a discrete signal. The amplitude spectrum of this signal is the funcBon X ( Ω ) vs. Ω The phase spectrum of this signal is the funcBon X ( Ω ) vs. Ω
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Example a = 0.8 x ( n ) = a n u s ( n ), 1 < a < 1, X ( z ) z = e j Ω = X Ω ( ) = 1 1 az 1 z = e j Ω = 1 1 ae j Ω
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Example x ( n ) = a n u s ( n ), 1 < a < 1, X ( z ) z = e j Ω = X Ω ( ) = 1 1 az 1 z = e j Ω = 1 1 ae j Ω a = 0.8
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Signal Energy (Sec 20.1.3) E x = x ( n ) 2 n = −∞ : Given the signal x(n) we defne the energy oF this signal as Theorem 20.1.5: Parseval’s Theorem Suppose that x(n) is an energy signal. Then the energy in this signal is given by E x = x ( n ) 2 n = −∞ = 1 2 π X ( Ω ) 2 d Ω 2 π . : The energy spectral density oF an energy signal x(n) is defned as D x ( Ω ) = X ( Ω ) 2
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Example D Ω ( ) = X Ω ( ) 2 = 1 1 ae j Ω 2
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Signal Energy (Sec 20.1.3) calculate the energy over the frequency interval E = (2) 1 2 π X ( Ω ) 2 d Ω Ω 1 Ω 2 0 ≤ Ω 1 < Ω 2 ≤ π
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This note was uploaded on 02/07/2011 for the course ECE 3704 taught by Professor Odenaal during the Spring '08 term at Virginia Tech.

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Chap 20 - SpectralContent ofDiscreteSignals...

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