Summary5 - | H ω | and Θ ω for ≤ ω ≤ π Summary 5...

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Summary 5 Hamid Jafarkhani Digital Signal Processing Summary 5 – p. 1/
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Frequency Domain Analysis of LTI Systems Consider the input x [ n ] = Ae jωn at a single frequency ω , then the output y [ n ] = AH ( ω ) e jωn . Ae jωn is an eigen-function of an LTI system. H ( ω ) evaluated at the frequency of the input signal is the corresponding eigenvalue. For an LTI system with a real-valued h [ n ] , we have | H ( ω ) | = | H ( - ω ) | and Θ( ω ) = - Θ( - ω ) . Therefore, we only need to specify
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Unformatted text preview: | H ( ω ) | and Θ( ω ) for ≤ ω ≤ π . Summary 5 – p. 2/ 3 Ideal Filters Energy Density Spectra: S Y Y ( ω ) = | Y ( ω ) | 2 = | H ( ω ) | 2 | X ( ω ) | 2 = | H ( ω ) | 2 S XX ( ω ) Ideal Filters: Lowpass Filter Highpass Filter Bandpass Filter Bandstop Filter Allpass Filter Summary 5 – p. 3/ 3...
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