Summary2 - includes the unit circle ROC cannot include any...

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Summary 2 Hamid Jafarkhani Digital Signal Processing Summary 2 – p. 1/ ? ?
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Z Transform X ( z ) = s n = -∞ x [ n ] z - n Region of Convergence (ROC): The set of values of z for which X ( z ) is finite. Inverse z -transform is not unique unless ROC is defined. Fourier Transform (FT) z = e X ( ω ) = s n = -∞ x [ n ] e - njω Summary 2 – p. 2/ ? ?
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Properties of ROC ROC is a ring or a disk centered at origin. FT converges absolutely if and only if ROC
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Unformatted text preview: includes the unit circle. ROC cannot include any pole. If x [ n ] is a finite-length sequence, ROC is entire z-plane except possibly z = 0 or z = ∞ . If x [ n ] is right-sided, ROC is outside a circle. If x [ n ] is left-sided, ROC is inside a circle. If x [ n ] is two-sided, ROC is a ring. ROC is a connected region. Summary 2 – p. 3/ ? ?...
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This note was uploaded on 12/13/2010 for the course ELECTRICAL EECS 152A taught by Professor Prof.hamidjafarkhani during the Fall '10 term at UC Irvine.

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Summary2 - includes the unit circle ROC cannot include any...

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