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Lecture_12_MoreROCs

# Lecture_12_MoreROCs - Poles ROC Stable Unit Circle in ROC...

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More About Regions of Convergence EE 341 Discrete Time Linear Systems Fall 2007 Howard Jay Chizeck University of Washington Seattle, Washington

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24 Oct 2007 4 Finite Length Signals ROC Stable? Unit Circle in ROC? h[n]= δ [n] Whole z plane YES YES h[n] =0 for n< 0 Whole z plane except z=0 YES YES h[n] =0 for n > 0 Whole z plane except z= YES YES h[n] 0 for some n >0 and n < 0 Whole z plane except z= ,0 YES YES
24 Oct 2007 7 Right Sided Signals with h[n]=0 for n<0 Poles ROC Stable? Unit Circle in ROC? All inside unit circle YES YES One or more poles outside unit circle No No Outside circle with radius that of largest magnitude pole

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24 Oct 2007 10 Right Sided Signals with h[n] 0 for some n<0 Poles ROC Stable? Unit Circle in ROC? All inside unit circle YES YES One or more poles outside unit circle No No Outside circle with radius that of largest magnitude pole, but not at z =
24 Oct 2007 13 Left Sided Signals with h[n]=0 for n>0

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Unformatted text preview: Poles ROC Stable? Unit Circle in ROC? All outside unit circle YES YES One or more poles inside unit circle No No Inside circle with radius that of smallest magnitude pole 24 Oct 2007 16 Left Sided Signals with h[n] ≠ 0 for some n>0 Poles ROC Stable? Unit Circle in ROC? All outside unit circle YES YES One or more poles inside unit circle No No Inside circle with radius that of smallest magnitude pole, except z=0 24 Oct 2007 19 Two- Sided Signals – made by adding left-sided and right-sided signals ROC Unit Circle in ROC? Stable? YES, if outside ring edge radius >1 and inside ring edge radius < 1 A ring, inside a circle with radius that of smallest magnitude pole from left-sided part, and outside a circle with radius that of largest magnitude pole of right-sided part No otherwise...
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