Final Solution 2005 Spring

Final Solution 2005 Spring - Problem 1(c): Answer is ii)....

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Problem 1(c): Answer is ii). Causality implies that the ROC extends from the outermost pole. Stability implies that the ROC should also include the unit circle. Therefore, the outermost pole should be inside the unit circle. Hence, all poles should be inside the unit circle. Problem 1(d): Direct form: Transposed direct form:

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Problem 2:
Problem 3(a): The zero-pole plot is shown below. ROC is given by: |z|>0.5 Problem 3(b): System is not minimum-phase, since there is a zero outside the unit circle. The minimum-phase system can be obtained by multiplying H(z) by an allpass filter that reflects the zero inside the unit circle: Note that the allpass filter can be multiplied by any unit modulus number, including -1. The resulting system is still minimum-phase. Problem 3(c): System is not maximum-phase, since there is a zero inside the unit circle. The maximum-phase system can be obtained by multiplying H(z) by an allpass filter that reflects the zero outside the unit circle:

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Note that the above allpass filter can be multiplied by any unit modulus number, including -1. The resulting system is still maximum-phase.
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This note was uploaded on 04/08/2008 for the course EE 448 taught by Professor - during the Spring '08 term at Stevens.

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Final Solution 2005 Spring - Problem 1(c): Answer is ii)....

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