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how can determine the region of convergence?

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sara on 1 Apr 2016
Commented: John BG on 2 Apr 2016
hi all. I am a student, I should solve this question in matlab. can you help me please?

Answers (1)

John BG
John BG on 2 Apr 2016
Edited: John BG on 2 Apr 2016
From Digital Signal Processing using MATLAB,
by Vinay K Ingle, John G Proakis
pg 104
Region of Convergence of z domain functions is defined
as the abs(z) where H(z) exists, z: complex frequency.
Since you have defined in the same question that X is the input signal,
H is the system, both have finite energy,
X(z) ROC is abs(z)>.25 and H(z) ROC is abs(z)>.25
X(z)=1/(1+.5*z^-1) % ROC abs(z)>.5
H(z)=1/(1-.25*z^-1) % ROC abs(z)>.25
if X(z) and H(z) had been defined with ROCs abs(z)<.5 and abs(z)<.25 respectively then
but it's not the case.
the overlapping ROCs define Y(z) ROC.
Y(z) has same ROC as input signal
If you find this answer of any help solving your question, please click on the thumbs-up vote link,
thanks in advance John
sara on 2 Apr 2016
Edited: sara on 2 Apr 2016
thanks dear John. it is so helpful. but I am confused. z is variable and changes. for x: abs(z)>.5 and for h: abs(z)>1/4... how can I define this? and is there any way to show this in a plot?
John BG
John BG on 2 Apr 2016
it's defined by the exercise, not you: signal X(z) gets in H(z), Y(z)=H(z)*X(z) out it goes.
z is complex, you usually plot the magnitude with abs(z) and phase with angle(z).

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