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Which of the following justifies the linearity property of ztransform?[x(n)↔X(z)].
Explanation: According to the linearity property of ztransform, if X(z) and Y(z) are the ztransforms of x(n) and y(n) respectively then, the ztransform of x(n)+y(n) is X(z)+Y(z).
What is the ztransform of the signal x(n)=[3(2^{n})4(3^{n})]u(n)?
Explanation: Let us divide the given x(n) into x1(n)= 3(2^{n})u(n) and x2(n)= 4(3^{n})u(n)
and x(n)=x1(n)x2(n)
From the definition of ztransform X1(z)= 3/(12z^{1}) and X2(z)= 4/(13z^{1})
So, from the linearity property of ztransform
X(z)=X1(z)X2(z)
=> X(z)= 3/(12z^{1})4/(13z^{1}).
What is the ztransform of the signal x(n)=sin(jω_{0}n)u(n)?
Explanation: By Euler’s identity, the given signal x(n) can be written as
According to Time shifting property of ztransform, if X(z) is the ztransform of x(n) then what is the ztransform of x(nk)?
Explanation: According to the definition of Ztransform
What is the ztransform of the signal defined as x(n)=u(n)u(nN)?
Explanation:
If X(z) is the ztransform of the signal x(n) then what is the ztransform of a^{n}x(n)?
Explanation: We know that from the definition of ztransform
If the ROC of X(z) is r1<z<r2, then what is the ROC of X(a^{1}z)?
Explanation: Given ROC of X(z) is r1<z<r2
Then ROC of X(a^{1}z) will be given by r1<a^{1}z <r2=ar1<z<ar2
What is the ztransform of the signal x(n)=a^{n}(sinω_{0}n)u(n)?
Explanation:
If X(z) is the ztransform of the signal x(n), then what is the ztransform of the signal x(n)?
Explanation: From the definition of ztransform, we have
X(z) is the ztransform of the signal x(n), then what is the ztransform of the signal nx(n)?
Explanation:
From the definition of ztransform, we have
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