This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Z Transform-1”.

1. Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)]
a) x(n)+y(n) ↔X(z)Y(z)

b) x(n)+y(n) ↔X(z)+Y(z)

c) x(n)y(n) ↔X(z)+Y(z)

d) x(n)y(n) ↔X(z)Y(z)

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Explanation: According to the linearity property of z-transform, if X(z) and Y(z) are the z-transforms of x(n) and y(n) respectively then, the z-transform of x(n)+y(n) is X(z)+Y(z).

2. What is the z-transform of the signal x(n)=[3(2^{n})-4(3^{n})]u(n)?

a) 3/(1-2z^{-1})-4/(1-3z^{-1})

b) 3/(1+2z^{-1})-4/(1+3z^{-1})

c) 3/(1-2z)-4/(1-3z)

d) None of the mentioned

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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 z-transform X1(z)= 3/(1-2z

^{-1}) and X2(z)= 4/(1-3z

^{-1})

So, from the linearity property of z-transform

X(z)=X1(z)-X2(z)

=> X(z)= 3/(1-2z

^{-1})-4/(1-3z

^{-1})

3. What is the z-transform of the signal x(n)=sin(jω_{0}n)u(n)?

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4. According to Time shifting property of z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)?

a) z^{k}X(z)

b) z^{-k}X(z)

c) X(z-k)

d) X(z+k)

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5. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?

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6. If X(z) is the z-transform of the signal x(n) then what is the z-transform of a^{n}x(n)?

a) X(az)

b) X(az^{-1})

c) X(a^{-1}z)

d) None of the mentioned

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7. If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a^{-1}z)?

a) |a|r1<|z|<|a|r2

b) |a|r1>|z|>|a|r2

c) |a|r1<|z|>|a|r2

d) |a|r1>|z|<|a|r2

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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=|a|r1<|z|<|a|r2

8. What is the z-transform of the signal x(n)=a^{n}(sinω_{0}n)u(n)?

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9. If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)?

a) X(-z)

b) X(z^{-1})

c) X^{-1}(z)

d) None of the mentioned

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10. X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal nx(n)?

a) -z(dX(z))/dz

b) zdX(z)/dz

c) -z^{-1}dX(z)/dz

d) z^{-1}(dX(z))/dz

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11. What is the z-transform of the signal x(n)=na^{n}u(n)?

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**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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