Digital Signal Processing Important Questions and Answers

(1) If x₁(n)={1,2,3} and x₂(n)={1,1,1}, then what is the convolution sequence of the given two signals?

[A] {1,2,3,1,1}

[B] {1,2,3,4,5}

[C] {1,3,5,6,2}

[D] {1,2,6,5,3}

Answer: {1,2,6,5,3}

(2) What are the values of z for which the value of X(z)=0?

[A] Poles

[B] Zeros

[C] Solutions

[D] None of the mentioned

Answer: Zeros

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(3) What are the values of z for which the value of X(z)=∞?

[A] Poles

[B] Zeros

[C] Solutions

[D] None of the mentioned

Answer: Poles

(4) If X(z) has M finite zeros and N finite poles, then which of the following condition is true?

[A] |N-M| poles at origin(if N>M)

[B] |N+M| zeros at origin(if N>M)

[C] |N+M| poles at origin(if N>M)

[D] |N-M| zeros at origin(if N>M)

Answer: |N-M| zeros at origin(if N>M)

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

[A] |a|r1<|z|<|a|r2

[B] |a|r1>|z|>|a|r2

[C] |a|r1<|z|>|a|r2

[D] |a|r1>|z|<|a|r2

Answer: |a|r1<|z|<|a|r2

(6) Which of the following signals have a pole-zero plot as shown below?(Let M=8 in the figure)

[A]

x(n)=an, 0≤n≤8
    =0, elsewhere

[B]

x(n)=an, 0≤n≤7
    =0, elsewhere

[C]

x(n)=a-n, 0≤n≤8
    =0, elsewhere

[D]

x(n)=a-n, 0≤n≤7
    =0, elsewhere

Answer:

x(n)=an, 0≤n≤7
    =0, elsewhere

(7) The z-transform X(z) of the signal x(n)=aⁿu(n) has:

[A] One pole at z=0 and one zero at z=a

[B] One pole at z=0 and one zero at z=0

[C] One pole at z=a and one zero at z=a

[D] One pole at z=a and one zero at z=0

Answer: One pole at z=a and one zero at z=0

(8) What is the nature of the signal whose pole-zero plot is as shown?

[A] Rising signal

[B] Constant signal

[C] Decaying signal

[D] None of the mentioned

Answer: Decaying signal

(9) What are the values of z for which the value of X(z)=0?

[A] Poles

[B] Zeros

[C] Solutions

[D] None of the mentioned

Answer: Zeros

(10) What is the unit sample response of the system described by the difference equation y(n)=0.5y(n-1)+2x(n)?

[A] 0.5(2)ⁿu(n)

[B] 2(0.5)ⁿu(n)

[C] 0.5(2)ⁿu(-n)

[D] 2(0.5)ⁿu(-n)

Answer: 2(0.5)ⁿu(n)

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