Digital Signal Processing Mock Test 2

10%

Question 1 of 10

1. What is the one sided z-transform of x(n)=δ(n+k)?

z^k

z^-k

Question 1 of 10

Question 2 of 10

2. What is the partial fraction expansion of the proper function X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\)?

\(\frac{2z}{z-1}-\frac{z}{z-0.5}\)

\(\frac{2z}{z-1}+\frac{z}{z-0.5}\)

\(\frac{2z}{z-1}+\frac{z}{z+0.5}\)

\(\frac{2z}{z-1}-\frac{z}{z+0.5}\)

Question 2 of 10

Question 3 of 10

3. What is the signal x(n) whose z-transform X(z)=log(1+az^-1);|z|>|a|?

\((-1)^{n-1}.\frac{a^n}{n}.u(n+1)\)

\((-1)^n.\frac{a^n}{n}.u(n+1)\)

\((-1)^n.\frac{a^n}{n}.u(n-1)\)

\((-1)^{n-1}.\frac{a^n}{n}.u(n-1)\)

Question 3 of 10

Question 4 of 10

4. Which of the following method is used to find the inverse z-transform of a signal?

Expansion into a series of terms

Partial fraction expansion

Counter integration

All of the mentioned

Question 4 of 10

Question 5 of 10

5. Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient c_k?

none of the mentioned

c_k=X(F₀/k)

c_k= 1/T_P (X(F₀/k))

c_k= 1/T_P(X(kF₀))

Question 5 of 10

Question 6 of 10

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

\(\frac{3}{1-2z^{-1}}-\frac{4}{1+3z^{-1}}\)

\(\frac{3}{1-2z^{-1}}-\frac{4}{1-3z^{-1}}\)

None of the mentioned

\(\frac{3}{1-2z}-\frac{4}{1-3z}\)

Question 6 of 10

Question 7 of 10

7. If all the poles of H(z) are inside the unit circle, then the system is said to be ____________

Only BIBO stable

BIBO stable and causal

None of the mentioned

Only causal

Question 7 of 10

Question 8 of 10

8. Which of the following is the Fourier series representation of the signal x(t)?

\(c_0+2\sum_{k=1}^{\infty}|c_k|cos(2πkF_0 t+θ_k)\)

\(c_0+2\sum_{k=1}^{\infty}|c_k|tan(2πkF_0 t+θ_k)\)

\(c_0+2\sum_{k=1}^{\infty}|c_k|sin(2πkF_0 t+θ_k)\)

None of the mentioned

Question 8 of 10

Question 9 of 10

9. If Z{x₁(n)}=X₁(z) and Z{x₂(n)}=X₂(z) then Z{x₁(n)*x₂(n)}=?

None of the mentioned

X₁(z)*X₂(z)

X₁(z)+X₂(z)

X₁(z).X₂(z)

Question 9 of 10

Question 10 of 10

10. The impulse response of a relaxed LTI system is h(n)=aⁿu(n), |a|<1. What is the value of the step response of the system as n→∞?

\(\frac{1}{1+a}\)

\(\frac{a}{1-a}\)

\(\frac{a}{1+a}\)

\(\frac{1}{1-a}\)

Question 10 of 10