Z-Transform MCQs : This section focuses on the "Z-Transform". These Multiple Choice Questions (MCQs) should be practiced to improve the Z-Transform skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
Question 1
A sequence x (n) with the z-transform X (z) = Z4 + Z2 – 2z + 2 – 3Z-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:
A. -6
B. Zero
C. 2
D. -4
Question 2
H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:
A. Poles must be inside the unit circle and zeros must be outside the unit circle
B. Poles and zeroes must be inside the unit circle
C. Poles and zeroes must be outside the unit circle
D. Poles must be outside the unit circle and zeros must be inside the unit circle
Question 3
If the region of convergence of x1[n]+x2[n] is 1/>|z|<2/3, the region of convergence of x1[n]-x2[n] includes:
A. 1/3>|z|<3
B. 2/3>|z|<3
C. 3/2>|z|<3
D. 1/3>|z|<2/3
Question 4
The discrete-time signal x (n) = (-1)n is periodic with fundamental period
A. 6
B. 4
C. 2
D. 0
Question 5
The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor
A. α
B. 1/α
C. α2
D. α
Question 6
The region of convergence of the z-transform of a unit step function is:
A. |z|>1
B. |z|<1
C. (Real part of z)>0
D. (Real part of z)<0
Question 7
Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are
A. The same
B. Reciprocal of each other
C. Negative of each other
D. Complements of each other
Question 8
Which one of the following is the correct statement? The region of convergence of z-transform of x[n] consists of the values of z for which x[n] is:
A. Absolutely integrable
B. Absolutely summable
C. Unity
D. <1
Question 9
Z and Laplace transform are related by:
A. s = ln z
B. s =ln z/T
C. s =z
D. s= T/ln z
Question 10
Find the Z-transform of y(n) = x(n+2)u(n).
A. z2 X(Z) – z2 x(0) – zx(1)
B. z2 X(Z) + z2 x(0) – zx(1)
C. z2 X(Z) – z2 x(0) + zx(1)
D. z2 X(Z) + z2 x(0) + zx(1)
Question 11
Find the Z-transform of δ(n+3).
A. z
B. z2
C. 1
D. z3
Question 12
For a right hand sequence, the ROC is entire z-plane.
A. TRUE
B. FALSE
Question 13
For causal sequences, the ROC is the exterior of a circle of radius r.
A. TRUE
B. FALSE
Question 14
When do DTFT and ZT are equal?
A. When σ = 0
B. When r = 1
C. When σ = 1
D. When r = 0
Question 15
x(n) = an u(n) and x(n) = -an u(-n-1) have the same X(Z) and ROC.
A. TRUE
B. FALSE