Control Systems Questions and Answers – The Z-transform Analysis of Sampled-Data Control Systems

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This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Z-transform Analysis of Sampled-Data Control Systems”.

1. The DFT of a signal x(n) of length N is X(k). When X(k) is given and x(n) is computed from it, the length of x(n)
a) Is increased to infinity
b) Remains N
c) Becomes 2N – 1
d) Becomes N2
View Answer

Answer: a
Explanation: When X (k) is given and x (n) is computed from it, the length of x (n) is increased to infinity.
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2. The system having input x (n) related to output y(n) as y (n) = log |x (n)| is:
a) Nonlinear, causal, stable
b) Linear, noncausal, stable
c) Nonlinear, causal, not stable
d) Linear, noncausal, not stable
View Answer

Answer: a
Explanation: As y (n) is the function of x (n) hence it is nonlinear but it is bounded and also depends upon past and present values therefore it is stable and causal respectively.

3. Zero-order hold used in practical reconstruction of continuous-time signals is mathematically represented as a weighted-sum of rectangular pulses shifted by:
a) Any multiples of the sampling interval
b) Integer multiples of the sampling interval
c) One sampling interval
d) 1 second intervals
View Answer

Answer: b
Explanation: Zero-order hold is used to reconstruct the continuous-time signal which is represented as a weighted sum of rectangular pulses shifted by integer multiples of the sampling interval.
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4. When two honest coins are simultaneously tossed, the probability of two heads on any given trial is:
a) 1
b) 3/4
c) 1/2
d) ¼
View Answer

Answer: d
Explanation: Total outcomes =4
Favorable outcomes =1
Hence probability =1/4.

5. A continuous-time periodic signal x(t), having a period T, is convolved with itself. The resulting signal is
a) Not periodic
b) Periodic having a period T
c) Periodic having a period 2T
d) Periodic having a period T/2
View Answer

Answer: b
Explanation: Periodic having a period T Convolution of a periodic signal (period T) with itself will give the same period T.
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6. If the Fourier series coefficients of a signal are periodic then the signal must be
a) Continuous-time, periodic
b) Discrete-time, periodic
c) Continuous-time, non-periodic
d) Discrete-time, non-periodic
View Answer

Answer: b
Explanation: Discrete-time, periodic these are the properties of the discrete-time periodic signal.

7. The region of convergence of a causal finite duration discrete-time signal is
a) The entire z-plane except z = 0
b) The entire z-plane except z = ∞
c) The entire z-plane
d) A strip in z-plane enclosing jω–axis
View Answer

Answer: a
Explanation: For discrete time signal for any causal system the region of convergence is always entire z-plane but except z =0.
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8. The probability cumulative distribution function must be monotone and
a) Increasing
b) Decreasing
c) Non-increasing
d) Non-decreasing
View Answer

Answer: d
Explanation: The cumulative distribution function that is monotone and non-decreasing or can be increasing.

9. Convolution is used to find:
a) The impulse response of an LTI System
b) Frequency response of a System
c) The time response of a LTI system
d) The phase response of a LTI system
View Answer

Answer: c
Explanation: Convolution is the combination of addition and multiplication of the signals and used to find the impulse response of the LTI system.
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10. The Fourier Transform of a rectangular pulse is
a) Another rectangular pulse
b) Triangular pulse
c) Sinc function
d) Impulse
View Answer

Answer: c
Explanation: The Fourier Transform of a rectangular pulse that is the sinc function.

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