The convolution process associated with the Laplace Transform, in time domain results into

Simple multiplication in complex frequency domain

Simple division in complex frequency domain

Simple multiplication in complex time domain

Simple division in complex time domain

ROC in Z plane excludes unity circle, it signifies….

Z transform converges but Fourier transform does not converge

Fourier transform converges but Z transform does not converge

Both Fourier and Z transform converge

Both Fourier and Z transform do no converge

Signals And Systems (Quiz-3)

1.

A signal x(t) is delayed by T time, corresponding ROC in the S – plane will shift by
- A.
  
  Exponential (-sT)
- B.
  
  Exponential (sT)
- C.
  
  T
- D.
  
  0
Correct Answer
D. 0

Explanation
When a signal x(t) is delayed by T time, it means that the signal is shifted to the right by T units on the time axis. However, this delay does not affect the region of convergence (ROC) in the S-plane. The ROC is determined by the properties of the original signal and not by any time shift. Therefore, the correct answer is 0, indicating that the ROC does not shift when the signal is delayed.

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2.

An LTI system’s transfer function is represented by (1/s). If unit step signal is applied at the input of this system, corresponding output will be
- A.
  
  Sinc function
- B.
  
  Cosine function
- C.
  
  Unit impulse
- D.
  
  Unit ramp function
Correct Answer
D. Unit ramp function

Explanation
The transfer function of an LTI system is given by (1/s), which represents a first-order integrator. When a unit step signal is applied at the input of this system, the output will be a unit ramp function. This is because the integral of a unit step function is a ramp function. Therefore, the correct answer is the unit ramp function.

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3.

An LTI system with rational system function having poles at -19, -6 and -1 and ROC is on the right side of the rightmost pole. The system is
- A.
  
  Causal-Unstable
- B.
  
  Non-causal-stable
- C.
  
  Causal-stable
- D.
  
  Non-causal-unstable
Correct Answer
C. Causal-stable

Explanation
The given system has poles at -19, -6, and -1. For a system to be causal, all the poles must be in the left half of the complex plane. Since the poles in this system are all negative, the system is causal. Additionally, the system is stable because the region of convergence (ROC) is on the right side of the rightmost pole. Therefore, the correct answer is causal-stable.

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4.

The convolution process associated with the Laplace Transform, in time domain results into
- A.
  
  Simple multiplication in complex frequency domain
- B.
  
  Simple division in complex frequency domain
- C.
  
  Simple multiplication in complex time domain
- D.
  
  Simple division in complex time domain
Correct Answer
A. Simple multiplication in complex frequency domain

Explanation
The Laplace Transform is a mathematical tool used to convert functions from the time domain to the complex frequency domain. During this transformation, the convolution process, which involves the integration of the product of two functions, results in a simple multiplication in the complex frequency domain. This means that when applying the Laplace Transform, the convolution of two functions in the time domain can be simplified to a multiplication operation in the complex frequency domain.

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5.

ROC in Z plane excludes unity circle, it signifies….
- A.
  
  Z transform converges but Fourier transform does not converge
- B.
  
  Fourier transform converges but Z transform does not converge
- C.
  
  Both Fourier and Z transform converge
- D.
  
  Both Fourier and Z transform do no converge
Correct Answer
A. Z transform converges but Fourier transform does not converge

Explanation
The statement "ROC in Z plane excludes unity circle" indicates that the region of convergence for the Z-transform does not include the unit circle in the complex plane. This implies that the Z-transform converges for certain values of the complex variable z, but not for points on the unit circle. On the other hand, the statement does not provide any information about the convergence of the Fourier transform. Therefore, the correct answer is that the Z-transform converges but the Fourier transform does not converge.

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Signals And Systems (Quiz-3)

A signal x(t) is delayed by T time, corresponding ROC in the S – plane will shift by

An LTI system’s transfer function is represented by (1/s). If unit step signal is applied at the input of this system, corresponding output will be

An LTI system with rational system function having poles at -19, -6 and -1 and ROC is on the right side of the rightmost pole. The system is

The convolution process associated with the Laplace Transform, in time domain results into

ROC in Z plane excludes unity circle, it signifies….