# Topic: Signals and Systems (Test 1)

Topic: Signals and Systems
Q.1
A dual trace oscilloscope is set to operate in the Alternate mode. The control input of the multiplexer used in the y-circuit is fed with a signal having a frequency equal to
A. the highest frequency that the multiplexer can operate properly
B. twice the frequency of the time base (sweep) oscillator
C. the frequency of the time base (sweep) oscillator
D. haif the frequency of the time base (sweep) oscillator
Explaination / Solution:
No Explaination.

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Q.2
A Hilbert transformer is a
A. non-linear system
B. non-causal system
C. time-varying system
D. low-pass system
Explaination / Solution:
No Explaination.

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Q.3
Given two continuous time signals  which exist for t > 0, the convolution z(t) = x(t)* y(t) is
A.
B.
C.
D.
Explaination / Solution:

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Q.4
A zero mean random signal is uniformly distributed between limits –a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is
A.
B.
C.
D.
Explaination / Solution:

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Q.5
Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is  then the system response is   If the itial state vector of the system changes to  the system response becomes
The system matrix A is

A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.6
Consider the function ݂f(z) = z + z* where z is a complex variable and z* denotes its complex conjugate. Which one of the following is TRUE?
A. f(z) is both continuous and analytic
B. f(z) is continuous but not analytic
C. f(z) is not continuous but is analytic
D. f(z) is neither continuous nor analytic
Explaination / Solution:

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Q.7
A linear, time - invariant, causal continuous time system has a rational transfer function with simple poles at s =- 2 and s =- 4 and one simple zero at s =- 1 . A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is
A. [exp(- 2t) + exp(- 4t)]u(t)
B. [- 4 exp(- 2t) - 12 exp(- 4t) - exp(- t)]u(t)
C. [- 4 exp(- 2t) + 12 exp(- 4t)]u(t)
D. [- 0.5 exp(- 2t) + 1.5 exp(- 4t)]u(t)
Explaination / Solution:

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Q.8
{ x(n)} is a real - valued periodic sequence with a period N . x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence  is
A.
B.
C.
D. 0
Explaination / Solution:

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Q.9
Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)
A.
B.
C.
D.
Explaination / Solution:

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Q.10
The ROC of z -transform of the discrete time sequence
A. 1/3< |Z| < 1/2
B.  |Z| > 1/2
C. |Z| < 1/2
D. 2<|Z| < 3