Signals and Systems - Online Test
Q1. The impulse response h(t) of linear time - invariant continuous time system is given by h(t) = exp(- 2t)u(t), where u(t) denotes the unit step function.
The output of this system, to the sinusoidal input x(t) = 2 cos 2t for all time t , is
Answer : Option D
Explaination / Solution:
Q2. 
For the two-port network shown below, the short-circuit admittance parameter matrix is
Answer : Option A
Explaination / Solution:
Given circuit is as shown below
By writing node equation at input port
By writing node equation at output port
From (1) and (2), we have admittance matrix
Q3. For parallel RLC circuit, which one of the following statements is NOT correct ?
Answer : Option D
Explaination / Solution:
A parallel RLC circuit is shown below :
Input impedance
Q4.
Two discrete time system with impulse response h1[n] = 𝛿[n - 1] and h2[n] = 𝛿[n - 2] are connected in cascade. The overall impulse response of the cascaded system is
Answer : Option C
Explaination / Solution:
Q5. 
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is
Answer : Option C
Explaination / Solution:
Impulse response of the matched filter is given by
Q6. 
In the circuit shown, the switch S is open for a long time and is closed at t = 0. The current i (t) for t ≥ 0+is
Answer : Option A
Explaination / Solution:
When the switch S is open for a long time before t < 0, the circuit is
At t = 0, inductor current does not change simultaneously, So the circuit is
Current is resistor (AB)
i(0) = 0.75/2 = 0.375 A
Similarly for steady state the circuit is as shown below
B = 0.375 - 0.5 =- 0.125
Q7. The current I in the circuit shown is
Answer : Option A
Explaination / Solution:
Q8. A continuous time LTI system is described by
Assuming zero initial conditions, the response y(t) of the above system for the input 
is given by
is given by
Answer : Option B
Explaination / Solution:
System is described as
Taking laplace transform on both side of given equation
Transfer function of the system
By Partial fraction
Taking inverse laplace transform
Q9. In the circuit shown, the power supplied by the voltage source is
Answer : Option A
Explaination / Solution:
Applying nodal analysis
Current from voltage source is
Since current through voltage source is zero, therefore power delivered is zero.
Q10. 
Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
Which one of the following statements is true about the system?
Answer : Option A
Explaination / Solution:
For an input-output relation if the present output depends on present and past input values then the given system is “Causal”.
For the given relation,
For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.
Stability
If x[n] is bounded for the given finite range of n i.e. 0 ≤ n ≤ 10 y[n] is also bounded.
Similarly x[n] - x[n-1] is also bounded at all other values of n
Thus the system is “stable”.
