Signals and Systems - Online Test
Q1.
Let x(t) be the input and y(t) be the output of a continuous time system.
Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4
Properties Relations
P1 : Linear but NOT time - invariant R1 : y(t) = t2x(t)
P2 : Time - invariant but NOT linear R2 : y(t) = t|x(t)|
P3 : Linear and time - invariant R3 : y(t) = |x(t)|
R4 : y(t) = x(t-5)
Answer : Option B
Explaination / Solution:
Mode function are not linear. Thus y(t) = |x(t)| is not linear but this functions is
time invariant. Option (A) and (B) may be correct.
The y(t) = t|x(t)| is not linear, thus option (B) is wrong and (a) is correct. We
can see that
R1 : y(t) = t2x(t) Linear and time variant.
R2 : y(t) = t|x(t)| Non linear and time variant.
R3 : y(t) = |x(t)| Non linear and time invariant.
R4 : y(t) = x(t-5) Linear and time invariant.
Q2. { 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
is
Answer : Option A
Explaination / Solution:
Q3. 
Group I lists a set of four transfer functions. Group II gives a list of possible step response y(t). Match the step responses with the corresponding transfer functions.
Answer : Option D
Explaination / Solution:
Q4. The Fourier series of a real periodic function has only (P) cosine terms if it is even (Q) sine terms if it is even (R) cosine terms if it is odd (S) sine terms if it is odd Which of the above statements are correct ?
Answer : Option A
Explaination / Solution:
The Fourier series of a real periodic function has only cosine terms if it is even and sine terms if it is odd.
Q5. The ROC of z -transform of the discrete time sequence 
Answer : Option A
Explaination / Solution:
Taking z transform we have
Taking z transform we have
Q6. 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:
Q7.
Two discrete time system with impulse response h1[n] = ๐ฟ[n - 1] and h2[n] = ๐ฟ[n - 2] are connected in cascade. The overall impulse response of the cascaded system is
Answer : Option C
Explaination / Solution:
Q8. 
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
Q9. 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
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 โCausalโ.
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 โCausalโ.
Stability
If x[n] is bounded for the given finite range of n i.e. 0 โค n โค 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 โstableโ.
