Signals and Systems - Online Test
Q1. Let f(x) be a real, periodic function satisfying f(−x) = −f(x). The general form of its Fourier series representation would be
Answer : Option B
Explaination / Solution:
Q2. Consider a linear time invariant system x = Ax, with initial condition x(0) at t = 0. Suppose α and β are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues λ1 and λ2 respectively.
Then the response x(t) of the system due to initial condition x(0) = α is
Answer : Option A
Explaination / Solution:
Q3. Let z(t) = x(t) * y(t), where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).
Answer : Option A
Explaination / Solution:
Q4. Consider the system with following input-output relation
where, x[n] is the input and y[n] is the output. The system is
where, x[n] is the input and y[n] is the output. The system is
Answer : Option D
Explaination / Solution:
Q5. 
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)
Answer : Option B
Explaination / Solution:
Q6. Let the signal 
be passed through an LTI system with frequency
response H(𝜔), as given in the figure below
be passed through an LTI system with frequency
response H(𝜔), as given in the figure belowThe Fourier series representation of the output is given as
Answer : Option C
Explaination / Solution:
Q7. The period of the signal 
is
is
Answer : Option D
Explaination / Solution:
No Explaination.
Q8. The system represented by the input-output relationship 
is
is
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. At t = 0, the function f(t) = sint/t has
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. x(t)is a positive rectangular pulse from t = −1 to t = +1 with unit height as shown in the figure. The value of 
{ where X(ω) is the Fourier transform of x(t)} is
{ where X(ω) is the Fourier transform of x(t)} is
Answer : Option D
Explaination / Solution:
No Explaination.
