Signals and Systems - Online Test
Q1. The frequency response of a linear, time-invariant system is given by 
The step response of the system is
The step response of the system is
Answer : Option B
Explaination / Solution:
Q2. The z −transform X(z) of a sequence x n is given by X 
It is given
that the region of convergence of X(z) includes the unit circle. The value of x is
It is given
that the region of convergence of X(z) includes the unit circle. The value of x is
Answer : Option B
Explaination / Solution:
Q3. 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 
then the system response is If the itial state vector of the system changes to the system response becomes The eigenvalue and eigenvector pairs (λivi)for the system are
Answer : Option A
Explaination / Solution:
Q4.
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
then the system response is If the itial state vector of the system changes to the system response becomes The system matrix A is
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system ?
Answer : Option C
Explaination / Solution:
The output of causal system depends only on present and past states only.
In option (A) y(0) depends on x(- 2) and x(4).
In option (B) y(0) depends on x(1).
In option (C) y(0) depends on x(- 1).
In option (D) y(0) depends on x(5).
Thus only in option (C) the value of y(t) at t = 0 depends on x(- 1) past value.
In all other option present value depends on future value.
Q6. The impulse response h(t) of a linear time invariant continuous time system is
described by 
where u(-t) denotes the unit
step function, and α and β are real constants. This system is stable if
where u(-t) denotes the unit
step function, and α and β are real constants. This system is stable if
Answer : Option D
Explaination / Solution:
This system is stable only when bounded input has bounded output For stability αt < 0 for t > 0 that implies α < 0 and βt > 0 for t > 0 that implies β > 0. Thus, α is negative and β is positive.
Q7. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems ?
Answer : Option C
Explaination / Solution:
Transfer function for the given pole zero plot is:
From the plot Re (P1 and P2)>(Z1 and Z2)
So, these are two lead compensator.
Hence both high pass filters and the system is high pass filter
Q8. 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
Answer : Option C
Explaination / Solution:
Q9. The signal x(t) is described by
Two of the angular frequencies at which its Fourier transform becomes zero are
Answer : Option A
Explaination / Solution:
Q10. A discrete time linear shift - invariant system has an impulse response h[n] with h[0] = 1,h[1] =- 1,h[2] = 2, and zero otherwise The system is given an input sequence x[n] with x[0] = x[2] = 1, and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are respectively
Answer : Option D
Explaination / Solution:
