Time Left - 30:00 mins

GATE 2019: Signal and System Champion Test

Attempt now to get your rank among 911 students!

Question 1

A Fourier transform pair is given by

where u[n] denotes the unit step sequence. The value of A is _________.

Question 2

Consider two real valued signals, x(t) band-limited to [−500 Hz, 500Hz] and y(t) band-limited to [−1kHz, 1kHz]. For z (t) = x(t). y(t), the Nyquist sampling frequency (in kHz) is __________

Question 3

Consider a system shown below

the value of k for which the system will be a linear system is _______.

Question 4

Consider a discrete LTI system, not necessarily stable but unit sample response of system is zero for n < 0. Which of the following can be transfer function of system.

Question 5

Consider an LTI system whose frequency response is given by

then the value of magnitude and phase plot is

Question 6

Consider a signal x(t) given by

, then x(t) is given by

Question 7

A real-valued signal x(t) limited to the frequency band

is passed through a linear time invariant system whose frequency response is

The output of the system is

Question 8

The unilateral Laplace transform of

Which one of the following is the unilateral Laplace transform of g(t) = t. f(t)?

Question 9

A stable linear time invariant (LTI) system has a transfer function

To make this system causal it needs to be cascaded with another LTI system having a transfer function

A correct choice for

among the following options is

Question 10

The input-output relationship of a causal stable LTI system is given as

.
If the impulse response h[n] of this system satisfies the condition

the relationship between

Question 11

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for