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A continuous time LTI system is described by<br>$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 4{{dy\left( t \right)} \over {dt}} + 3y\left( t \right) = 2{{dx\left( t \right)} \over {dt}} + 4x\left( t \right)$$<br>Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e<sup>-2t</sup>u(t) is given by

Correct Answer: (e<sup>-t</sup> - e<sup>-3t</sup>)u(t)

Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| S3 : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?

If h(n) is the impulse response of an LTI system and hI(n) is the impulse response of the inverse LTI system, then which of the following is true?

A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$    To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is

Consider the following statements for continuous-time linear time invariant (LTI) systems.
1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?

What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

A word arrangement machine, When given an input line of words, rearranges it in every step following a certain rule. Following is an illustration of an input line of words and various steps of rearrangement.
Input: gone are take enough brought station
Step 1: take gone are enough brought station
Step 2: take are gone enough brought station
Step 3: take are station gone enough brought
Step 4: take are station brought gone enough
And Step 4 is the last step for this input. Now, find out an appropriate step in the following question following the above rule. Question:
Input: car on star quick demand fat
What will be the third step for this input ?

If H(z) is the system function of an LTI system and HI(z) is the system function of the inverse LTI system, then which of the following is true?

Zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.

Consider the following statements regarding a linear discrete-time system: H (z) = z2+1/(z+0.5)(z-0.5) 1. The system is stable 2. The initial value of h(0) of the impulse response is -4 3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency Which of these statements are correct?