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Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$  Consider the following three statements:<br>S<sub>1</sub> : The system is stable.<br>S<sub>2</sub> : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$  independent of t for t &gt; 0.<br>S<sub>3</sub> : A non-causal system with the same transfer function is stable.<br>For the above system,

Correct Answer: Only S<sub>1</sub> and S<sub>2</sub> are true

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?

Let Y(s) be the unit-step response of a causal system having a transfer function
$$G\left( s \right) = {{3 - s} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$
That is, $$Y\left( s \right) = {{G\left( s \right)} \over s}.$$   The forced response of the system is

The impulse response functions of four linear systems S1, S2, S3, S4 are given respectively by
$${h_1}\left( t \right) = 1,$$   $${h_2}\left( t \right) = u\left( t \right),$$   $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$    $${h_4}\left( t \right) = {e^{ - 3t}}u\left( t \right)$$
Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?

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 impulse response and the excitation function of a linear time invariant causal system are shown in figure (a) and (b) respectively. The output of the system at t = 2 sec is equal to
Signal Processing mcq question image

In MATLAB, the impulse response of the step response of a system is ___ to the step response of the impulse response of the system.

Consider the signal x(t) shown in the figure. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interval 0 to 4 sec. The slope of h(t) in the interval 3 Digital Communication mcq question image

Let us suppose that the impulse response of a causal LTI system is given as h (t). Now, consider the following two statements: Statement 1- Principle of superposition holds Statement 2- h (t) = 0(for t<0) Which of the following is correct?

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

Fill the half-filled code snippet to get the following graph: impulse(1,, ‘red’); ____; impulse(1,, ‘blue’); impulse(1,, ‘yellow’); impulse(1,, ‘green’);