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Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is Correct Answer $$ - {1 \over 5}{e^{3t}}u\left( { - t} \right) + {1 \over 5}{e^{ - 2t}}u\left( { - t} \right)$$

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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?
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.
Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$  Consider the following three statements:
S1 : The system is stable.
S2 : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$  independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
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 system provides output yi(t) when xi(t) is applied. If the system is said to be LTI then which of the following properties must satisfy? (i).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) + by2(t) (ii).If the input is x(t – T), then the output must be y (t – T) (iii).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) * by2(t) (iv).If the input is x(t – T), then the output must be y(t + T)
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Each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled as P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet. S1 : He no longer dreamed of storms, nor of women, nor of great occurrences, nor of great fish, nor fights, nor contests of strength, nor of his wife.

S6 : He urinated outside the shack and then went up the road to wake the boy.

P : He never dreamed about the boy.

Q : He only dreamed of places and of the lions on the beach now.

R : He simply woke, looked out through the open door at the moon and unrolled his trousers and put them on.

S : They played like young cats in the dusk and he loved them as he loved the boy.

The correct sequence should be
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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?
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