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The impulse response h(t) of a linear time-invariant continuous time system is described by h(t) = exp(αt)u(t) + exp(βt)u(-t), where u(t) denotes the unit step function, and α and β are real constants. This system is stable if

Correct Answer: α is negative and β is positive

An electronic device rearranges numbers step-by-step in a particular order according to set of rules. The device stops when the final result is obtained.
Input: 84 15 35 04 18 96 62 08
Step 1: 96 84 15 35 04 18 62 08
Step 2: 96 84 62 15 35 04 18 08
Step 3: 96 84 62 35 15 04 18 08
Step 4: 96 84 62 35 18 15 04 08
Step 5: 96 84 62 35 18 15 08 04
And Step 5 is the last step for this input. Now, find out an appropriate step in the following question following the above rule. Question:
Input: 16 09 24 28 15 04
What will be the third step for this input ?

An electronic device when fed with the numbers, rearranges them in a particular order following certain rules. The following is a step-by-step process of rearrangement for the given input of numbers. Input :- 85 16 36 04 19 97 63 09 Step I :- 97 85 16 36 04 19 63 09 Step II :- 97 85 63 16 36 04 19 09 Step III :- 97 85 63 36 16 04 19 09 Step IV :- 97 85 63 36 19 16 04 09 Step V :- 97 85 63 36 19 16 09 04 (for the given input step V is the last step). Which of the following will be the last step for the given input ? Input :- 03 31 43 22 11 09

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

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 ?

A word arranging device rearranges words step-by-step in a particular order according to set of rules. The device stops when the final result is obtained.
Input: but going for crept te light sir
Step 1: crept but going for te light sir
Step 2: crept going light but for te sir
Step 3: crept going light but for sir te
And Step 3 is the last step for this input. Now, find out an appropriate step in the following question following the above rules. Question:
Input: more fight cats cough sough acts idea
What will be the last step for this input ?

Assertion (A): It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function. Reason (R): From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.

The unit impulse response of a linear time invariant system is the unit step function u(t). For t > 0, the response of the system to an excitation e-at u(t), a > 0 will be

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

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?

The response of an initially relaxed linear constant parameter network to a unit impulse applied at t = 0 is 4e-2tu(t). The response of this network to a unit step function will be