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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<sup>-at</sup> u(t), a > 0 will be
A
ae<sup>-at</sup>
B
$$\left( {{1 \over a}} \right)\left( {1 - {e^{ - at}}} \right)$$
C
a(1 - e<sup>-at</sup>)
D
1 - e<sup>-at</sup>
Correct Answer:
a(1 - e<sup>-at</sup>)
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
A
0
B
$$\frac{1}{2}$$
C
$$\frac{3}{2}$$
D
1
Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P
1
, P
2
and P
3
with system relations R
1
, R
2
, P
3
, P
4
.
Properties
P
1
: Linear but NOT time-invariant
P
2
: Time-invariant but NOT linear
P
3
: Linear and time-invariant
Relations
R
1
: y(t) = t
2
x(t)
R
2
: y(t) = t |x(t)|
R
3
: y(t) = |x(t)|
R
4
: y(t) = x(t - 5)
A
(P<sub>1</sub>, R<sub>1</sub>), (P<sub>2</sub>, R<sub>3</sub>), (P<sub>3</sub>, R<sub>4</sub>)
B
(P<sub>1</sub>, R<sub>2</sub>), (P<sub>2</sub>, P<sub>3</sub>), (P<sub>3</sub>, R<sub>4</sub>)
C
(P<sub>1</sub>, R<sub>3</sub>), (P<sub>2</sub>, R<sub>1</sub>), (P<sub>3</sub>, R<sub>2</sub>)
D
(P<sub>1</sub>, R<sub>1</sub>), (P<sub>2</sub>, R<sub>2</sub>), (P<sub>3</sub>, R<sub>3</sub>)
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 ?
A
28 24 15 16 04 09
B
28 24 16 15 09 04
C
24 28 15 16 09 04
D
28 24 16 15 04 09
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
A
IV
B
V
C
VI
D
None of these
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
A
α is positive and β is positive
B
α is negative and β is negative
C
α is positive and β is negative
D
α is negative and β is positive
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
star car demand quick on fat
B
star quick car demand on fat
C
star car quick demand on fat
D
none of these
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 ?
A
cough fight sough acts cats idea more
B
cough fight sough acts cats more idea
C
cough more fight sough acts idea cats
D
none of these
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
Equal
B
Not Equal
C
Greater
D
Lesser
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.
A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is not correct explanation of A
C
Both A is True but R is false
D
Both A is False but R is true
The impulse response functions of four linear systems S
1
, S
2
, S
3
, S
4
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?
A
S<sub>1</sub>
B
S<sub>2</sub>
C
S<sub>3</sub>
D
S<sub>4</sub>
