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Electronics and Communication Engineering - Signals and Systems

Exercise : Signals and Systems - Section 2
21.

Assertion (A): Intergal of a unit step function is a ramp of slope unity.

Reason (R): If

Both A and R are correct and R is correct explanation of A
Both A and R are correct but R is not correct explanation of A
A is true, R is false
A is false, R is true
Answer: Option
Explanation:

If f(t) = sin ωt, Hence A is wrong.

22.
If then, f(0+) and f(∞) are given by
0 and 2
2, 0
0, 1
, 0
Answer: Option
Explanation:

Use initial and final value theorems.

23.
The signal define by the equations u(t - a) = 0 for t < a and u(t - a) = 1 for t ≥ a is
a unit step function
a shifted unit step function orginating at t = a
a pulse function
none of the above
Answer: Option
Explanation:

u(t) is a unit step function u(t - a) is a unit step function shifted in time by a.

24.
For the system in the given figure
yk = uk + 0.5 yk - 2
yk = uk + 0.5 uk - 2
yk = uk - 0.5 yk - 2
yk = uk - 0.5 uk - 2
Answer: Option
Explanation:

yk has two unit delays and then a multiplier of 0.5 before being fedback.

25.
The Laplace transform of the waveform shown in the below figure is
Answer: Option
Explanation:

x(t) = ∪(t - 1) + ∪(t - 2) - 2∪(t - 3).

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