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Electronics and Communication Engineering - Signals and Systems

Exercise : Signals and Systems - Section 4
41.
The initial value theorem is
Answer: Option
Explanation:

£f(t) =

£-1F(s) = f(t)

£[a f1(t) + bf2(t)] = aF1(s) + bF2(s)

where

£[f(t - T)] = e-sT F(s)

£[e-at f(t)] = F(s + a)

Initial value theorem

Final value theroem

Convolution Integral

where t is dummy variable for t.

42.

Assertion (A): The rms value of v = 1 + sin ωt is 1.5

Reason (R): If i = I0 + I1m sin ω1t + I3m sin 3ω1t, then

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:

.

43.
The exponential form of Fourier series is
Both (a) and (b)
Answer: Option
Explanation:

Both a and b are exactly the same except the way of writing.

44.
Principle of superposition is applicable to
linear systems only
nonlinear systems only
both linear and non linear system
linear systems and some nonlinear systems
Answer: Option
Explanation:

Superposition is valid if response is linearly related to cause.

45.
The range of value "a" for which system will be stable. If impulse response of DT system is = an ∪[n]
a > 1
a < 1
1 < a < ∞
-1 < a < 1
Answer: Option
Explanation:

Given n(n) = an ∪(n)

ROC is |z| > a open the mod function

when z > 0

⇒ z > a

z < 0 ⇒ - z > a or ⇒ z < - a

For stability ROC must include unit circle, so

|z| > a or - a < z < + a or -1 < a < + 1.

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