Unit 2 analysis of continuous time signals-mcq questions

1. Unit 2- ANALYSIS OF CONTINUOUS TIME SIGNALS
Part-A
1. The Trigonometric Fourier series of an evenfunction of time does not have the
a) Dc term
b) Cosine terms
c) Sine terms
d) Odd harmonic terms
c) Sine terms
2. The Trigonometric Fourier series of an odd function of time have only the
a) Sine terms
b) Cosine terms
c) Odd harmonic terms
d) Dc term
a)Sine terms

2. 3. The Trigonometric Fourier series of a half wave symmetric signal [𝐱(𝐭) = −𝐱(𝐭 ±
𝐓
𝟐
)]
have only the
a) Dc term
b) Cosine terms
c) Odd harmonic terms
d) Sine terms
c)Odd harmonic terms
4. If f(t) = f(-t) and f(t) satisfy the Dirchlet’s conditions ,then f(t) can be expanded in a
Fourier series containing
a) Only Sine terms
b) Only Cosine terms
c) Constant and Cosine terms
d) Both Sine and Cosine terms
c)Constant and Cosine terms
5. Which among the following statement is is not a Dirichlet condition?
a) The signal (𝑡) must be single valued function.
b) The function x(t) should have finite number of maxima and minima in the period T.
c) The function x(t) should have finite number of discontinuities in the period T.
d) The function should not be absolutely integrable.
d)The function should not be absolutely integrable.
6. The trigonometric form of Fourier series of a periodic signal, 𝑥(𝑡) with period 𝑇 is defined as
a) x( 𝑡) = 𝑎0 + ∑ ( 𝑎 𝑛 cos 𝑛𝜔𝑡 + 𝑏 𝑛 sin 𝑛𝜔𝑡)∞
𝑛=1
b) x( 𝑡) = ∑ ( 𝑎 𝑛 cos 𝑛𝜔𝑡 + 𝑏 𝑛 sin 𝑛𝜔𝑡)∞
𝑛=1
c) x( 𝑡) = 𝑎0 + ∑ (𝑎 𝑛 cos 𝑛𝜔𝑡∞
𝑛=1 )
d) x( 𝑡) = 𝑎0 + ∑ ( 𝑏 𝑛 sin 𝑛𝜔𝑡)∞
𝑛=1
a)x( 𝑡) = 𝑎0 + ∑ ( 𝑎 𝑛 cos 𝑛𝜔𝑡 + 𝑏 𝑛 sin 𝑛𝜔𝑡)∞
𝑛=1
7. The fourier series expansion of a real periodic signal with fundamental period f0 is given by
gp(t) = ∑ Cn 𝑒 𝑗2𝜋𝑓0 𝑡∞
𝑛=−∞
.It is given that C3=3+j5.Then C-3 is
a) 5+j3
b) -3-j5
c) -5+j3
d) 3-j5
d)3-j5

3. 8.The Fouriertransformof continuoustime signal,x(t) isdefinedas,
a) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(−𝑡)𝑒𝑗𝜔𝑡 𝑑𝑡
−∞
∞
b) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒𝑗𝜔𝑡 𝑑𝑡
∞
−∞
c) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(−𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
d) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
d) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
9.The inverse FourierTransformof 𝑋(𝑗𝜔) isdefinedas
a) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
−∞
∞

4. b) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
c) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
d) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(-j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
c)(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
10. The AnalysisEquationisgivenby
a) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
b) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(−𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
c) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
d) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
c) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
11. Selectthe Synthesisequation:
a) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
b) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(−𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
c) X(j𝜔)=𝐹[ 𝑥(𝑡)]=∫ 𝑥(𝑡)𝑒−𝑗𝜔𝑡 𝑑𝑡
∞
−∞
d) 𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
d)𝑥(t)=𝐹-1
[X(j𝜔)]=
1
2π
∫ X(j𝜔)𝑒𝑗𝜔𝑡 𝑑𝜔
∞
−∞
12. The Fouriertransformof impulse signal δ[(𝑡)]isgivenas
a) 1
b) 0
c) ∞
d) -1
a)1
13. FindFouriertransformof stepsignal oru(𝒕)
a)
1
ω
b) 1
c) ∞

5. d) π ∂(ω) +
1
jω
d) π ∂(ω) +
1
jω
14. The Initial of Laplace Transformisgivenas
a) 𝑥(0) = lim
𝑠→∞
𝑋(𝑆)
b) 𝑥(0) =lim
𝑠→0
𝑆𝑋(𝑆)
c) 𝑥(0) = lim
𝑠→∞
𝑆𝑋(𝑆)
d) 𝑥(0) =lim
𝑠→0
𝑆
𝑋(𝑆)
𝑆
c) 𝑥(0) = lim
𝑠→∞
𝑆𝑋(𝑆)
15. Final Value theoremof Laplace Transformis
a) 𝑥(∞) =lim
𝑠→0
𝑆𝑋(𝑆)
b) 𝑥(∞) =lim
𝑠→∞
𝑆𝑋(𝑆)
c) 𝑥(∞) =lim
𝑠→∞
𝑋(𝑆)
d) 𝑥(∞) =lim
𝑠→0
𝑋(𝑆)
a)𝑥(∞) =lim
𝑠→0
𝑆𝑋(𝑆)
16. If x(t) isa rightsidedsequencethenROC is

6. a) Re{s} > σo
b) Re{s} < σo
c) entire s-plane
d) Re{s} > 0
a) Re{s} > σo
17. Parseval’srelationforcontinuoustimeFouriertransformisgivenby
a) E=∫ x( 𝑡) 𝑑𝑡
∞
−∞ =
1
2π
∫ X(𝑗𝜔)𝑑𝜔
∞
−∞
b) E=∫ x( 𝑡) 𝑑𝑡
∞
−∞ =
1
2π
∫ |X(𝑗𝜔)|2 𝑑𝜔
∞
−∞
c) E=∫ |x( 𝑡)|2 𝑑𝑡
∞
−∞ =
1
2π
∫ X(𝑗𝜔)𝑑𝜔
∞
−∞
d) E=∫ |x( 𝑡)|2 𝑑𝑡
∞
−∞ =
1
2π
∫ |X(𝑗𝜔)|2 𝑑𝜔
∞
−∞
d) E=∫ |x( 𝑡)|2 𝑑𝑡
∞
−∞ =
1
2π
∫ |X(𝑗𝜔)|2 𝑑𝜔
∞
−∞
18. Time Scalingpropertyof Fouriertransformisgivenby
a) 𝐹[ 𝑥(a𝑡)]=X(
𝑗𝜔
𝑎
)
b) 𝐹[ 𝑥(a𝑡)]=
1
|𝑎|
X(
𝑗𝜔
𝑎
)
c) 𝐹[ 𝑥(a𝑡)]=
1
|𝑎|
X(𝑗𝜔)
d) 𝐹[ 𝑥(a𝑡)]=
1
|𝑎|
X(𝑎)
b) 𝐹[ 𝑥(a𝑡)]=
1
|𝑎|
X(
𝑗𝜔
𝑎
)
19. Convolutionpropertyof Fouriertransform isgivenby
a) 𝐹[𝑥(𝑡)∗y(t)]=Y(j𝜔)
b) 𝐹[𝑥(𝑡)∗y(t)]=X(j𝜔)
c) 𝐹[𝑥(𝑡)∗y(t)]=X(j𝜔)Y(j𝜔)
d) 𝐹[𝑥(𝑡)∗y(t)]=X(j𝜔)*Y(j𝜔)
c)F [(𝑡)∗y(t)]=X(j𝜔)Y(j𝜔)
20. Differentiationpropertyof Fouriertransformisgivenby
a) 𝐹[
𝑑𝑥(𝑡)
𝑑𝑡
]= j𝜔 X(j𝜔)
b) 𝐹[
𝑑𝑥(𝑡)
𝑑𝑡
]= 𝜔3 X(j𝜔)
c) 𝐹[
𝑑𝑥(𝑡)
𝑑𝑡
]= -j𝜔 X(j𝜔)
d) 𝐹[
𝑑𝑥(𝑡)
𝑑𝑡
]= X(
1
j𝜔
)

7. a)F[
𝒅𝒙(𝒕)
𝒅𝒕
]= j𝜔 X(j𝜔)
21. Time shiftingpropertyof Fouriertransformisgivenby
a) 𝐹[𝑥(𝑡-𝑡0)]= 𝑒𝑗𝜔𝑡0
X(j𝜔)
b) 𝐹[𝑥(𝑡-𝑡0)]= 𝑒−𝑡0
X(j𝜔)
c) 𝐹[𝑥(𝑡-𝑡0)]= 𝑒−𝑗𝜔 X(
𝑗𝜔
𝑎
)
d) 𝐹[𝑥(𝑡-𝑡0)]= 𝑒−𝑗𝜔𝑡0
X(j𝜔)
d)F[x(𝑡-𝑡0)]= 𝑒−𝑗𝜔𝑡0
X(j𝜔)
22. If x(t) isa leftsidedsequence thenROCis
a) Re{s} > σo
b) Re{s} < σo
c) entire s-plane
d) Re{s} > 0
b) Re{s} < σo
23. FindLaplace transformof x(𝒕) = 𝑒 𝑎𝑡 𝑢(𝒕)
a)
1
𝑠−𝑎
b)
1
𝑠+𝑎
c)
𝑆
𝑠−𝑎
d)
𝑆
𝑠+𝑎
a)
1
𝑠−𝑎
24. FindLaplace transform and ROCof x(𝒕) =- 𝑒−𝑎𝑡 𝒖(-𝒕)
a)
1
𝑠−𝑎
, σ>-a
b)
1
𝑠+𝑎
, σ>-a
c)
1
𝑠+𝑎
, σ<-a
d)
𝑆
𝑠+𝑎
, σ<-a
c)
1
𝑠+𝑎
, σ<-a
25. FindLaplace transform of x(t)=Cos𝜔0 𝑡

8. a)
𝜔
𝑠2−𝜔2
b)
𝜔
𝑠2+𝜔2
c)
𝑠
𝑠2−𝜔2
d)
𝑠
𝑠2+𝜔2
d)
𝑠
𝑠2 +𝜔2
26.FindLaplace transform of x(t)=Sin𝜔0 𝑡
a)
𝜔
𝑠2−𝜔2
b)
𝜔
𝑠2+𝜔2
c)
𝑠
𝑠2−𝜔2
d)
𝑠
𝑠2+𝜔2
b)
𝜔
𝑠2+𝜔2
27.Frequencyshiftingpropertyof Laplace transform isgivenby,
a) L[ 𝑒−𝑎𝑡x(t)]= X(s+a)
b) L[ 𝑒−𝑎𝑡x(t)]= X(s-a)
c) L[ 𝑒−𝑎𝑡x(t)]= X(as)
d) L[ 𝑒−𝑎𝑡x(t)]= X(
𝑠
a
)
a) L[ 𝑒−𝑎𝑡x(t)]= X(s+a)
28.FindLaplace transform of x(t)= 𝑒−𝑎𝑡Sin𝜔0 𝑡u(t)
a)
𝜔
(𝑠+𝑎)2−𝜔2
b)
𝜔
(𝑠+𝑎)2+𝜔2
c)
𝑠
(𝑠−𝑎)2+𝜔2
d)
𝑠
(𝑠+𝑎)2−𝜔2
b)
𝜔
(𝑠+𝑎)2+𝜔2
FrequencyshiftingpropertyL[ 𝑒−𝑎𝑡x(t)]= X(s+a)
29.FindLaplace transform of x(t)= 𝑒−𝑎𝑡Cos𝜔0 𝑡u(t)
a)
𝜔+𝑎
(𝑠+𝑎)2−𝜔2

9. b)
𝜔
(𝑠+𝑎)2+𝜔2
c)
𝑠
(𝑠−𝑎)2+𝜔2
d)
𝑠+𝑎
(𝑠+𝑎)2+𝜔2
𝑑)
𝑠+𝑎
(𝑠+𝑎)2+𝜔2
FrequencyshiftingpropertyL[ 𝑒−𝑎𝑡x(t)]= X(s+a)
30. FindLaplace transform of x(t)=u(t-2)
a)
𝑒−2𝑠
𝑠
b)
𝑒−𝑠
𝑠
c)
𝑒−𝑠
2𝑠
d)
𝑒−2𝑠
2𝑠
a)
𝑒−2𝑠
𝑠
(Time shiftingProperty) L[𝑥(𝑡-𝑡0)]= 𝑒−𝑠𝑡0
X(s)
31. FindLaplace transform of x(t)=𝜕(t-t0)
a)
𝑒−𝑠𝑡0
𝑠
b) 𝑒−𝑠𝑡0
c)
𝑒−𝑠𝑡0
2𝑠
d) 𝑒−𝑡0
b) 𝑒−𝑠𝑡0 (Time shiftingProperty)L[𝑥(𝑡-𝑡0)]= 𝑒−𝑠𝑡0
X(s)
32.Fouriertransformof DC signal of amplitude 1isgivenby
a) j𝜋𝜔
b)
𝑗
𝜋𝜔
c) 2𝜋𝜕(𝜔)
d)
1
2𝜋
c) 2𝜋𝜕(𝜔)

10. 33.FindLaplace transform of x(t)=tu(t)
a)
1
𝑠2
b)
1
𝜔2
c)
𝑠
𝜔2
d)
𝑠
𝜔
a)
1
𝑠2
34.FindLaplace transform of x(t)= 𝑡𝑒−𝑎𝑡 u(t)
a)
1
(𝑠+𝜔)2
b)
𝑠
(𝑠−𝑎)2
c)
𝑠
(𝑠+𝑎)2
d)
1
(𝑠+𝑎)2
d)
1
(𝑠+𝑎)2

11. 35. The Transferfunctionof an ideal integratorisgivenby,
a) s
b)
𝑠
𝜔
c)
1
𝑠
d)
𝜔
𝑠
c)
1
𝑠
36. The Transferfunctionof an ideal differentiatorisgivenby,
a)
1
𝑠
b) s
c)
𝑠
𝜔
d)
𝜔
𝑠
b)s
37. ROC of the impulse functionis
a) Re{s} > σo
b) Re{s} < σo
c) entire s-plane
d) Re{s} > 0
c) entire s-plane
38. The Fouriertransformof Sgn (t)
a) j𝜋𝜔
b)
𝑗
𝜋𝜔
c)
2
𝑗𝜔
d)
2𝜔
𝑗
𝑐)
2
𝑗𝜔
39.Findthe inverse fouriertransformof 𝜕(𝜔)
a) j𝜋𝜔
b)
𝑗
𝜋𝜔
c)
2
𝑗𝜔

12. d)
1
2𝜋
(d)
1
2𝜋
40.Findthe inverse Fouriertransformof 𝜕(𝜔 − 𝜔0)
a) j𝜋𝜔
b)
𝑗
𝜋𝜔
c)
𝑒 𝑗𝜔𝑡0
2𝜋
d)
𝑒−𝑠𝑡0
2𝑠
c)
𝑒 𝑗𝜔𝑡0
2𝜋
41. One of the conditionstobe satisfiedforthe existence of Fouriertransformis
a) ∫ |𝑥( 𝑡)|𝑑𝑡
∞
−∞ < ∞
b) ∫ |𝑥( 𝑡)|𝑑𝑡
∞
−∞ = ∞
c) ∫ |𝑥( 𝑡)|2 𝑑𝑡
∞
−∞ < ∞
d) ∫ |𝑥( 𝑡)|𝑑𝑡
−∞
∞ < ∞
a) ∫ |𝑥( 𝑡)|𝑑𝑡
∞
−∞ < ∞
42.The Transferfunctionof an ideal delayof Tseconds isgivenby,
a) 𝑒 𝑠𝑇
b)
𝑠
𝜔

13. c)
1
𝑠
d) 𝑒−𝑠𝑇
d) 𝑒−𝑠𝑇
43.FourierTransformand Laplace Transformare identical at
a) s= j𝜋𝜔
b) s=j𝜔
c) s=- j𝜔
d) s=
𝑖
j𝜔
b) s=j𝜔
44. Time Differentiationpropertyof Laplace Transform isgivenby
a) L[
𝑑𝑥(𝑡)
𝑑𝑡
]= j𝜔 X(j𝜔)
b) L[
𝑑𝑥(𝑡)
𝑑𝑡
]= 𝜔3 X(s)
c) L [
𝑑𝑥(𝑡)
𝑑𝑡
]= sX(s)
d) L [
𝑑𝑥(𝑡)
𝑑𝑡
]=
X(s)
𝑠
c)L [
𝑑𝑥(𝑡)
𝑑𝑡
]= sX(s)
45.The Laplace Transformof [
𝑑
𝑑𝑡2
2
𝑥(𝑡)] is givenby
a) s2
X(s)
b) s3
X(s)
c)
X(s)
s2
d) sX(s)
a) s2
X(s)
46.Linearitypropertyof FourierTransformisgivenby
a) F[ax(t) +by(t)] = aX(j𝜔) + bY(j𝜔)
b) F[ax(t) +by(t)]=aX(j𝜔) - bY(j𝜔)
c) F[ax(t) +by(t)]=aX(j𝜔)
d) F[ax(t) +by(t)]=bY(j𝜔)
a) F[ax(t) +by(t)] = aX(j𝜔) + bY(j𝜔)
47. Conjugationpropertyof FourierTransform statesthat
a) F[x(t)] =X*(-j𝜔)

14. b) F[x(t)] =X*(j𝜔)
c) F[x*(t)] =X*(-j𝜔)
d) F[x*(t)] =X (-j𝜔)
c) F[x*(t)] =X*(-j𝜔)
48. Time reversal propertyof Fouriertransformisgivenby
a) F[x(t)] =X(-j𝜔)
b) F[x(-t)] =X*(-j𝜔)
c) F[x*(t)] =X (-j𝜔)
d) F[x(-t)] =X(-j𝜔)
d) F[x(-t)] =X(-j𝜔)
49.Frequencyshiftingpropertyof Fourier transformisgivenby,
a) F[ ejω0tx(t)] = X[j(ω+ω0)]
b) F[ ejω0tx(t)] = X[j(ω-ω0)]
c) F[ ejω0tx(t)] = ejω0tX(j(ω-ω0))
d) F[ ejω0tx(t)] = ejω0tX(jω)
b) F[ ejω0tx(t)] = X[j(ω-ω0)]
50. Multiplication propertyof Fouriertransformisgivenby,
a) 𝐹[𝑥(𝑡)y(t)]=
1
2π
∫ X(𝑗𝜃)𝑌(𝑗( 𝜔 − 𝜃))𝑑𝜔
∞
−∞
b) 𝐹[𝑥(𝑡)y(t)]=
1
2π
∫ X(𝑗𝜃)𝑌(𝑗( 𝜃))𝑑𝜃
∞
−∞
c) 𝐹[𝑥(𝑡)y(t)]=
1
2π
∫ X(𝑗𝜃)𝑌(𝑗( 𝜔 − 𝜃))𝑑𝜃
∞
−∞
d) 𝐹[𝑥(𝑡)y(t)]=
1
2π
∫ X(𝑗𝜔)𝑌(𝑗( 𝜔 − 𝜃))𝑑𝜔
∞
−∞
c)F [x(𝑡)y(t)]=
1
2π
∫ X(𝑗𝜃)𝑌(𝑗( 𝜔 − 𝜃))𝑑𝜃
∞
−∞
Part B
1. Determine initial value and final value of the followingsignal X(𝑆)=
𝟏
𝒔(𝒔+𝟐)
a) Initial value :0, Final value:0
b) Initial value :1, Final value:
1
2

15. c) Initial value :0, Final value:
1
2
d) Initial value :2, Final value:3
1.c)Initial value :0,Final value:
1
2
(0) = lim
𝑠→∞
𝑆𝑋(𝑆)
𝑥(∞) =lim
𝑠→0
𝑆𝑋(𝑆)
2.Findthe Laplace transformof 𝜕( 𝑡) + 𝑢(𝑡)
a) 1+
1
𝑠
b) 1-
1
𝑠
c) 0
d)
1
𝑠
2.a) 1+
1
𝑠
3.Findthe FourierTransform of x(t) = 𝑒−𝑎|𝑡|
a)
2𝑎
𝑎2−𝜔2
b)
𝑎
𝑎2+𝜔2
c)
𝑎
𝑠2+𝑎2
d)
2𝑎
𝑎2+𝜔2
3.d)
2𝑎
𝑎2+𝜔2
4.Findthe FourierTransform of x(t) = 𝑒2𝑡 𝑢(𝑡)
a)
2𝑎
𝑎2−𝜔2
b)
2𝑎
2+𝑗𝜔
c)
1
2+𝑗𝜔
d) Fouriertransformdoesn’texist
4.d) Fouriertransformdoesn’texist The Signal doesn’tconvergebecause of 𝑒2𝑡
5.Findthe FourierTransform of x(t) = 𝑒−|𝑡|

16. a)
2
1−𝜔2
b)
2
1+𝜔2
c)
𝑎
𝑠2+𝑎2
d)
2𝑎
𝑎2+𝜔2
5.b)
2
1+𝜔2
6.Findthe Fouriertransform of x(t-2)
a) 𝑒𝑗𝜔2 X(j𝜔)
b) 𝑒−2 X(j𝜔)
c) 𝑒−𝑗𝜔 X(
𝑗𝜔
𝑎
)
d) 𝑒−𝑗𝜔2 X(j𝜔)
6.d) 𝑒−𝑗𝜔2 X(j𝜔)
7.FindFouriertransform of x(𝒕) = 𝑒 𝑎𝑡 𝒖(-𝒕)
a)
1
𝑎−𝑗𝜔
b)
1
𝑎+𝑗𝜔
c)
1
𝑗𝜔−𝑎
d)
1
𝑠+𝑎
7.a)
1
𝑎−𝑗𝜔
8.FindLaplace transformof x(t)=𝑒−5𝑡u(t-1)
a)
𝑒−5𝑠
𝑠
b)
𝑒−𝑠
5
c)
𝑒−(𝑠+5)
𝑠+5
d)
𝑒−(𝑠+5)
𝑠−5
8.c)
𝑒−(𝑠+5)
𝑠+5
9. FindLaplace transform of unitramp function

17. a)
1
𝑠2
b)
1
𝜔2
c)
𝑠
𝜔2
d)
𝑠
𝜔
9.a)
1
𝑠2
10. FindLaplace transform of u(t)-u(t-2)
a) 1 −
𝑒−2𝑠
𝑠
b)
1
𝑠
−
𝑒2𝑠
𝑠
c)
1
𝑠
+
𝑒−2𝑠
𝑠
d)
1
𝑠
−
𝑒−2𝑠
𝑠
10.d)
1
𝑠
−
𝑒−2𝑠
𝑠
11.Findthe laplace inverseof X(s)=
1
𝑠+2
a) 𝒙(𝒕) = 𝑒−2𝑡 𝒖(𝒕)
b) 𝒙(𝒕) = 𝑒2𝑡 𝒖(𝒕)
c) 𝒙(𝒕) = 𝑒 𝑡 𝒖(𝒕)
d) 𝒙(𝒕) = 2𝑒−2𝑡 𝒖(𝒕)
11. a) 𝒙(𝒕) = 𝑒−2𝑡 𝒖(𝒕)
12. FindFouriertransform of x(𝒕) = 𝑒−0.5𝑡 𝒖(𝒕)
a)
1
0.5−𝑗𝜔
b)
1
0.5+𝑗𝜔
c)
1
𝑗𝜔−0.5
d)
1
𝑠+0.5
12.b)
1
0.5+𝑗𝜔
13.Findthe laplace inverseof X(s)=
1
𝑠−𝑎
a) 𝑒 𝑎𝑡
b) 𝑒−𝑎𝑡
c) 𝑒 𝑡
d) 𝑒−𝑡

18. 13.a) 𝑒 𝑎𝑡
14. Findthe laplace inverseof X(s)=
1
(𝑠−𝑎)2
a) 𝑡𝑒−𝑎𝑡
b) t𝑒 𝑡
c) 𝑡𝑒−𝑡
d) 𝑡𝑒 𝑎𝑡
14.d) 𝑡𝑒 𝑎𝑡
15.Findthe inverse Fouriertransformof 𝜕(𝜔 + 𝜔0)
a) j𝜋𝜔
b)
𝑗
𝜋𝜔
c)
𝑒−𝑗𝜔𝑡0
2𝜋
d)
𝑒−𝑠𝑡0
2𝑠
15.c)
𝑒−𝑗𝜔𝑡0
2𝜋
16. FindFouriertransform of x(t-3)
a) e−j3ωX(-jω)
b) e−j3ωX(jω)
c) ej3ωX(-jω)
d) ej3ωX(jω)
16.b) e−j3ωX(jω)
17. FindFouriertransform of x(𝒕) =x(2-t)
a) e−j2ωX(-jω)
b) e−j2ωX(jω)
c) ej2ωX(-jω)
d) ej2ωX(jω)
17.a) e−j2ωX(-jω)
   2(txF e−j2ωX(-jω)
    jXtxF 

19. 17. FindFouriertransform of x(𝒕) =x(-2-t)
a) e−j2ωX(-jω)
b) e−j2ωX(jω)
c) ej2ωX(-jω)
d) ej2ωX(jω)
17.c) ej2ω X(-jω)
19. FindLaplace transform of x(t)=2𝑒−2𝑡 𝒖(𝒕)+4𝑒−4𝑡 𝒖(𝒕)
a)
2
𝑠+2
+
4
𝑠−4
b)
2
𝑠+2
−
4
𝑠+4
c)
2
𝑠−2
+
4
𝑠−4
d)
2
𝑠+2
+
4
𝑠+4
19.d)
2
𝑠+2
+
4
𝑠+4
20.FindLaplace transform of x(t)=𝑒−5(𝑡−5) 𝒖(𝒕-5)
a)
𝑒−5𝑠
𝑠+5
b)
𝑒−𝑠
𝑠+5
c)
𝑒−(𝑠+5)
𝑠+5
d)
𝑒−(𝑠+5)
𝑠−5
20.a)
𝑒−5𝑠
𝑠+5
21.FindLaplace transform of x(t)=- 𝑡𝑒−2𝑡 u(t)
a)
1
(𝑠+2)2
b)
𝑠
(𝑠−2)2
c)
𝑠
(𝑠+2)2
d)
−1
(𝑠+2)2
21.d)
−1
(𝑠+2)2

20. 22.Determine the initial value of the following function 𝑋( 𝑠) =
3
𝑠2+5𝑠−1
a) 0
b) 1
c) ∞
d) -1
22.a)0
(0) = lim
𝑠→∞
𝑆𝑋(𝑆)
23.Determine the Final value of the following function 𝑋( 𝑠) =
𝑠 −1
𝑠(𝑠+1)
a) 0
b) 1
c) ∞
d) -1
23.d)-1
𝑥(∞) =lim
𝑠→0
𝑆𝑋(𝑆)
24.FindLaplace transform of x(t)= 𝑒−2𝑡Sin2𝑡u(t)
a)
2
(𝑠+2)2−4
b)
2
(𝑠+2)2+4
c)
2
(𝑠−2)2+4
d)
1
(𝑠+2)2+4
24.b)
2
(𝑠+2)2+4
25.Find the convolution of 𝑒−2𝑡 𝑎𝑛𝑑 𝑒−3𝑡
a)
1
𝑠+2
+
1
𝑠−3
b)
1
𝑠+2
−
1
𝑠−3
c) (
1
𝑠+2
)(
1
𝑠+3
)
d) (
1
𝑠+2
)(
1
𝑠−3
)

21. 25.c) (
1
𝑠+2
) (
1
𝑠+3
)