Continuous Time Fourier Analysis
7
Chapter Test Signals and Systems : 080-617 66 222, [email protected] ©Copyright reserved. Web:www.thegateacademy.com 1 Continuous Time Fourier Analysis Answer Keys and Explanations 1. [Ans. B] () () 2. [Ans. D] () → () ( ) → ( ) → ( ) ( ) → () ( ) () 3. [Ans. B] () ∫ () () () () () ( ) () 4. [Ans. *] Range: 2 to 2 () → ∫ () () ∫ () ()
Transcript of Continuous Time Fourier Analysis
Chapter Test Signals and Systems
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Continuous Time Fourier Analysis
Answer Keys and Explanations
1. [Ans. B]
( )
( )
2. [Ans. D]
( ) →
( ) ( ) →
( ) →
( )
( ) → ( )
( )
( )
3. [Ans. B]
( ) ∫ ( )
( ) ( ) ( )
( )
( )
( )
4. [Ans. *] Range: 2 to 2
( ) →
∫ ( ) ( )
∫ ( )
( )
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5. [Ans. A]
( ) →
( ) →
( ) →
( ) →
( )
6. [Ans. A]
( )
( )
7. [Ans. C]
Fourier Transform is only applicable for energy and power signal.
( )
8. [Ans. A]
( )
( )
( )
9. [Ans. C]
( ) → ( )
[ (
)] →
*
+
10. [Ans. C]
Trigonometric Fourier series of an odd function contain only sine harmonics of all term.
( )
( )
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11. [Ans. B]
( ) →
( ) →
( )
12. [Ans. C]
( ) ( ) ( ) → ( ) ( ) ( )
*
+ →
( )
( )
( )
→ [
]
( )
( )
( )
→ *
+
( )
( )
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13. [Ans. C]
( ) → ( ) → ( ) ( )
( ) ( ) →
( ) ( ) →
( ) ( ) ( ) → ( ) (
) (
)
( )
( )
( )
( )
√( ) ( )
√
√
( )
14. [Ans. *] Range:2.5 to 2.5
( )
( )
→ ( )
( ) →
( )
( )
( )
( )
→ (
)
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( ) →
( ) →
( )
15. [Ans. *] Range: 0.5 to 0.5
( ) ∑
∫ ( ) ( )
( )
∫ ( )
( )
16. [Ans. A]
( ) (
) *
+
[
]
( )
( )
( )
( )
( ) →
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17. [Ans. B]
( )
Let
( ) →
( ) →
( ) →
{ }
( )
18. [Ans. D]
( )
( )
( ) ( ) ( ) →
( ) ( )
( )
( )
( ) ( )
( )
→
→
→
( )
(
) →
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19. [Ans. C]
x(t) ( )
1. [Real + Even] [Real + Even]
2. Real + odd Imaginary + odd
3. Imaginary + even Imaginary + even
4. Imaginary + odd Real + odd
( )
20. [Ans. *] Range: 0.125 to 0.125
( ) ( )
∫ ( )
→
2nd Method:
( )
→
∫ ( )
∫ (
)
[
]
[
]
( )
→
( )
[
] →
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