# Anna University Coimbatore 2009 B.E Two k with Answers for Transforms and Partial Differential Equations( Unit-2) - Question Paper

__TRANSFORMS AND
PARTIAL DIFFERENTIAL EQUATIONS__

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__ANNA____ UNIVERSITY____ (2
Marks) QUESTIONS WITH ANSWERS__

__UNIT____-II__

__FOURIER TRANSFORM__

__TWO MARKS__

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1) Write the Fourier transform pair.

Ans :Let f(x) be a given function defined in (-∞,+∞) then the fourier transform is given by corresponding inverse formula is given by . Equation (1) & (2) jointly called as fourier transform pair.

2)
If is
the Fourier cosine transform of *f(x),* prove that the Fourier cosine
transform of f*(ax)* is .

Ans : we know that .

Put then

3)
If F(S) is Fourier
transform of *f(x)*, write the Fourier transform of *f(x)cos(ax)* in
terms of F.

Ans:

4) State the Convolution theorem for Fourier transforms.

Ans: The Fourier transform of the convolution of is the product of their Fourier transform. .

5) If F(S) is Fourier transform of f(x), then find the Fourier transform of f(x-a).

Ans :

6)
If is
the Fourier Sine transform of *f(x), *show that .

Ans:

7) Solve the integral equation . (April 2004)

Ans :

8)
Find the Fourier
transform of *f(x)* if .
(April 2004)

Ans :

9) Find the Fourier cosine transform of . (Nov 2004)

Ans :

10)
Find a) and
b) in
terms of the Fourier transform of *f *

(b)

11) State Fourier integral theorem. (April 2005) (May/June 2009)

Ans :

12) Find the Fourier Sine transform of . (April 2005),(Dec 2008)

Ans :

13) Find the Fourier transform of . (Nov/Dec 2005)

Ans:

14) Find the Fourier cosine integral representation of .

Ans :

15)
Find the Fourier
Sine transform of *f(x)=* .
(May 2006)

Ans :

16)
Prove that ,
*a>0. *(May 2006)

Ans :

17) If then give the value of . (May 2006)

Ans : Sama as 16

18) Find the Fourier transform of . (May 2006)Ans :

19)
Find the Fourier
cosine transform of *f(x) *defined as

. (Nov/Dec 2006) Ans :

20) P.T where . (M/J 2007)

Ans :

21) Write down the Fourier cosine transform pair formulae. (M/J 2007)

Ans:

22) If prove that . (N/D 2003),(Nov 2005)

Ans :

23) Prove that if , then (Dec 2008)

Ans :

24) Find the Fourier transform of defined by

.(Dec 2008)

Ans:

25) Find the Fourier Cosine transform of . (Dec 2008)

Ans :

26) If , prove that . (Dec 2008)

Ans : By property,

27) Find the Fourier sine transform of . (Dec 2008)

Ans : We know that ,

28) State Parsevals identity on complex Fourier transforms. (Dec 2008)

29) If then prove that . (Dec 2008)

Ans :

30) State Modulation theorem in Fourier transform. (Dec 2008)

Ans :

31) Give a function which is self reciprocal under Fourier sine and cosine transforms. (Dec 2008)

Ans :

32) If , then prove that . (Dec 2008)

Ans :

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Earning: Approval pending. |