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

Wednesday, 16 January 2013 06:15Web

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

ANNA UNIVERSITY (2 Marks) QUESTIONS WITH ANSWERS

UNIT-II

FOURIER TRANSFORM

TWO MARKS

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)

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