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
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)
Ans :
****************************************
Earning: Approval pending. |