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 :
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