# Fourier Transform Sine

Document Sample

```					                   Fourier Transform Sine
To learn Fourier Transform Sine ,let’s have a look at Fourier transform of a
function. Transformation refers to the change of one function into another
function.

This can be achieved by various transformation formulae defined by different
mathematicians. Following are few important transformation formulae: Laplace
transform Fourier transform Hankel transform Mellin transform.

These all transformations are widely used in the field of engineering and
research.

As we have already discussed about Laplace transform of a function, now let’s
discuss about another important and interesting transformation i.e. Fourier sine
Transforms.

Know More About Real World Problems with Rational Numbers
To study Fourier sine transform lets first define Fourier transform of a function: If
k(s,x) = eisx, then the Fourier transform of a function f(x) can be defined by the
formula F(s) = -∞∫ -∞f(x)eisxdx.

This is an definite integral which has -∞ and +∞ as lower and upper limits.
Fourier transform is classified into two transforms i.e. Fourier sine transform and
Fourier cosine transform, Now let’s define,

Fourier sine transform: Fourier sine transform is also given by a Fourier sine
integral which can be defined as F(x)= 2/π∞∫ 0 [sinλx]dx ∞∫ 0 f(t) sinλtdtdλ, now
to obtain the Fourier transform sine, we have to perform some changes in the
above Fourier sine integral,

First of all replacing λ by s, we get f(x)= 2/π∞∫ 0 [sinsx]dx ∞∫ 0 f(t) sinstdtds
Now, in this integral denote the value of the inner integral i.e. ∞∫ 0 [sinsx]dx by
F(s) we have F(x)= 2/π∞∫ 0 F(s)sinsxdx And F(s)= ∞∫ 0 [sinsx]dx In the above
two expressions the function defined by f(s) is known as the Fourier transform
sine of the function f(x) in the interval 0<x>∞.

To solve the problems involving “Fourier transform sine” we should have good
knowledge of integral calculus.

Thank You

TutorCircle.com

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 6 posted: 3/9/2012 language: pages: 3
How are you planning on using Docstoc?