Biology Reference
In-Depth Information
236
FOURIER TRANSFORM
As we have discussed in Chapter 8, X-ray diffraction study connects the
physical space
x
to the reciprocal space
h
. Similarly, time t can be related to
frequency Such connections are through a mathematical operation known
as Fourier transform. The Fourier transform
of a function f(t) can be
defined as (Carrier
et al
., 1966):
and the inverse Fourier transform is:
This transform and many other transforms are valuable mathematical tools
to solve differential and integral equations. One of the important results is
the Convolution Integral which gives an expression for the inverse Fourier
transform of the product of two Fourier transforms:
Cochran
et al.
(1952) used this result to derive the X-ray diffraction pattern
of a discontinuous helix as the summation of various Bessel functions.
