FREQUENCY DOMAIN
•
Frequency domain analysis
•
In spatial domain signals are analyzed with
respect to time.
•
In frequency domain, signals are analyzed with
respect to frequency.
•
In spatial domain, images are dealt with as is.
The value of the pixels of the image change with
respect to scene.
•
Frequency domain, deals with the rate at which
the pixel values are changing in spatial domain.
10/22/2019
1

•
Spatial domain
•
In simple spatial domain, we directly deal with
the image matrix.
10/22/2019
2

•
Frequency Domain
•
First, transform the image to its frequency distribution.
•
Then the black box system perform whatever
processing it has to, and the output of the black box,
an image, is a transformation.
•
After performing inverse transformation, it is
converted into an image which is then viewed in
spatial domain.
10/22/2019
3

•
Transformation
–
A signal can be converted from time domain into
frequency domain using mathematical operators
called transforms which include.
•
Fourier Series
•
Fourier transformation
•
Laplace transform
•
Z transform
10/22/2019
4

•
Frequency components
•
Any image in spatial domain can be
represented in a frequency domain.
•
Frequency components can be divided into
two major components.
–
High frequency components
•
High frequency components correspond to edges in an
image (High contrast/conspicuous).
–
Low frequency components
•
Low frequency components in an image correspond to
smooth regions (Low contrast/Blurred).
10/22/2019
5

•
Fourier Series and Transform
–
Fourier series and Fourier transform are used to convert a
signal to frequency domain.
•
Fourier
–
Fourier was a mathematician in 1822. He gave Fourier
series and Fourier transform to convert a signal into
frequency domain.
•
Fourier Series
–
Fourier series simply states that, periodic signals can be
represented into sum of sines and cosines when multiplied
with a certain weight.
–
It further states that periodic signals can be broken down
into further signals with the following properties.
•
The signals are sines and cosines
•
The signals are harmonics of each other
10/22/2019
6

•
Pictorially
•
In this signal, the last signal is
actually the sum of all the
above signals. This was the
idea of the Fourier.
•
Computing Fourier Series
–
To process an image in frequency domain, get its
frequency distribution, transform it, and take inverse
of the output to convert it back into spatial domain.

#### You've reached the end of your free preview.

Want to read all 30 pages?

- Summer '16
- Hardy James