Connexions

You are here: Home » Content » Image Querying with Complex Wavelets: The 2D Discrete Fourier Transform
Content Actions
Lenses

What is a lens?

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

  • This module is included inLens: Rice University ELEC 301 Project Lens
    By: Rice University ELEC 301As a part of collection:"ECE 301 Projects Fall 2003"

    Click the "Rice University ELEC 301 Projects" link to see all content affiliated with them.

    Rice University ELEC 301 Projects

  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collection:"ECE 301 Projects Fall 2003"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Image Querying with Complex Wavelets: The 2D Discrete Fourier Transform

Module by: Tom Mowad, Venkat Chandrasekaran

Summary: Introduces the 2D DFT.

The two-dimensional Discrete Fourier Transform is another important transform in image processing. It is taken by applying the one-dimensional transform to each row, and then to each column, as seems to be the common practice for increasing the dimension of transforms in signal and image processing.
The 2D DFT has many properties that are useful in image processing; however, most useful is its shift invariance. The DFT of an image and its shifted version differ only by the multiplication with a complex exponential. Since multiplication by a complex exponential changes the phase but not the magnitude, taking the magnitude of the DFT of an image can give us a different kind of “shift-invariance”; that is, the DFT of two versions of the same thing will, rather than being shifted versions of one another, be identical.
High frequency basis function.
real.jpg
Figure 1: Real part of a 2D DFT basis function

Comments, questions, feedback, criticisms?

Send feedback