4.7 Java1491-2d fourier transforms using java, part 2

Revised: Wed Oct 21 16:16:44 CDT 2015

This page is included in the following book: Digital Signal Processing - DSP

Table of contents

• Table of contents
• Preface
  • Two separate programs
    • Using the class named ImgMod30
    • Digital signal processing (DSP)
    • Will use in subsequent modules
  • Viewing tip
    • Figures
    • Listings
• General discussion
  • The space domain
  • A purely real space domain
• Preview
• Sample programs
  • The class named ImgMod30
    • The xform2D method
    • The inverseXform2D method
    • The shiftOrigin method
  • The program named ImgMod31
    • Command line parameters
    • Forward and inverse Fourier transforms
    • Fourteen cases
    • A stack of output images
    • Numeric output
    • How to use the program named ImgMod31
    • Program code for ImgMod31
  • Code and graphic output for fourteen example cases
    • Case 0
    • Case 1
    • Case 2
    • Case 3
    • Case 4
    • Case 5
    • Case 6
    • Case 7
    • Case 8
    • Case 9
    • Case 10
    • Case 11
    • Case 12
    • Case 13
• Run the program
• Summary
• Complete program listings
• Miscellaneous

Preface

This is the second module in a two-part series. The first part published earlier was titled Java1490-2D Fourier Transforms using Java, Part 1 . In this module, I will teach you how to perform two-dimensional (2D) Fourier transforms using Java. Iwill

• Explain the conceptual and computational aspects of 2D Fourier transforms
• Explain the relationship between the space domain and the wavenumber domain
• Provide sufficient background information that you will be able to appreciate the importance of the 2D Fourier transform
• Provide Java software to perform 2D Fourier transforms
• Provide Java software to test and exercise that capability

Two separate programs

I will present and explain two separate programs. One program consists of a single class named ImgMod30 . The purpose of this class is to satisfy the computational requirements for forward and inverse 2D Fouriertransforms. This class also provides a method for rearranging the spectral data into a more useful format for plotting. The second program named ImgMod31 will be used to test the 2D Fourier transform class, and also to illustrate the use of 2D Fourier transforms for some well known samplesurfaces.

A third class named ImgMod29 will be used to display various 3D surfaces resulting from the application of the 2D Fourier transform. Iexplained this class in an earlier module titled Plotting 3D Surfaces using Java .

Using the class named ImgMod30

The 2D Fourier transform class couldn't be easier to use. To perform a forward transform execute a statement similar to the following:

The first parameter in the above statement is a reference to an array object containing the data to be transformed. The other three parameters refer to arrayobjects that will be populated with the results of the transform.

To perform an inverse transform execute a statement similar to the following: