4.6 Java1490-2d fourier transforms using java, part 1

Revised: Tue Oct 20 11:48:13 CDT 2015

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

Table of contents

• Table of contents
• Preface
  • Two separate programs
    • Digital signal processing (DSP)
    • Will use in subsequent modules
  • Viewing tip
    • Figures
• General discussion
  • Time domain and frequency domain
    • A one-dimensional Fourier transform
    • Time domain data is purely real
    • The space domain
    • Time and space are analogous
    • Frequency and wavenumber are analogous
    • Period and wavelength are analogous
  • Some real world examples
    • A commercial radio station
    • Basic concepts
    • A one-dimensional space
    • How can we compute the array response?
    • Three example wavenumber spectra
    • Plots of 3D surfaces
    • A wavenumber filter
    • Let's apply some weights
    • A weighted three-element array
    • A three-element array with negative weighting
    • What can we learn from these scenarios?
  • Extending into two dimensions
    • Move the array to a table top
    • The 2D wavenumber response of a linear array
  • A two-dimensional array
    • Computing the wavenumber response
  • Arrays are used in various applications
    • Radio astronomy
    • Seismology
    • Sonar
    • Radar
    • Petroleum exploration
    • Image processing
• Summary
• What's next?
• Miscellaneous

Preface

This is the first module of a two-part series. In this module, I will:

• 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

Two separate programs

In Part 2 of this series, I will present and explain two separate programs. One program consists of asingle 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 ..

Digital signal processing (DSP)

This and the following module will cover some technically difficult material in the general area of Digital Signal Processing, or DSP for short. As usual, the betterprepared you are, the more likely you are to understand the material. For example, it would be well for you to already understand the one-dimensionalFourier transform before tackling the 2D Fourier transform. If you don't already have that knowledge, you can learn about one-dimensional Fourier transforms bystudying the following modules :