4.5 Java1486-fun with java, understanding the fast fourier transform

Revised: Mon Oct 19 13:36:25 CDT 2015

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

Table of contents

• Table of contents
• Preface
  • Viewing tip
    • Figures
    • Listings
• General discussion
  • A general-purpose transform
  • Transforming from space domain to wave number domain
    • Two-dimensional Fourier transforms
    • Wave-number response to seismic waves
  • A general purpose mathematical transform
    • Fourier transform images
    • Will discuss underlying concepts
    • A linear transform
    • Output display of the FFT applet
    • Back to the concept of the linear transform
    • A mirror-image pulse
    • Now add the two input series
    • Single sample real pulse (impulse) with a delay
    • Equations to describe the real and imaginary parts of the transform
• A sample program
  • Separate processes in an FFT algorithm
    • How the processes are implemented
    • Three cases are examined
  • The program named Fft02
    • Instantiate a Transform object
    • The class named Transform
    • Performing the transform
    • The correctAndRecombine method
    • Back to the main method
    • The graphic form of Case A
    • The numeric output for Case A
    • Case B code
    • Case B in graphical form
    • Case B output in numeric form
    • Case C code
    • The graphic form of Case C
    • Case C output in numeric form
    • The display method
• Run the program
• Summary
• Complete program listings
• Miscellaneous

Preface

Programming in Java doesn't have to be dull and boring. In fact, it's possible to have a lot of fun while programming in Java. This module wastaken from a series that concentrates on having fun while programming in Java.

Viewing tip

I recommend that you open another copy of this module in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1. Transform of pulse with negative slope.
• Figure 2. Transform of pulse with positive slope.
• Figure 3. Transform of the sum of two pulses.
• Figure 4. Transform of an impulse with no shift.
• Figure 5. Transform of an impulse with a shift equal to one sample interval and a negative value.
• Figure 6. Transform of an impulse with a shift equal to two sample intervals and a positive value.
• Figure 7. Transform of an impulse with a shift equal to four sample intervals and a positive value.
• Figure 8. Transform of a complex impulse with a shift equal to two sample intervals.
• Figure 9. Case A. Transform of a real sample with two non-zero values.
• Figure 10. The numeric output for Case A.
• Figure 11. Case B in graphical form.
• Figure 12. Case B output in numeric form.
• Figure 13. The graphic form of Case C.
• Figure 14. Case C output in numeric form.

Listings

• Listing 1. Beginning of the program named Fft02?
• Listing 2. The class named Transform.
• Listing 3. Performing the transform.
• Listing 4. The correctAndRecombine method.
• Listing 5. The remainder of the main method.
• Listing 6. Case B code.
• Listing 7. Case C code.
• Listing 8. The display method.
• Listing 9. Fft02.java.

General discussion

The purpose of this module is to help you to understand how the Fast Fourier Transform (FFT) algorithm works. In order to understand theFFT, you must first understand the Discrete Fourier Transform (DFT). I explained how the DFT works in an earlier module titled Fun with Java, How and Why Spectral Analysis Works .