4.4 Java1485-spectrum analysis using java, forward and inverse

Revised: Sat Oct 17 17:00:21 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
• Preview
• Discussion and sample code
  • Description of the program named Dsp035
    • The order of the plotted results
    • The format of the plots
    • The forward Fourier transform
    • The inverse Fourier transform
    • Results
  • The program named Dsp035
    • The beginning of the class named Dsp035
    • Beginning of the constructor
    • Compute the complex spectrum
    • Perform the inverse Fourier transform
  • The InverseComplexToReal01 class
    • Parameters for the inverseTransform method
    • Beginning of the inverseTransform method
  • The program named Dsp036
    • The output from Dsp036
    • Some code from Dsp036
    • The signature of the complexToComplex method
  • Using a Fourier transform to perform frequency filtering
    • Operation of the program
    • Beginning of the class for Dsp037
    • Beginning of the constructor
    • Compute the Fourier transform
    • Apply the filter to the frequency data
    • Re-compute the magnitude
    • Compute the inverse Fourier transform
    • Display the results
  • One more example, Dsp038
    • Compare the results
• Run the programs
• Summary
• Complete program listings
• Miscellaneous

Preface

A previous module titled Fun with Java, How and Why Spectral Analysis Works explained some of the fundamentals regarding spectral analysis.

The module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm presented and explained several Java programs for doing spectral analysis, including both DFT programs and FFT programs. That module illustratedthe fundamental aspects of spectral analysis that center around the sampling frequency and the Nyquist folding frequency.

The module titled Spectrum Analysis using Java, Frequency Resolution versus Data Length used similar Java programs to explain spectral frequency resolution.

The module titled Spectrum Analysis using Java, Complex Spectrum and Phase Angle explained issues involving the complex spectrum, the phase angle, and shifts in the timedomain.

This module will illustrate and explain forward and inverse Fourier transforms using both DFT and FFT algorithms. I will also illustrate andexplain the implementation of frequency filtering by modifying the complex spectrum in the frequency domain and then transforming the modified complexspectra back into the time domain.

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. Forward and inverse transform of a time series using DFT algorithm.
• Figure 2. Forward and inverse transform of a time series using FFT algorithm.
• Figure 3. The signature of the complexToComplex method.
• Figure 4. Filtering in the frequency domain.
• Figure 5. Filtering in the frequency domain.