4.2 Java1483-spectrum analysis using java, frequency resolution

Revised: Fri Oct 16 23:18:32 CDT 2015

This page is included in the following books:

• Digital Signal Processing - DSP

Table of contents

• Table of contents
• Preface
  • Viewing tip
    • Figures
    • Listings
• Preview
• Discussion and sample code
  • Five pulses in the time domain
    • The lengths of the pulses
  • The program named Dsp031a
    • Time series containing sinusoidal pulses
    • Beginning of the class named Dsp031a
    • Spectral analysis results
  • The program named Dsp031
    • Description
    • Uses a DFT algorithm
    • Beginning of the class named Dsp031
    • Perform the spectral analysis
  • Separating closely spaced frequencies
    • Five new pulses
  • The program named Dsp032a
    • Spectral analysis output
  • The program named Dsp032
    • One more experiment
    • The five pulses
    • Spectral analysis results
  • The program named Dsp033
    • The spectral analysis
• Run the programs
• Summary
• What's next?
• Complete program listings
• Miscellaneous

Preface

The how and the why of spectral analysis

A previous module titled Fun with Java, How and Why Spectral Analysis Works explained some of thefundamentals regarding spectral analysis. An understanding of that module is a prerequisite to an understanding of this module.

Another previous module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm presented and explained several Java programs for doing spectral analysis. In that module, I used a DFT program to illustrate several aspects ofspectral analysis that center around the sampling frequency and the Nyquist folding frequency.

I also used and briefly explained two different plotting programs that were originally explained in the earlier module titled Plotting Engineering and Scientific Data using Java .

An understanding of the module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm is also a prerequisite to an understanding of this module.

Frequency resolution versus data length

In this module I will use similar programs to explain and illustrate the manner in which spectral frequency resolution behaves with respect to datalength.

A hypothetical situation

Consider a hypothetical situation in which you are performing spectral analysis on underwater acoustic signals in an attempt to identify enemysubmarines.

You are aware that the enemy submarine contains a device that operates occasionally in short bursts. You are also aware that this device contains tworotating machines that rotate at almost but not quite the same speed.

During an operating burst of the device, each of the two machines contained in the device will emit acoustic energy that may appear as a peak in yourspectral analysis output. (Note that I said, "may appear" and did not say, "will appear.") If you can identify the two peaks, you can conclusively identify the acoustic source as an enemy submarine.

The big question

How long must the operating bursts of this device be in order for you to resolve the peaks and identify the enemy submarine under ideal conditions? Thatis the question that I will attempt to answer in this module by teaching you about the relationship between frequency resolution and data length.