# 4.3 Java1484-spectrum analysis using java, complex spectrum and

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Baldwin discusses the complex spectrum and explains the relationship between the phase angle and shifts in the time domain.

Revised: Fri Oct 16 18:22:28 CDT 2015

## Preface

Spectral analysis

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.

In this module, I will deal with issues involving the complex spectrum, the phase angle, and shifts in 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. Sample parameters for testing.
• Figure 2. Spectral analysis of a damped pulse.
• Figure 3. Fourier transform equations.
• Figure 4. The simplest pulse of all, an impulse.
• Figure 5. Spectral analysis of an impulse at zero time.
• Figure 6. Introduce a time delay.
• Figure 7. Spectral analysis of an impulse with a one-sample delay.
• Figure 8. Introduce a large time delay.
• Figure 9. Spectral analysis of impulse with five-sample delay.
• Figure 10. A boxcar pulse.
• Figure 11. Spectral analysis of 11-sample boxcar pulse.
• Figure 12. Shift the time base.
• Figure 13. Spectral analysis of 11-sample boxcar centered in time.

## Preview

In this module, I will present and explain a program named Dsp034 . This program will be used to illustrate the behavior of the complex spectrum andthe phase angle for several different scenarios.

In addition, I will use the following programs that I explained in the module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm .

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