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Baldwin kicks off a new miniseries on DSP. He discusses periodic motion and sinusoids. He introduces time series analysis, sine and cosine functions, and frequency decomposition. He discusses composition, and provides examples for square and triangular waveforms.

Revised: Fri Oct 16 23:09:45 CDT 2015

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Table of contents

Preface

This module is the first in a series of modules designed to teach you about Digital Signal Processing (DSP) using Java. The purpose of theminiseries is to present the concepts of DSP in a way that can be understood by persons having no prior DSP experience. However, some experience in Javaprogramming would be useful. Whenever it is necessary for me to write a program to illustrate a point, I will write it 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 Figures while you are reading about them.

Figures

  • Figure 1 . A sinusoidal function.
  • Figure 2 . Complex harmonic motion.
  • Figure 3 . Separate cosine and sine functions.
  • Figure 4 . Sinusoid with frequency modification.
  • Figure 5 . An approximate square waveform.
  • Figure 6 . An improved approximate square waveform.
  • Figure 7 . First five sinusoidal components of a square waveform.
  • Figure 8 . A triangular waveform.

Preview

Many physical devices (and electronic circuits as well) exhibit a characteristic commonly referred to as periodic motion .

I will use the example of a pendulum to introduce the concepts of

  • periodic motion,
  • harmonic motion, and
  • sinusoids.

I will introduce you to the concept of a time series .

I will introduce you to sine and cosine functions and the Java methods that can be used to calculate their values.

I will introduce you to the concepts of period and frequency for sinusoids.

I will introduce you to the concept of radians versus cycles .

I will introduce you to the concept of decomposition by decomposing a time series into a (possibly very large) set of sinusoids, each having its own frequency and amplitude. (We will learn much more about this in a subsequent module when we discuss frequency spectral analysis.)

I will introduce you to the concept of composition , where (theoretically) any time series can be created by adding together the correct (possibly very large) set of sinusoids, each having its own frequency and amplitude.

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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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