Dsp00100-periodic motion and sinusoids

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

This page is included in the following books:

• Digital Signal Processing - DSP

Table of contents

• Preface
  • Viewing tip
    • Figures
• Preview
• Discussion and sample code
  • Periodic motion
    • Motion of a pendulum
    • A bag of sand
  • Harmonic motion
  • Sinusoids
    • Separate the cosine and sine components
    • Plotting separate sine and cosine functions
  • Time varying functions
  • Sampled data
  • The period of the sine and cosine functions
    • Different periods or frequencies
    • Modified arguments
    • Why does pi appear in the arguments?
    • Radians versus cycles
    • The horizontal scale
    • The argument to the sine and cosine functions
    • Where does sin(arg) equal zero?
    • Where are the peaks in the cosine function?
  • Composition and decomposition
    • An approximate square waveform
    • Successive approximations
    • An approximate triangular waveform
  • So what?
  • A practical example
    • The frequency filters
    • The spectrum analyzer
• Summary
• Miscellaneous

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.