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The individual terms

I'm not going to plot the individual sinusoidal terms in the triangular waveform. After the first couple of terms, they have such a small amplitude thatit is difficult to see them.

So what ?

By now, you are may be saying "So what?" What in the world does DSP have to do with bags of sand with holes in the bottom? The answer is everything.

Almost everything that we will discuss in the area of DSP is based on the premise that every time series, whether generated by sand leaking from a bagonto a moving carpet, or acoustic waves generated by your favorite rock band, can be decomposed into a large (possibly infinite) number of sine and cosine waves, each having its own amplitude and frequency.

A practical example

You have probably seen, the kind of stereo music component commonly known as an equalizer. An equalizer typically has about a dozen adjacent slider switchesthat can be moved up and down to cause the music that you hear to be more pleasing. This is a crude form of a frequency filter .

Many equalizers also have a set of vertical display lights that dance up and down as your music is playing. This is a crude form of a frequency spectrum analyzer .

The frequency filters

The purpose of each slider is to attenuate or amplify a band of adjacent frequencies (sine and cosine components, each having its own amplitude and frequency), before they make their way to the output amplifier and impinge on the system speakers. Thus, while you don't have the ability to attenuate oramplify each individual sine and cosine component, you do have the ability to attenuate or amplify them in groups.

In subsequent modules, we will learn how to use digital filters to attenuate or amplify the sine and cosine waves that make up a time series.

The spectrum analyzer

At an instant in time, the height of one of the vertical display lights is an indication of the combined power of the sine and cosine waves contained in asmall band of adjacent frequencies.

In subsequent modules, you will learn how to use Fourier analysis to perform spectral analysis on time series.


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

I used the example of a pendulum to introduce the concepts of periodic motion, harmonic motion, and sinusoids.

I introduced you to the concept of a time series.

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

I told you that almost everything we will discuss in this series on DSP is based on the premise that every time series can be decomposed into a largenumber of sinusoids, each having its own amplitude and frequency.

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

I introduced you to the concept of radians versus cycles.

I introduced you to the concept of decomposing a time series into a (possibly very large) set of sinusoids, each having its own frequency and amplitude. I told you that we will learn more about this later when we discuss frequencyspectrum analysis.

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

I showed you examples of using composition to create a square waveform and a triangular waveform.

I identified the frequency equalizer in your audio system as an example of frequency filtering.

I identified the frequency display that may appear on your frequency equalizer as an example of real-time spectrum analysis


This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Dsp00100: Digital Signal Processing (DSP) in Java, Periodic Motion and Sinusoids
  • File: Dsp00100.htm
  • Published: 12/01/02

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.


Financial : Although the Connexions site makes it possible for you to download a PDF file for thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing me as the author. Ineither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, please beaware that it is a copy of a module that is freely available on cnx.org and that it was made and published withoutmy prior knowledge.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.


Questions & Answers

who was the first nanotechnologist
Lizzy Reply
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Norio Taniguchi
I need help
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
Naeem Reply
what happen with The nano material on The deep space.?
pedro Reply
It could change the whole space science.
the characteristics of nano materials can be studied by solving which equation?
sibaram Reply
plz answer fast
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
hydrothermal synthesis
how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
STM - Scanning Tunneling Microscope.
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