<< Chapter < Page Chapter >> Page >

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

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?