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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.

Summary

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

Miscellaneous

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.

Disclaimers:

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.

-end-

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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