# 2.2 Dsp00108-averaging time series

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Baldwin begins with a discussion of averaging time series, and ends with a discussion of spectral resolution, covering several related topics in between.

Revised: Fri Oct 16 23:12:34 CDT 2015

## Preface

This is one in a series of modules designed to teach you about Digital Signal Processing (DSP) using Java. The purpose of the miniseries is topresent the concepts of DSP in a way that can be understood by persons having no prior DSP experience. However, some experience in Java programmingwould be useful. Whenever it is necessary for me to write a program to illustrate a point, I will write it in Java.

## Some of what you have previously learned

In a previous module, I explained the meaning of sampling, and discussed some of the problems that occur as a result of high-frequency componentsin the analog signal.

Measure and record the signal amplitude

I told you that to sample an analog signal means to measure and record its amplitude at a series of points in time. The values that you record constitute a sampled time series intended to represent the analog signal.

Avoiding frequency folding

I told you that to avoid problems, the sampling frequency must be a least twice as great as the highest frequency component contained in the analogsignal, and as a practical matter, should probably be somewhat higher.

Sinusoids, frequency, and period

I introduced you to sinusoids, taught you about sine and cosine functions, and introduced the concepts of period and frequency for sinusoids.

Decomposition of time series

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.

The notion of DSP

I told you that DSP is based on the notion that signals in nature can be sampled and converted into a series of numbers. The numbers can be fed into somesort of digital device, which can process the numbers to achieve some desired objective.

## 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 Figureswhile you are reading about them.

## Figures

• Figure 1 . Products of sinusoids.
• Figure 2 . Products of sinusoids.
• Figure 3 . More products of sinusoids.
• Figure 4 . Five Sampled Sinusoids.
• Figure 5 . Computed average value of a time series.
• Figure 6 . Expanded average value of a time series.
• Figure 7 . Computed average value of a time series.
• Figure 8 . Computed average value of a time series.
• Figure 9 . Computed average value of a time series.
• Figure 10 . Spectra of five different sinusoids of different lengths.
• Figure 11 . Spectra of five different sinusoids of different lengths.
• Figure 12 . Spectra of five different time series of different lengths.
• Figure 13 . Spectra of five different time series of different lengths
• Figure 14 . Average values of sinusoid products.
• Figure 15 . Illustration of frequency resolution.
• Figure 16 . Illustration of frequency resolution.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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