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An expanded view

Figure 6 shows a greatly expanded view of the red average values in Figure 5 .

Figure 6. Expanded average value of a time series.
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The ideal value for this average is 0.5, and that is the value represented by the blue line. The plot in Figure 6 shows the same horizontal scale as Figure 5 . However, the entire vertical plotting area in Figure 6 represents the values from 0.48 to 0.52.

Ideal value is never reached

As you can see, the ideal value is never reached in Figure 6 except at isolated points where the red curve crosses the horizontal line. Even if Iextended the horizontal axis to 1200 or more points, that would continue to be the case.

A more serious case

Figure 7 computes and displays the average value of the bottom plot in Figure 2 (recall that this plot shows 1200 points on the horizontal axis, whereas Figure 5 shows only 400 points on the horizontal axis). Recall also that this time series was produced by multiplying two sinusoids having nearly thesame but not exactly the same frequency.

Figure 7. Computed average value of a time series.
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Red curve is the average

As before, the black curve in Figure 7 shows the time series, and the red curve shows the computed average value as a function of the number of pointsincluded in the average.

(In this case, I didn't even bother to show the short axis containing only 400 points. The horizontal axis in Figure 7 contains 1200 points, the same as in Figure 2 .)

The ideal average value is zero

In this case, the ideal average value is zero, as indicated by the green horizontal axis. As you can see, even for a 1200-point averaging window, theaverage value deviates significantly from the ideal. We will see the detrimental impact of this problem later when I perform spectral analysis in an attempt toseparate two closely-spaced peaks in the frequency spectrum.

Some additional examples of average values

Figure 8 computes and displays the average value of the third plot down from the top in Figure 3 . This plot was produced by multiplying the two sinusoids in the top two plots in Figure 3 .

Figure 8. Computed average value of a time series.
missing image

As before, the black curve in Figure 8 represents the time series, and the red curve represents the computed average value of the time series as a functionof the number of points included in the average.

For this case also, the ideal average value is zero, as represented by the green horizontal axis. The positive and negative peaks in the red average valuecan be seen to approach the ideal value asymptotically within the 400 horizontal points plotted in Figure 8 .

Figure 9 computes and displays the average value of the bottom plot in Figure 3 . This time series was produced by multiplying the top plot in Figure 3 by the fourth plot in Figure 3 .

Figure 9. Computed average value of a time series.
missing image

Once again, the black curve in Figure 9 represents the time series, and the red curve represents the computed average value of the time series as a functionof the number of points included in the average. In this case, the average converges on zero rather nicely within the 400 points included on the horizontalaxis.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket 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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