# 2.2 Dsp00108-averaging time series  (Page 7/14)

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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.

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.

## 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.

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.

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

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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