# 2.1 Dsp00104-sampled time series  (Page 7/10)

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## The locations of the spectral peaks

The spectral peaks in Figure 7 appear where you would expect to see them. For example, the location of the peak in the first plot corresponds to a frequencyof 0.25 cycles per second within a total frequency range extending from zero to two cycles per second. This matches the information given in the above table forthe first sinusoid.

The location of the spectral peak in the fifth plot corresponds to a frequency of 1.75 cycles per second within a total frequency range extendingfrom zero to two cycles per second. This matches the information given in the above table for the fifth sinusoid.

The location of the peak in each of the three plots between the first and the last are correct for the frequency of the sinusoid involved.

## Introduce a sampling problem

Now I will introduce a sampling problem by keeping the frequencies of the sinusoids the same and reducing the sampling frequency from four samples persecond to two samples per second.

The result of this change is shown in Figure 8 .

Figure 8. Spectral analyses of five sinusoids with sampling problem.

As before, each of the plots in Figure 8 shows the frequency spectrum of an individual sinusoid. The spectrum is plotted from zero frequency on the left tothe folding frequency on the right.

## Sampling frequency was two samples per second

In this case, the sampling frequency was two samples per second, giving a folding frequency of one cycle per second. Therefore, the horizontal scale oneach plot represents the frequencies from zero on the left to one cycle per second on the right.

## The heights of the spectral peaks

Once again, the height of each spectral peak is consistent with the amplitude of the sinusoid.

## The locations of the spectral peaks

As before, the spectral peaks in the first three plots appear where you would expect to see them. The peak in the first plot is about twenty-five percent ofthe way across the total spectrum, corresponding to 0.25 cycles per second.

The spectral peak in the second plot is at the center, corresponding to 0.5 cycles per second. The third peak is in the correct location for 0.75 cycles persecond.

## A problem with the location of two spectral peaks

However, a problem exists with the spectral peaks in the last two plots.

(I marked the two problem peaks with a red oval to make it obvious which ones I am talking about. You may find it helpful to compare Figure 8 side-by-side with Figure 7 .)

The spectral peak in the fourth plot also appears about midway between zero and one cycle per second. This indicates that the corresponding sinusoid had afrequency of 0.5 cycles per second.

However, the frequency of the sinusoid for the fourth plot was 1.50 cycles per second, not 0.5 cycles per second as indicated. Thus, that spectral peakshould have been off the scale on the right-hand side of the plot.

## The folding frequency

Recall, however, that the right edge of the plot is the folding frequency. Therefore, any spectral components that should appear to the right of thefolding frequency fold around and appear to the left of the folding frequency. Therefore, the spectral peak in the fourth plot, which should appear at 0.50cycles per second above the folding frequency, appears instead at 0.50 cycles per second below the folding frequency.

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
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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