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What happened to the peak structure:

In case you are wondering why the peaks in Figure 9 have less structure than the peaks in Figure 7 , this is because the points at which I computed the spectral data in Figure 9 were twice as far apart as the points at which I computed the spectral data in Figure 7 .

(The total frequency range in Figure 9 is twice as wide as in Figure 7 , but I computed the same number of points in both cases.)

Although it's not obvious at this plotting scale, there are zero-valued points between the side lobes on the peaks in Figure 7 .

The points in the spectral display of Figure 9 simply missed the side lobes and hit the zeros between the side lobes. I willhave a lot more to say about this in a future module discussing spectral analysis.

Back to the case with the sampling problem

Now let's take another look at the case with the sampling problem. This is the case where the sampling frequency was reduced from four samples per secondto two samples per second but the frequencies of the sinusoids was not changed. This view of the problem is shown in Figure 10 . It will probably be useful for you to compare Figure 10 with Figure 8 .

Figure 10. Spectral analyses of five sinusoids with sampling problem
missing image

Folding frequency is at the center

As with the previous case, each of the plotted spectra in Figure 10 shows the frequency range from zero frequency to the sampling frequency of two samples persecond. The folding frequency of one cycle per second appears in the center of each plot.

Peaks to left correspond to Figure 8

The peaks to the left of center in Figure 10 correspond to the peaks in Figure 8 . Because the right edge of Figure 8 is the folding frequency, the peaks to the right of center in Figure 10 don't appear in Figure 8 .

A mirror image

As is always the case, everything to the right of the folding frequency in Figure 10 is a mirror image of everything to the left of the folding frequency.

I have identified the artifacts created by the sampling process with a red oval in Figure 10 .

Raw data frequency exceeds folding frequency

The problem, as you will recall, is that the frequency of the sinusoids corresponding to the two bottom plots in Figure 10 is above the folding frequency. Thus the peaks to the right of center in the bottom two plots of Figure 10 actually represent the frequencies of the corresponding sinusoids.

Unfortunately, these two peaks appear to the right of the folding frequency, which the area of the spectra that we normally ignore.

Artifacts to the left of the folding frequency

Furthermore, these two peaks are reflected through the folded mirror image process into the area to the left of the folding frequency. For these twosinusoids, the peaks to the left of the folding frequency are artifacts, and I have identified them as such with ovals.

Normally can't identify artifacts

I am able to identify these two peaks as artifacts only because I know the true frequency makeup of the raw data. In most real-world situations withunknown data, there would be no way for me to identify these particular peaks to the left of the folding frequency as artifacts.

Questions & Answers

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
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
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
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
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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