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The peak in the fifth plot

Similarly, the frequency of the sinusoid for the fifth plot was 1.75 cycles per second. The peak for this sinusoid should have appeared 0.75 cycles persecond above the folding frequency, but appeared instead 0.75 cycles per second below the folding frequency. In other words, the spectrum folded around thefolding frequency so that this peak appeared below the folding frequency.

I am going to show you two more views of the spectra of these sinusoids to help you better understand the folding phenomena.

Back to the case with no problems

Let's go back and examine another view of the case that has no sampling problems. This view is shown in Figure 9 .

Figure 9. Spectral analyses of five sinusoids with no sampling problems.
missing image

Sampled at four samples per second

This is the case where all five sinusoids are sampled at a sampling frequency of four samples per second, resulting in a folding frequency of two cycles persecond. If you compare Figure 9 with Figure 7 , you will see that the left half of Figure 9 is very similar to Figure 7 .

Figure 9 Shows twice the frequency range

In Figure 7 , the spectral data was computed and displayed from zero frequency on the left to the folding frequency (two cycles per second) on the right. In Figure 9 , the spectral data was computed and displayed from zero frequency on the left to the sampling frequency (four cycles per second) on the right.

Thus, the total frequency range for Figure 9 is twice the frequency range for Figure 7 .

Folding frequency at the center

In Figure 9 , the folding frequency is exactly in the center of each plot. In other words, the center of the plots in Figure 9 corresponds to the right edge of the plots in Figure 7 . Everything to the left of center in Figure 9 corresponds to the plots in Figure 7 . The material to the right of center in Figure 9 was not shown in Figure 7 .

Why is it called the folding frequency?

Hopefully the display in Figure 9 will explain why the frequency that is half the sampling frequency is called the folding frequency. The computed spectrumfolds around that frequency. Everything to the right of the folding frequency is a mirror image of everything to the left of the folding frequency.

Peaks below folding frequency are valid

All the peaks to the left of center in Figure 9 are valid spectral peaks associated with the corresponding sinusoids. However, all the peaks to the rightof center, which I marked with red ovals, are artifacts of the sampling process. Those peaks do not exist in the true spectrum of the original raw data. Theywere created by the sampling process.

Normally don't compute the mirror image

Normally we don't worry about this mirror image above the folding frequency when doing spectral analyses. We know it is there and we simply ignore it.

In fact, for reasons of economy, when doing spectral analyses using discrete Fourier transforms, we usually don't even compute the spectrum at frequenciesabove the folding frequency. Since it is always a mirror image of the spectrum below the folding frequency, we know what it looks like without even computingit.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
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.
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
for teaching engĺish at school how nano technology help us
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
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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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