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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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