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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.
missing image

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.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
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?
s. Reply
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
Devang Reply
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
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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