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Size of the peak at the folding frequency

Note that the peak in the bottom graph is approximately twice the height of the peaks in the other graphs. This is because the peak at the folding frequencyhas no mirror-image partner, and all the energy is concentrated in that single peak.

(Another interpretation is that two mirror-image peaks converge at the folding frequency causing the resulting peak to be twice as large aseither mirror-image peak. I will illustrate this effect with another example later.)

A short fat peak at the top

You may also have noticed that the peaks in the top graph are shorter and wider than the peaks in the other graphs. This may be because the actualfrequency of the sinusoid for the top graph is about half way between the values of the twelfth and thirteenth bins for which spectral energy was computed. Thus,the energy in the sinusoid was spread between the bins on either side of the actual frequency.

This frequency spreading effect can be minimized by increasing the data length to 800 samples. This causes the frequency bins to be only half as wideand the peak in the top graph becomes tall and narrow just like the peaks in the other graphs. You should try this and observe the result when you run theprogram later.

It is also instructive to plot these spectra with a data length of 400 using the program named Graph06 . This will show you how the energy is distributed between the frequency bins. This is most effective when the graph isexpanded as described in the next section.

Mapping the peaks to pixels

The broadening of the peak in the top graph may also have to do with the requirement to map the peaks in the spectrum to the locations of the actualpixels on the screen. If the location of the peak falls between the positions of two pixels, the plotting program must interpolate the energy in the peak so asto display that energy in actual pixel locations.

This effect can be minimized by plotting the same number of spectral values across a wider area of the screen. When you run this program later, click themaximize button on the Frame to cause the display to occupy the entire screen. That will give you a much better look at the actual shape of eachof the peaks. Do this using both Graph03 and Graph06 to plot the results.

(Note: When switching between the plotting programs, you may need to delete the class files from the old program and compile the new program toavoid having class files with the same names from the two programs becoming intermingled in the same directory.)

Another DFT example

This next example is designed to illustrate the following features of the DFT algorithm which don't generally apply to an FFT algorithm:

  • Ability to do spectral analysis on data of arbitrary lengths. (With many FFT algorithms, the data length must be a power of two.)
  • Ability to zero in on an arbitrary range of frequencies and to ignore all other frequencies. (Most FFT algorithms always compute the spectrum at uniform frequency increments from zero to one unit less than the samplingfrequency.)

Questions & Answers

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
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
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.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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