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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

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.
Damian
yes that's correct
Professor
I think
Professor
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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