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As mentioned earlier, the DFT algorithm is much more flexible while the FFT algorithm is much faster, particularly for large data lengths.

Peaks merge at the folding frequency

In addition to illustrating these fundamental aspects of the DFT algorithm, this example also illustrates how the mirror image peaks on either side of thefolding frequency merge into a single larger peak as the data frequency approaches the folding frequency.

The input parameters

The input parameters are shown in Figure 10 . Note in particular the values for the following parameters:

  • Data length: 200
  • Sample for zero time: 0
  • Lower frequency bound: 0.4
  • Upper frequency bound: 0.6
Figure 10. The input parameters.
Data length: 200 Sample for zero time: 0Lower frequency bound: 0.4 Upper frequency bound: 0.6Number spectra: 5 Frequencies0.492 0.4940.496 0.4980.5 Amplitudes90.0 90.090.0 90.090.0

A different data length

As you can see, the data length for this experiment is different from the data length of 400 used earlier. In addition, neither data length is a power oftwo.

Computational frequency bounds

As you can also see, the lower and upper frequency bounds are not 0.0 and 1.0 as in the earlier cases. In this case, the frequency bounds describe a muchnarrower range centered on the folding frequency.

Frequencies are close to the folding frequency

Finally, the frequencies of each of the five sinusoids specified in Figure 10 is progressively closer to the folding frequency with the frequency of the fifthsinusoid being equal to the folding frequency.

The spectral analysis output

The output from the spectral analysis for each of the five sinusoids is shown in Figure 11 . (Another interesting view of the same results is shown later in Figure 14 .)

Figure 11. Spectral analysis of five sinusoids.
missing image

Peaks are symmetrical about the folding frequency

The spectral peaks shown in Figure 11 are symmetrical about the folding frequency, which in turn is centered horizontally in each of the graphs. As youalready know, the peaks are always symmetrical about the folding frequency due to the frequency folding at that frequency.

The folding frequency is centered horizontally due to the way that I defined the lower and upper frequency bounds, and the way that I adjusted the plottingparameters.

Peaks are well defined and wider than before

The peaks are well defined because I computed the spectral energy at 200 points across the specified frequency range from 0.4 to 0.6. Thus, the frequencybins at which I computed spectral energy were much narrower than before.

The peaks are wider because I displayed a much smaller slice of the entire frequency spectrum in the same physical screen space.

Peaks merge at the folding frequency

As the frequency of each sinusoid approaches the folding frequency, the two mirror-image peaks corresponding to that sinusoid merge into a single peak withtwice the height at the folding frequency. This agrees with what you saw in Figure 9 , but on a much more detailed basis.

It would be difficult to perform this experiment using an FFT algorithm because of the inherent limitations built into the algorithm. The FFT algorithmsacrifices flexibility for speed.

Questions & Answers

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
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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