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The complexToComplex method can be used to perform either a forward or an inverse transform. The value of the first parameter determineswhether the method performs a forward or an inverse Fourier transform.

The first parameter of the complextocomplex method

A value of +1 for the first parameter causes the complexToComplex method to perform a forward Fourier transform.

A value of -1 for the first parameter causes the complexToComplex method to perform an inverse Fourier transform.

The forward transform

Although I didn't include the code in this module, (because it was shown in an earlier module) , the transform method in Figure 7 passes a value of +1 to the complexToComplex method to cause it to perform a forward Fourier transform.

The inverse transform

Similarly, the inverseTransform method shown in Listing 17 passes a value of -1 to the complexToComplex method to cause it to perform an inverse Fourier transform.

Fft and dft produce equivalent results

As evidenced in Figure 1 and Figure 2 , the program named Dsp035 , which uses a DFT algorithm, produces the same results as the program named Dsp036 , which uses an FFT algorithm. However, if you were to put a timer on each of the programs, you would find that Dsp036 runs faster due to the improved speed of the FFT algorithm over the DFTalgorithm.

Using a Fourier transform to perform frequency filtering

The program named Dsp037 illustrates frequency filtering accomplished by modifying the complex spectrum in the frequency domain and thenperforming an inverse Fourier transform on the modified frequency-domain data. The results are shown in Figure 4 .

Figure 4. Filtering in the frequency domain.
missing image

Operation of the program

The program begins by using an FFT algorithm to perform a forward Fourier transform on a single impulse in the time domain.

(A DFT algorithm could have been used equally as well, but it would have been slower.)

The impulse is shown as the input time series in the topmost plot in Figure 4 .

(Although I didn't show the complex spectrum of the impulse, we know that the magnitude of the spectrum of an impulse is constant across allfrequencies. In other words, the magnitude spectrum of an impulse is a flat line from zero to the sampling frequency and above.)

Modify the complex spectrum

Then the program eliminates all energy between one-sixth and five-sixths of the sampling frequency by setting the real and imaginary parts of the FFT outputto zero.

The second, third, and fourth plots in Figure 4 show the real part, imaginary part, and amplitude respectively of the modified complex spectrum.

(The two boxes in the fourth plot in Figure 4 show what's left of the spectral energy after the energy in the middle of the band has beeneliminated.)

The folding frequency in these three plots is near the center of the plot at the eighth tick mark.

The plotting format

The input data length was 256 samples. All but one of the input data values was set to zero resulting in a single impulse in the input time series near thesecond tick mark in Figure 4 .

Questions & Answers

How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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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
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what king of growth are you checking .?
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Kyle
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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?
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absolutely yes
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it is a goid question and i want to know the answer as well
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Abigail
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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
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Lily
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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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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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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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