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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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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