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The method named transform does not implement an FFT algorithm. Rather, it implements a DFT algorithm, which is more general than,but much slower than an FFT algorithm. (See the program named Dsp030 in the module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm for the use of an FFT algorithm.)


Before getting into the technical details of the program, let's take a look at some results. Figure 2 shows the results produced by using the program named Graph06 to plot the output for the program named Dsp034 using default parameters.

(The file named Dsp034.txt did not exist in the current directory when the results shown in Figure 2 were generated.)

Figure 2. Spectral analysis of a damped pulse.
missing image

The input pulse

First consider the input pulse shown in the top plot of Figure 2 . This is the sort of pulse that you would get if you hung a mass on a spring, gave it a swiftdownward kick, and then allowed the mass to come to rest in an unimpeded fashion.

The horizontal axis represents time moving from left to right. The values above and below the axis represent the position of the mass over time relativeto its position at rest.

Potential energy in the spring

When the mass is at the most extreme positions and getting ready to reverse directions, the spring is extended. Thus, potential energy is stored in thespring. At these points in time, there is no kinetic energy stored in the mass.

Kinetic energy in the mass

As the mass goes through the rest position heading towards the other side, the spring is no longer extended, and there is no potential energy stored in thespring. However, at that point in time, the mass is moving causing it to have kinetic energy.

An exchange of energy

The behavior of the spring/mass system is to exchange that energy between potential energy and kinetic energy until such time as energy losses due tofriction dissipate the energy. At that point in time, the entire system comes to rest, which is the case about one-third of the way across the top plot in Figure 2 .

Now that our physics lesson for the day is over, let's get back to programming and digital signal processing.

Capturing the position of the mass as a sampled time series

Assume that you use an analog to digital converter to capture the position ofthe mass at a set of uniformly spaced intervals in time and then you plot those samples along a time axis. You should see something resembling the top plot in Figure 2 .

Having captured that positional information as a set of uniformly spaced samples, you are now in a position to perform a Fourier transform on the sampledtime series.

Computing the Fourier transform

In the module titled Fun with Java, How and Why Spectral Analysis Works , I explained that you could compute the Fourier transform of an input time series at any givenfrequency F by evaluating the first two expressions in Figure 3 . (The notation used in Figure 3 was also explained in that module.)

Figure 3. Fourier transform equations.
Real(F) = S(n=0,N-1)[x(n)*cos(2Pi*F*n)] Imag(F) = S(n=0,N-1)[x(n)*sin(2Pi*F*n)]ComplexAmplitude(F) = Real(F) - j*Imag(F)

Questions & Answers

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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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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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