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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.)

Results

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

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Bob Reply
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Bob
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brayan
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Damian
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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.
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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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Lily
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s. Reply
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NANO
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Lily
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Devang Reply
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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
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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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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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