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Figure 5. Filtering in the frequency domain.
missing image

Compare the results

The basic plotting format of Figure 5 is the same as Figure 4 .

Compare Figure 5 With Figure 4

The first difference to note between the two figures is that I moved the impulse in the input time series in the topmost plot sixteen samples further tothe right in Dsp038 .

(This has no impact on the final result, which you can verify by modifying the program to move the impulse to a different position and thencompiling and running the modified program.)

Compare the bandwidth of the pass band

The second difference to note is shown in the modified amplitude spectrum in the fourth plot in the two figures. The bandwidth of the pass band issignificantly narrower in Figure 5 than in Figure 4 . Also, the pass band in Figure 4 extends all the way down to zero frequency, while Figure 5 eliminates all energy below a frequency of three thirty-seconds of the sampling frequency.

Waveforms of filtered impulse

Finally, note the waveforms of the two filtered impulses. The overall amplitude of the filtered impulse in Figure 5 is less than in Figure 4 , simply because it contains less total energy. In addition, the filtered impulse in Figure 5 is broader than the filtered impulse in Figure 4 . This is because it has a narrower bandwidth.

(Pulses that are narrow in terms of time duration require a wider bandwidth than pulses that have a longer time duration. The time duration ofthe pulse tends to be inversely related to the required bandwidth for the pulse.)

Run the programs

I encourage you to copy, compile, and run the programs provided in this module. Experiment with them, making changes and observing the results of yourchanges.

Create more complex experiments. For example, use more complex input time series when experimenting with frequency filtering. Apply differentmodifications to the complex spectrum when experimenting with frequency filtering.

Most of all enjoy yourself and learn something in the process.

Summary

This module illustrates and explains forward and inverse Fourier transforms using both DFT and FFT algorithms.

The module also illustrates and explains the implementation of frequency filtering by modifying the complex spectrum in the frequency domain and thentransforming the modified complex spectrum back into the time domain.

Complete program listings

Complete listings of the programs discussed in this module are provided below.

Listings for other programs mentioned in the module, such as Graph03 and Graph06 , are provided in other modules. Those modules are identified in the text of this module.

Listing 14. Dsp035.java.
import java.util.*; class Dsp035 implements GraphIntfc01{final double pi = Math.PI; int len = 256;double[] timeDataIn = new double[len]; double[]realSpect = new double[len];double[] imagSpect = new double[len]; double[]angle = new double[len];//unuseddouble[] magnitude = new double[len]; double[]timeDataOut = new double[len];int zero = 0; public Dsp035(){//constructor//Create the raw data pulses timeDataIn[0]= 0; timeDataIn[1]= 50; timeDataIn[2]= 75; timeDataIn[3]= 80; timeDataIn[4]= 75; timeDataIn[5]= 50; timeDataIn[6]= 25; timeDataIn[7]= 0; timeDataIn[8]= -25; timeDataIn[9]= -50; timeDataIn[10]= -75; timeDataIn[11]= -80; timeDataIn[12]= -60; timeDataIn[13]= -40; timeDataIn[14]= -26; timeDataIn[15]= -17; timeDataIn[16]= -11; timeDataIn[17]= -8; timeDataIn[18]= -5; timeDataIn[19]= -3; timeDataIn[20]= -2; timeDataIn[21]= -1; timeDataIn[240]= 80; timeDataIn[241]= 80; timeDataIn[242]= 80; timeDataIn[243]= 80; timeDataIn[244]= -80; timeDataIn[245]= -80; timeDataIn[246]= -80; timeDataIn[247]= -80; timeDataIn[248]= 80; timeDataIn[249]= 80; timeDataIn[250]= 80; timeDataIn[251]= 80; timeDataIn[252]= -80; timeDataIn[253]= -80; timeDataIn[254]= -80; timeDataIn[255]= -80; //Create raw data sinusoidfor(int x = len/3;x<3*len/4;x++){ timeDataIn[x]= 80.0 * Math.sin( 2*pi*(x)*1.0/20.0);}//end for loop //Compute DFT of the time data and save it in// the output arrays. ForwardRealToComplex01.transform(timeDataIn,realSpect, imagSpect,angle, magnitude,zero, 0.0,1.0); //Compute inverse DFT of spectral data and// save output time data in output array InverseComplexToReal01.inverseTransform(realSpect, imagSpect,timeDataOut); }//end constructor//-------------------------------------------// //The following six methods are required by the// interface named GraphIntfc01. public int getNmbr(){//Return number of curves to plot. Must not // exceed 5.return 5; }//end getNmbr//-------------------------------------------// public double f1(double x){int index = (int)Math.round(x); if(index<0 || index>timeDataIn.length-1){ return 0;}else{ return timeDataIn[index]; }//end else}//end function //-------------------------------------------//public double f2(double x){ int index = (int)Math.round(x);if(index<0 || index>realSpect.length-1){ return 0;}else{ //scale for convenient viewingreturn 5*realSpect[index];}//end else }//end function//-------------------------------------------// public double f3(double x){int index = (int)Math.round(x); if(index<0 || index>imagSpect.length-1){ return 0;}else{ //scale for convenient viewingreturn 5*imagSpect[index];}//end else }//end function//-------------------------------------------// public double f4(double x){int index = (int)Math.round(x); if(index<0 || index>magnitude.length-1){ return 0;}else{ //scale for convenient viewingreturn 5*magnitude[index];}//end else }//end function//-------------------------------------------// public double f5(double x){int index = (int)Math.round(x); if(index<0 || index>timeDataOut.length-1){ return 0;}else{ return timeDataOut[index]; }//end else}//end function }//end sample class Dsp035

Questions & Answers

what is the stm
Brian Reply
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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
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LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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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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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
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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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
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
absolutely yes
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How can I make nanorobot?
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there is no specific books for beginners but there is book called principle of nanotechnology
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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
what is the actual application of fullerenes nowadays?
Damian
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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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