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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.


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
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
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
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.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
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
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
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