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This program can be run with either Graph03 or Graph06 in order to plot the results. Enter the following at the command-line prompt to run the program with Graph03 after everything is compiled:

java Graph03 Dsp035

The program was tested using JDK 1.8 under Windows 7.

The order of the plotted results

When the data is plotted (see Figure 1 ) using the programs Graph03 or Graph06 , the plots appear in the following order from top to bottom:

  • The input time series
  • The real spectrum of the input time series
  • The imaginary spectrum of the input time series
  • The amplitude spectrum of the input time series
  • The output time series produced by the inverse Fourier transform

The format of the plots

There were 256 values plotted horizontally in each section. I plotted the values on a grid that is 270 units wide to make it easier to view the plots onthe rightmost end. This leaves some blank space on the rightmost end to contain the numbers, preventing the numbers from being mixed in with the plotted values.The last actual data value coincides with the rightmost tick mark on each plot.

The forward Fourier transform

A static method named transform belonging to the class named ForwardRealToComplex01 was used to perform the forward Fourier transform.

(I explained this class and the transform method in the earlier module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm .)

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 anFFT algorithm.

(See the program named Dsp036 later in the module for the use of an FFT algorithm.)

The inverse Fourier transform

A static method named inverseTransform belonging to the class named InverseComplexToReal01 was used to perform the inverse Fourier transform. I will explain this method later in this module.

Results

Before getting into the technical details of the program, let's take a look at the results shown in Figure 1 .

The top plot in Figure 1 shows the input time series used in this experiment.

Figure 1. Forward and inverse transform of a time series using DFT algorithm.
missing image

Length is a power of two

The time series is 256 samples long. Although the DFT algorithm can accommodate time series of arbitrary lengths, I set the length of this timeseries to a power of two so that I can compare the results with results produced by an FFT algorithm later in the module.

(Recall that most FFT algorithms are restricted to input data lengths that are a power of two.)

The input time series

As you can see, the input time series consists of three concatenated pulses separated by blank spaces. The pulse on the leftmost end consists simply of somevalues that I entered into the time series to create a pulse with an interesting shape.

The middle pulse is a truncated sinusoid.

The rightmost pulse is a truncated square wave.

The objective

The objective of the experiment is to confirm that it is possible to transform this time series into the frequency domain using a forward Fouriertransform, and then to recreate the time series by using an inverse Fourier transform to transform the complex spectrum back into the time domain.

Questions & Answers

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
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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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how did you get the value of 2000N.What calculations are needed to arrive at it
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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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