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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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