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Output display of the FFT applet

A sample of the output produced by the FFT applet is shown in Figure 1 .

Figure 1. Transform of pulse with negative slope.
missing image

An examination of Figure 1 shows that the display produced by the applet contains two sections. One section is labeled f(x) and the other section islabeled F(k).

This is an interactive applet with the ability to transform the complex samples represented by f(x) into complex samples represented by F(k).Alternatively, the applet can be used to transform complex samples represented by F(k) into complex samples represented by f(x).

Real and imaginary sections

Each section contains two boxes, one labeled Real and the other labeled Imaginary. One box contains a visual representation of a set of real samplesand the other box contains a visual representation of a set of imaginary samples.

With one exception, each sample is represented by a black circle. In each box, one of the samples is represented by an empty circle. The empty circle represents an index value of zero. Samples to the right of the sample withthe empty circle are samples at positive indices, and samples to the left of the sample with the empty circle are samples at negative indices.

A complex sample

A pair of values, one taken from the Real box and one taken from the Imaginary box, represents a complex sample.

Any of the circles can be interactively moved up or down with the mouse. The value of each sample is represented by the distance of the correspondingcircle from the horizontal line.

When a change is made to the value of any sample belonging to either f(x) for F(k), the transformation is recomputed and the display of the otherfunction is modified accordingly. If you modify the value of a sample in f(x), the values in F(k) are automatically modified to show the Fouriertransform of f(x). If you modify the value of a sample in F(k), the values in f(x) are automatically modified to show the inverse Fourier transform ofF(k).

This is an extremely powerful interactive tool.

Powers of two

Many and perhaps most FFT algorithms require the input series to contain a number of complex samples that is a power of two such as 2, 4, 8, 16, 32,etc. Most FFT algorithms also produce the same number of complex samples in the output as are provided in the input. The FFT algorithm used in thisapplet is no exception to those rules.

A pull-down list at the bottom of the applet lets the user specify 16, 32, or 64 complex samples for both the input and the output. All of theexamples in this module use 16 complex samples for input and output.

Location of the origin

The applet also provides a check box that allows the user to cause the origin (the empty circle at index value zero) to either be centered or placed at the left end. The display in Figure 1 has the origin centered. Other displays that I will use later have the origin at the left end.

Other applet controls

The other pull-down list and the button at the bottom of the applet provide other control features that don't need to be discussed here. Istrongly urge you to download this applet and experiment with it. The results can be very enlightening.

Questions & Answers

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.
yes that's correct
I think
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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