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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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