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Example of time domain and frequency domain

If you were to draw a graph of the voltage impinging on the speaker coils on your stereo system over time, that would be a time series, which is a member ofthe time domain.

If you were to observe the lights dancing up and down on the front of your equalizer while the music is playing, you would be observing the sameinformation presented in the frequency domain. Typically the lights on the left represent low frequencies or bass while the lights on the right side representhigh frequencies or treble. Often there is a slider associated with each vertical group of lights that allows you to apply filters to emphasize certainparts of the frequency spectrum and to de-emphasize other parts of the frequency spectrum.

Forward and inverse transforms

There are two very similar forms of the Fourier transform. The forward transform is typically used to transform information from the time domain intothe frequency domain. The inverse transform is typically used to transform information from the frequency domain back into the time domain.

Sampled time series

The theoretical Fourier transform is defined using integral calculus as applied to continuous functions. As a practical matter, in the digital world, wealmost never deal with continuous functions. Rather, we deal with functions that have been reduced to a series of discrete numbers (or samples), which are theresult of some discrete measurement system.

(As mentioned earlier, recording the temperature in your office once each minute for twenty-four hours would produce such a discrete series ofnumbers.)

Integration and summation

In many cases, the integration operation encountered in integral calculus can be approximated in the digital world by a summation operation using discrete data. That is the case with the Fourier transform. Thus, the (simple) summation form of the Fourier transform that is applied to a discrete time series is known as the Discrete Fourier Transform , or DFT .

The FFT algorithms

The DFT is a computationally intense operation. Given certain restrictions involving the number of values in the time series and the number of frequenciesat which the spectral analysis will be performed, there is are special algorithm that can result in computational economy in performing the transform.The algorithms that are used to realize that economy are commonly referred to as Fast Fourier Transform or FFT algorithms.

DFT versus FFT

The DFT is more general than the FFT, but the FFT is much faster than the DFT. It is important to understand that these are simply two differentalgorithms for doing the same thing. Either can be used to produce the same results (but as mentioned earlier, the FFT is somewhat more restricted as to the number of time-domain and frequency-domain samples) .

Because the DFT algorithm is somewhat easier to understand than the FFT algorithm, and also more general, I will concentrate on the DFT algorithm to explain how and why theFourier transform accomplishes what it accomplishes.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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