<< Chapter < Page
  Digital signal processing - dsp     Page 5 / 9
Chapter >> Page >

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

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
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
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
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
hi
Loga
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?

Ask