<< 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

how to study physic and understand
Ewa Reply
what is conservative force with examples
Moses
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
what is isotopes
Nangun Reply
nuclei having the same Z and different N s
AI-Robot
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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