how does fourier transform transforms time to freq domain

[Indian]

How does fourier transform transforms time to freq domain.
i know mathematically but want to know how does physically it transform what happens when the time domain signal is multiplied by exponential signal. how does the fourier arrives on that particular formula

 

[GroundCtrl]

Re: how does fourier transform transforms time to freq domai

Fourier Transforn just represent the function of time (your input signal in time domain) as the sum of weighted sines and cosines of certain frequences. This sum of sines and cosines can rewrite throu complex exponents. This is the transformation from time domain to frequency domain.

So if u take a lot of sine and cosine generators that can work infinetely in the past and in the future u can obtain your time-domain signal.

 

[electronics_kumar]

Re: how does fourier transform transforms time to freq domai

. how does the fourier arrives on that particular formula

Fourier formulated that formula based on the fact expoential is the signal which will be retained after almost all mathematical manipulation(diff ,integration)..


here time domain signal is converted into frequency domain by multiplying it with exp.signal...that expontial signal is retained after all manipulations....so it easy to convert that frequency signal to time domain by simply multiplying it with a expo.signal with inverse polarity (expo.signal with inverse polarity will cancel the original expon.signal then original time domain will be retained)..hope it clears

 

[artem]

result of fourier transform is - frequencies phase and amplitute . To restore signal to original form, phase of freqs is important as well as their amplitute .

 

[ee_expert2000]

Re: how does fourier transform transforms time to freq domai

to compute the fourier transform, you put some sinousiodal signals with specific frequencies i.e. exp(jnω) whose amplitude is equal to the signal time domain value x.
ω is computed in a way to have a relationship with the signal values.
at the end you have some values that say which frequrencies you have in the signal.
this can be used to compute the power distribution.

have a look at this:

"A mathematical description of the relationship between functions of time and corresponding functions of frequency; a map for converting from one domain to the other. For example, if we have a signal that is a function of time--an impulse response--then the Fourier Transform will convert that time domain data into frequency data, for example, a frequency response."

www.keithyates.com/glossary.htm

Reagards

 

[ChepRidwan]

Re: how does fourier transform transforms time to freq domai

for FFT algorithm:|
to transform signal from time domain to frequency domain..
1. decomposing in time domain will make come to frequency domain.
Step for decomposing is log2N. ex : if N= 8, step is 3.
0 1 2 3 4 5 6 7
0 2 4 6 1 3 5 7
0 4 2 6 1 5 3 7 - final decomposing:|
( if you convert to bit number you can see reverse bit)
to compute the process using buterfly method.

2. Now you come to frequency domain...

more...
download free... www.dspguide.com
or you can read book DSP 3e, Proakis and manolakis

 

[coros]

Re: how does fourier transform transforms time to freq domai

Fourier transform approximates one function using another functions. Like a vector can be expressed by a sum of another vectors ( especially orthonormal basis vectors ), a function can be expressed by a sum of orthogonal functions. As a orthogonal basis Fourier took an infinite set of sine and cosine waves. The coefficients can be calculated by solving the least squares ( the nearest solution ).
This idea applies to other transforms too, only the basis set is diffrent.

 

[steve10]

Re: how does fourier transform transforms time to freq domai

Have you ever got any experience to count total amount of money consisting of only coins? Assume that you got a load of coins on the table and you want to count how much they add up to. There are two ways to do it. In the first way, you start to count from one side of the table. A penny ... and a quarter ... they add up to 26 pennies.... then a dime .. the total ..um... is 36 pennies .. and so on. In the second way, you first pick out all the pennies and put aside, you then pick out all nickles ... and then the dimes ... quarters. This way, it's easy for you to see how many coins you have in each case and, therefore, easier to count the total.

The first way is like the time domain analysis, in which you move like a bulldozer, from the beginning to the end. The second way is like the freq domain analysis, in which you move from the top to the bottom (from high freq to low freq). If you multiply your signal by a COMPLEX signal, it is just like adding a constant number to all the coins. For example, if the fixed number (the freq that COMPLEX signal has) is 10, then all quarters become "35 pennies", dimes "20 pennies" ... ain't they cute?

 

[dervisakyuz]

Re: how does fourier transform transforms time to freq domai

f.t. is the addition of the sin. signals. by adding them you obtain fourier transform.you can represent any signal by adding sin signals. exp^jwn =coswn+jsinwn

 

[alizadeh_m]

Re: how does fourier transform transforms time to freq domai

in the fourier transform integral, the limit on t is from -inf to +inf. therefore the t parameter is not present in the result, and only f remains.