Signal & Fourier series

[nanoha]

Hello, anybody mind to tell me what is the relation between signal and fourier series. Why we need to represent the signal in form of fourier?

And besides that, I am also not understand so much about fourier. I have made a little googling and find that fourier is just like laplace. But I don't know how...

 

[rainbow]

Hello, anybody mind to tell me what is the relation between signal and fourier series.


Why we need to represent the signal in form of fourier?

And besides that, I am also not understand so much about fourier. I have made a little googling and find that fourier is just like laplace. But I don't know how...

fourier is a mathmatical method to write any function in an infinity number of terms in sin & cos
so using fourier is very important to represent a signal because it represent the signal as a series of diffrent frequency that will simplify the signal analysis

 

[nanoha]

Ok. Get it a little. Thanks for the info.

 

[AceOfHearts]

Also, the signal you want to represent as Fourier (using a sum of sin and cos waves) must be a periodic signal. Periodic signals cannot carry any information since they are of a regular pattern. Information signals are non-periodic. Thus, application of the Fourier Series is very limited.

To represent non-periodic signals as summations of sin and cos waves, one needs to use Fourier Transform and not Fourier Series. Laplace Transforms also deal with non-periodic signals.

Hope this helps.

 

[johankj]

As stated, fourier is important because it can be used to describe (almost) any periodic signal (or wave or function).

It is also important as a signal analysis tool, for example in studying harmonics.

So, if f is your original signal, then in (a very) general way, it can be described as a series of (second) periodic functions g:
f = g1 + g2 + g3 + g4 ... and so on...

-or more accurately:
f = a0 + a1*g1 + a2*g2 + a3*g3 + a4*g4 + ... and so on...
Where a0, a1, a2,... are just scaling factor.

There are a few recuirements to your choice of your periodic g signal, but that quickly becomes technical. The sinus function is a safe choice, as they were in the Fouriers original theorem. The functions g are related in real applications(a basic set), and in fourier they are multiples of a fundamental frequency.

There are a few ways to calculate the scaling factors, a0,a1,a2..., the elementary way involving some intergration. In basic term, the scaling factors represent how 'well' the f and g 'fits' for that particular gx

In a computer (or an electronic machine) then, this means that once you know your scaling factors a0, a1, a2,..., you can store these values, and then synthesise your original signal.

 

[nanoha]

Thanks a lot guy... that really benefits me so much. So far I don't really know all about that.

Thanks again...

 

[3iMaJ]

Also, the signal you want to represent as Fourier (using a sum of sin and cos waves) must be a periodic signal. Periodic signals cannot carry any information since they are of a regular pattern. Information signals are non-periodic. Thus, application of the Fourier Series is very limited.

To represent non-periodic signals as summations of sin and cos waves, one needs to use Fourier Transform and not Fourier Series. Laplace Transforms also deal with non-periodic signals.

Hope this helps.

The Fourier series can represent any time domain signal (over a finite time interval, otherwise we refer to it as the Fourier Transform) as an infinite summation of complex frequency samples and complex sinusoids.

There are many uses for the Fourier series, as such has many applications. Don't be so quick to dismiss the use of it. Even your "information" signals can be represented as a Fourier series (what do you think the FFT is?).

 

[nanoha]

Even your "information" signals can be represented as a Fourier series (what do you think the FFT is?).

Can you explain to me what is FFT? Curious to know.

 

[3iMaJ]

A version of the discrete Fourier transform that takes advantage of symmetry.