[Scilab-users] fourier series and fft

[Rafael Guerra]

Hi Paul,



Fyi, Tom Co's simple tutorial: http://www.chem.mtu.edu/~tbco/cm416/fft1.pdf

shows how to obtain the Fourier coefficients via the fft



Regards,

Rafael



-----Original Message-----
From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of paul.carrico at free.fr
Sent: Friday, September 23, 2016 8:45 AM
To: tim at wescottdesign.com; Users mailing list for Scilab <users at lists.scilab.org>
Subject: Re: [Scilab-users] fourier series and fft



Thanks Tim for this answer; well I notice I need to "dig" deeper on that topic



Paul



----- Mail original -----

De: "Tim Wescott" <tim at wescottdesign.com<mailto:tim at wescottdesign.com>>

À: "Users mailing list for Scilab" <users at lists.scilab.org<mailto:users at lists.scilab.org>>

Envoyé: Jeudi 22 Septembre 2016 23:17:27

Objet: Re: [Scilab-users] fourier series and fft



Hey Paul:



If you mean the Fourier series of a continuous-time periodic signal (or

a continuous-time function of finite scope), then no, Scilab doesn't do

that, because the FFT is different from the Fourier Series.  If you have

a signal that's symbolically defined as f(t) over some span of time,

then Maxima may help you get a symbolic definition of the Fourier

Series.



The FFT is essentially the Fourier series of a sampled-time periodic (or

finite-scope) signal, so if that sampled-time signal is a sufficiently

accurate approximation of your continuous-time signal, and if your a0,

a_k and b_k are defined to match the way that Scilab does the FFT, then

the real part of the FFT are the a coefficients, and the imaginary part

are the b coefficients.



If you gather up half a dozen books that include signal processing,

especially if some are from applications areas a bit removed from

"normal" signal processing, you'll find that everyone specifies their

Fourier stuff differently.  So what comes out of Scilab's FFT may not

match _your_ definitions of a0, etc., but they match _someone's_.



On Thu, 2016-09-22 at 23:09 +0200, paul.carrico at free.fr<mailto:paul.carrico at free.fr> wrote:

> dear all

>

> I'm novice in Fourier series and other and my question is probably

> naive (sorry for this) => I'm wondering if scilab can directly

> calculate the Fourier coefficient a0, a_k and b_k ?

>

>

> I'm currently doing it "by hand" is order to familiarise myself with

> it (and I'm looking at the same time to documents on  FFT use and

> rules to refind the 2 natural frequencies of the example here bellow),

> but it seems I'll need to code the coefficient calculations ... Am I

> right ?

>

> Thanks

>

> Paul


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