Re: [Scilab-users] fourier series and fft
Le 22/09/2016 23:09, paul.carr...@free.fr a écrit : 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 ? . Doing that is the main purpose of fft(). fft() returns the (bilateral) complex coefficients c_k of the series. a_k and b_k are easily computed from them. // Example #1: n = 100; x = linspace(0, 1, n+1); x = x(1:n); y = sin(2*%pi*x); ft = fft(y); ft = clean(ft); c = ft/n; c0 = c(1) // c(k) = ft(k+1) // c(-k) = ft(n+1-k) a0 = c0 // average a = (c(2:(n/2)) + c(n:-1:(n/2+2))) // a_k = c_k + c_(-k) b = %i*(c(2:n/2) - c(n:-1:n/2+2)) // b_k = %i*(c_k - c_(-k)) // Example #2: n = 100; x = linspace(0, 2, n+1); x = x(1:n); y = 2*sin(2 * %pi * x) - 3*cos(%pi * x); ft = fft(y); ft = clean(ft); c = ft/n; c0 = c(1) a0 = c0 a = (c(2:(n/2)) + c(n:-1:(n/2+2))) b = %i*(c(2:n/2) - c(n:-1:n/2+2)) --> a = (c(2:(n/2)) + c(n:-1:(n/2+2))) a = column 1 to 22 -3. 0. 0. 0. 0. 0. 0. ... // here is the "-3" coeff of the first even cos() harmonic --> b = %i*(c(2:n/2) - c(n:-1:n/2+2)) b = column 1 to 22 0. 2. 0. 0. 0. 0. 0. ... // here is the "3" coeff of the second odd sin() harmonic Anyway, the full x-range is considered as the period. If it is not actually the case, some artefacts appear in the results. To avoid them, it is mandatory to sample /x/ over a multiple of its "natural" period. Example #1: The period of sin(2*%pi*x) is 2*pi, this is why x must be sampled from 0 to 1. Example #2: The period of 2*sin(2 * %pi * x) - 3*cos(%pi * x)is also 2*pi, this is why x must be sampled from 0 to 2 (in the cos() argument). HTH Samuel ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
Re: [Scilab-users] fourier series and fft
sound interesting ... many thanks for the information Paul - Mail original - De: "Rafael Guerra" À: "Users mailing list for Scilab" Envoyé: Vendredi 23 Septembre 2016 13:57:31 Objet: Re: [Scilab-users] fourier series and fft 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-boun...@lists.scilab.org] On Behalf Of paul.carr...@free.fr Sent: Friday, September 23, 2016 8:45 AM To: t...@wescottdesign.com; Users mailing list for Scilab 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 " < t...@wescottdesign.com > À: "Users mailing list for Scilab" < users@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.carr...@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 ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
Re: [Scilab-users] fourier series and fft
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-boun...@lists.scilab.org] On Behalf Of paul.carr...@free.fr Sent: Friday, September 23, 2016 8:45 AM To: t...@wescottdesign.com; Users mailing list for Scilab 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" mailto:t...@wescottdesign.com>> À: "Users mailing list for Scilab" mailto:users@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.carr...@free.fr<mailto:paul.carr...@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 ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
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" À: "Users mailing list for Scilab" 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.carr...@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 > > > # > mode(0) > > function y=f(x) > y=2.*sin(2 * %pi * x) - 3.*cos(%pi * x); > endfunction > > periode = 2; > number_of_periodes = 1; > n = periode * number_of_periodes; > > x = [0 : %pi/100 : n]'; > y = f(x); > N = size(x,"*"); > > scf() > plot2d(x,y); > > a = fft(y,-1); > ___ > users mailing list > users@lists.scilab.org > http://lists.scilab.org/mailman/listinfo/users -- Tim Wescott www.wescottdesign.com Control & Communications systems, circuit & software design. Phone: 503.631.7815 Cell: 503.349.8432 ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
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.carr...@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 > > > # > mode(0) > > function y=f(x) > y=2.*sin(2 * %pi * x) - 3.*cos(%pi * x); > endfunction > > periode = 2; > number_of_periodes = 1; > n = periode * number_of_periodes; > > x = [0 : %pi/100 : n]'; > y = f(x); > N = size(x,"*"); > > scf() > plot2d(x,y); > > a = fft(y,-1); > ___ > users mailing list > users@lists.scilab.org > http://lists.scilab.org/mailman/listinfo/users -- Tim Wescott www.wescottdesign.com Control & Communications systems, circuit & software design. Phone: 503.631.7815 Cell: 503.349.8432 ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
[Scilab-users] fourier series and fft
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 # mode ( 0 ) function y = f ( x ) y = 2. * sin ( 2 * %pi * x ) - 3. * cos ( %pi * x ) ; endfunction periode = 2 ; number_of_periodes = 1 ; n = periode * number_of_periodes ; x = [ 0 : %pi / 100 : n ] ' ; y = f ( x ) ; N = size ( x , " * " ) ; scf ( ) plot2d ( x , y ) ; a = fft ( y , - 1 ) ; ___ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users
