Re: glitch in cosine

[sfeam <sf...@us...>]

On Sunday, 20 October 2013 08:22:51 PM you wrote:
> Hi,
> 
> I have a curious glitch in plotting the sum of three cosines.
> 
> set samples 1700
> 
>             twopi=2*pi
>            c1(x)=a1*cos(twopi*(x-yz+ph1)/p1)
>            c2(x)=a2*cos(twopi*(x-yz+ph2)/p2)
>            c3(x)=a3*cos(twopi*(x-yz+ph3)/p3)
>            f3(x)=c1(x)+c2(x)+c0+c3(x)
> 
>   a1=a2=a3=1; c0=3.; yz=1958; p1=1.0;p2=0.5;p3=.25; ph1=ph2=ph3=.1
>   a3=1;ph3=0.1;p3=0.25
> 
> fit f3(x) datafile   u (($1)/365.25+1945):2 via 
> a1,a2,c0,ph1,ph2,p2,p3,a3,ph3
> 
>   plot  datafile u (($1)/365.25+1945):(f3($1)) w l

I suspect that despite your large value for "set sample"
you are still sampling too coarsely by a factor of a thousand or so.
The smooth curve you see is probably an aliasing artifact.

	Ethan




> 
> data either side of that point seem fine and if I use it directly with 
> plot "-" I don't get the glitch.
> 
> 
> Closing gnuplot session and repeating the plot from file gives same 
> result seen in attached png flie.
> 
> For the benefit of the list that don't see the file, it looks like a 
> cosine ranging -0.07 and + 0.014 pk to pk with some small ripple with 
> sporadic spikes ranging from 0.025 to 0.075 , glitches are just single 
> points.
> 
> Irrespective of the actual data fed in , I fail to see how the sum of 
> cosines can have such glitches.
> 
> 
> If anyone can explain how that could happen I'd like to know, otherwise 
> it looks like a bug.
> 
> Thanks, Peter.
> 
> 
> 
> 
> 
>    plot  "-" u (($1)/365.25+1945):(f3($1)) w l
> 
> 22629  381.81
> 22636  381.88
> 22643  381.65
> 22650  382.62
> 22657  382.25
> 22664  381.37
> 22678  383.09
> 22685  383.59
> 22692  384.19
> 22699  383.76
> 22706  383.71
> 22713  383.64
> 22720  384.28
> e
> 
> 
> 
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> 
> a1              = 0.0486237        +/- 0.001654     (3.402%)
> a2              = 0.0265777        +/- 0.001788     (6.728%)
> c0              = 0.00416031       +/- 0.001169     (28.1%)
> ph1             = -0.0557476       +/- 0.005409     (9.703%)
> ph2             = 0.163801         +/- 0.009924     (6.059%)
> p2              = 0.49982          +/- 0.0001585    (0.03171%)
> p3              = 0.258274         +/- 0.0005954    (0.2305%)
> a3              = -0.00192983      +/- 0.00202      (104.7%)
> ph3             = -0.923156        +/- 0.06458      (6.996%)
> 
>   G N U P L O T
>          Version 4.7 patchlevel 0    last modified 2012-10-16
>          Build System: Linux i686
> 
>