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--- b:slope_compensation [2022/01/25 03:48]
sz created
+++ b:slope_compensation [2022/01/25 17:41] (current)
sz
@@ Line 2: / Line 2: @@
 Miller compensates for the interferometer drift or slope over each page, ie 20 turns.
-Advantage calculation are on single page.
+Advantage calculation are on single page. see p214
+The purpose of this test is to find the
+effect of slope on the sin[ ] component in an interval of 2 Pi.
+=== FindFit Approach ===
+See ApexMeansTest.nb
+Fourier analysis assumes that a signal repeats on some fixed cycle. If a signal does not do this, then FA cannot be used. At least without closing the cycle or the like.
+This program shows that when the "c" parameter is removed from the model expression, then the "a" parameter  (on Sin[]) increases wildly. But when the "c" is present, the "a" parameter matches the "a1" in the data(xy) generation code.
+This means that the linear term "c x" completely prevents the linear slope from affecting the true Sin[ ] component.
+also to find out how to structure data for FindFit
+ "data"
+<code mathematica>
+Clear[x,y,x1];
+imax=20;
+x2=Table[i/2.,{i,imax}];
+Print["x  ",x2];
+a1=1.01; b1=25; c1=10;
+xy= Table[{x1/2.,a1 Sin[2 Pi .1 x1/2.]+ b1 + c1 x1/2.},{x1,imax}];
+Print["xy  ",xy];
+ff=FindFit[xy,a  Sin[2 Pi .1 x] + b + c  x,{a,b,c},x];
+Print["angles ",Table[2 Pi .1 x1/2.,{x1,imax}]];
+Print["ff  ",ff];
+x  {0.5,1.,1.5,2.,2.5,3.,3.5,4.,4.5,5.,5.5,6.,6.5,7.,7.5,8.,8.5,9.,9.5,10.}
+xy  {{0.5,30.3121},{1.,35.5937},{1.5,40.8171},{2.,45.9606},{2.5,51.01},{3.,55.9606},{3.5,60.8171},{4.,65.5937},{4.5,70.3121},{5.,75.},{5.5,79.6879},{6.,84.4063},{6.5,89.1829},{7.,94.0394},{7.5,98.99},{8.,104.039},{8.5,109.183},{9.,114.406},{9.5,119.688},{10.,125.}}
+angles {0.314159,0.628319,0.942478,1.25664,1.5708,1.88496,2.19911,2.51327,2.82743,3.14159,3.45575,3.76991,4.08407,4.39823,4.71239,5.02655,5.34071,5.65487,5.96903,6.28319}
+ff  {a->1.01,b->25.,c->10.}
+</code>
+=== First approach. ===
 I could do the same over whole day: 24h * 60t/h = 1440 turns.
@@ Line 8: / Line 52: @@
 This would cause a daily cycle in the interferometric sin component, albeit 1/1440 as large each day.
-Or even entire set of days in name-list.
+Or even an entire set of days in name-list.
+Effect of slope on sin[ ] in interval 2 Pi.

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