XProfan

English

p.specht

Fourier-Interpolation: Bekanntlich can mathematical functions through klassischer Fourier-Zerlegung spektral-analyse, speak: Analytisch in reason- and Oberwellenanteile decompose. sometimes has one but too only a simple scheduler (z.B. Meßergebnisse) with of/ one geraden (!) amount of Stützwerten in equal (!) intervals available. Faßt one these as itself regularly wiederholenden Wellenzug on, is 'Diskrete Fourieranalyse' angesagt, also under Bezeichnung 'Harmonische Analyse' famous is.

the works too inverse: If one The ursprüngliche function again from the Wellensalat rekonstruiert, speaks one of 'Fourier-Synthese'. benefit the again zusammengesetzten function: she's kontinuierlich, d.h. it can also arbitrary Zwischenwerte between whom Stützwerten determined go, what maths-Freaks with the concept Interpolation bezeichnen.

details: but not of/ one Tabelleneingabe watts in the nachstehenden example a Formel to investigation the Stützwerte uses. but the can naturally anytime Change, as long as one The x_i-values of 0 To 2*Pi walk can. The must one erforderlichenfalls hold there hintransformieren.

to employment this Verfahrens ought to one short above cogitate, whether whom individual Frequencies in the 'richtigen Leben' objectively a weight comes up to, - whether means defined causes the unterschiedlichern Frequencies for the Result Responsible his could - otherwise there namely explicit einfachere types the Interpolation...

Compile Mark Separation

'The Umsetzung in XProfan is a pure DEMO solely for private tack!
Window Title "Trigonometrische Interpolation             terminate with x = -1"
' Angelehnt on "B.Brand: Algorithms to virtually Mathematik", Oldenbourg Vlg.1981, s.78
' Algorithmus portiert to XProfan-11 in 2014-09 by P.woodpecker, Wien; without jedwede Gewähr!
Window Style 24:randomize:set("decimals",18):Window %maxx/4,0-%maxx/2,%maxy-40
var xh&=width(%hwnd)/2:var yh&=height(%hwnd)/2 :   Var m&=16' <<<<<<<<<<<<<<<<<<<<<<<<<<<
declare i&,j&,k&,a![2*m&],b![2*m&],f!,x![2*m&],y![2*m&],x!,p!
print mkstr$("-",64)+"\n i            X[i]                 F=Y(x[i])\n"+mkstr$("-",64)

whileloop 0,2*m&:i&=&Loop:x![i&]=Pi()*i&/m& : y![i&]=cos(x![i&]+x![i&]*2)' <<<<<<<<<<<<<<<<

    casenot i& mod (1+m&\16):print if(i&>9,""," ");i&,tab(6);x![i&],tab(30);if(y![i&]<0,""," ");y![i&]
    endwhile :print mkstr$("-",64)

    whileloop 2*m&:i&=&Loop : a![0]=a![0]+y![i&]:a![i&]=a![i&]+y![i&]*(1-2*(i& mod 2))

        endwhile :a![0]=a![0]/m&/2:a![m&]=a![m&]/m&/2:print " a[ 0] = ";if(a![0]<0,""," ");a![0]

        whileloop m&-1:k&=&Loop

            whileloop 2*m&:i&=&Loop

                a![k&]=a![k&]+y![i&]*cos(k&*x![i&]) : b![k&]=b![k&]+y![i&]*sin(k&*x![i&])
                endwhile : a![k&]=a![k&]/m& : b![k&]=b![k&]/m&
                print " a[";if(k&<=9," ","");k&;"] = ";if(a![k&]<0,""," ");a![k&];\
                tab(33);"  b[";if(k&<=9," ","");k&;"] = ";if(b![k&]<0,""," ");b![k&]
                endwhile :print " a[";if(m&<=9," ","");m&;"] = ";if(a![m&]<0,""," ");a![m&];\
                tab(33);"  b[";if(m&<=9," ","");m&;"] = ";if(b![m&]<0,""," ");b![m&]
                print mkstr$("-",64)+"\n              x                      P(x)\n"+mkstr$("-",64)
                repeat :f!=0:print " x = ";:input x!:case x!= -1:end

                whileloop m&-1:k&=&Loop : f!=f!+(a![k&]*cos(k&*x!)+b![k&]*sin(k&*x!))

                    endwhile : p!=f!+a![0]+a![m&]*cos(m&*x!):locate %csrlin-1,1:
                    print "    ";if(x!<0,""," ");x!,tab(29);if(p!<0,""," ");p!

                until %key=27:end