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John F. Ehlers' article, “Fourier Series Model of the Market”, explained how to reduce market action to a sinewave using his fourier series analysis. The MetaStock formula for that indicator is below:
Fourier Series AnalysisCode:x:= Input("fundemental cycle length", 2, 100, 20);
bw:= 0.1; {bandwidth}
L1:= Cos(360/x);
G1:= Cos((bw*360)/x);
S1:= 1/G1 - Sqrt(1/(G1*G1) -1);
L2:= Cos( 360 / (x/2));
G2:= Cos((bw*360)/(x/2));
S2:= 1/G2 - Sqrt(1/(G2*G2) -1);
L3:= Cos( 360 / (x/3));
G3:= Cos((bw*360)/(x/3));
S3:= 1/G3 - Sqrt(1/(G3*G3) -1);
{fundemental band pass}
BP1:= .5*(1-S1)*(C-Ref(C,-2)) + L1*(1+S1)*PREV - S1*Ref(PREV,-1);
Q1:= (x/6.28)*(BP1-Ref(BP1,-1));
{second harmonic band pass}
BP2:= .5*(1-S2)*(C-Ref(C,-2)) + L2*(1+S2)*PREV - S2*Ref(PREV,-1);
Q2:= (x/6.28)*(BP2-Ref(BP2,-1));
{third harmonic band pass}
BP3:= .5*(1-S3)*(C-Ref(C,-2)) + L3*(1+S3)*PREV - S3*Ref(PREV,-1);
Q3:= (x/6.28)*(BP3-Ref(BP3,-1));
{final calculations}
p1:= Sum((BP1*BP1) + (Q1*Q1), x);
p2:= Sum((BP2*BP2) + (Q2*Q2), x);
p3:= Sum((BP3*BP3) + (Q3*Q3), x);
BP1 + Sqrt(p2/p1)*BP2 + Sqrt(p3/p1)*BP3;
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