/*
Smoothed Adaptive Momentum, p. 166
From Ehlers book: Cybernetic Analysis for Stocks and Futures

*/

SetBarsRequired(1000000,1000000);
price=(H+L)/2;
alpha=Param("alpha",0.07,0.01,1,0.01);
Cutoff=Param("Cutoff",8,2,21,1);

pi=4*atan(1);DTR=pi/180;RTD=1/DTR;
Cycle=0;I1=0;Q1=0;InstPeriod=0;DeltaPhase=0;MedianDelta=0;DC=0;Value1=0;
DCPeriod=0;RealPart=0;ImagPart=0;DCPhase=0;Period=0;
V1=0;a1=0;b1=0;c1=0;coef1=0;coef2=0;coef3=0;coef4=0;filt3=0;

	Smooth = (Price + 2*Ref(Price,-1) + 2*Ref(Price,-2) + Ref(Price,-3))/6;
	
for(i=36;i<BarCount;i++)//BarCount-300
{
	Cycle[i]  = ((1-0.5*alpha[i])^2)*(Smooth[i] - 2*Smooth[i-1] + Smooth[i-2]) + 2*(1-alpha[i])*Cycle[i-1] - ((1-alpha[i])^2)*Cycle[i-2];
	if(i<7) Cycle[i]=(Price[i]-2*Price[i-1]+Price[i-2])/4;

		
//Hilbert Transform
	Q1[i] = (0.0962*Cycle[i] + 0.5769*Cycle[i-2] - 0.5769*Cycle[i-4] - 0.0962*Cycle[i-6]) * (0.5 + 0.08*InstPeriod[i-1]);
	I1[i] = Cycle[i-3];

	if (Q1[i] != 0 AND Q1[i-1] != 0) DeltaPhase[i] = (I1[i]/Q1[i] - I1[i-1]/Q1[i-1]) / (1 + I1[i]*I1[i-1]/(Q1[i]*Q1[i-1]));
	if (DeltaPhase[i] < 0.1) DeltaPhase[i] = 0.1;
	if (DeltaPhase[i] > 1.1) DeltaPhase[i] = 1.1;

	MedianDelta=Median(DeltaPhase , 5);
	
	if (MedianDelta[i] == 0) DC[i]=15;
	 else 
	DC[i] = 2*pi/MedianDelta[i] + 0.5; //changed from 0.5 (to 1.28)

	InstPeriod[i] = 0.33*DC[i] + 0.67*InstPeriod[i-1];
	Period[i] = (0.15*InstPeriod[i] + 0.85*Period[i-1]); //added int
//-----------------------------------------------------------------------------------------------------------------------------------------------------
	V1[i]=Price[i]-Price[i-(int(Period[i])-1)];
	a1[i]=exp(-pi/Cutoff);
	b1[i]=2*a1[i]*cos((1.738*180/Cutoff)*DTR);
	c1[i]=a1[i]^2;
	coef2[i]=b1[i]+c1[i];
	coef3[i]=-(c1[i]+b1[i]*c1[i]);
	coef4[i]=c1[i]^2;
	coef1[i]=1-coef2[i]-coef3[i]-coef4[i];
	filt3[i]=coef1[i]*V1[i] + coef2[i]*filt3[i-1] + coef3[i]*filt3[i-2] + coef4[i]*filt3[i-3];
	if(i<4) filt3[i]=V1[i];
}

GraphXSpace=5;

Plot(filt3,"Smoothed Adaptive Momentum",colorBlue,styleStaircase );
PlotGrid(0,0);