_SECTION_BEGIN("cycle121"); 

SetChartBkColor(ParamColor("Panel color ",colorOrange)); 


PI = 3.1415926; 
Data = (H+L)/2; 
// detrending ( high-pass filter ) 
HFPeriods = Param("HP filter cutoff", 40, 20, 100 ); 
alpha1 = ( 1-sin(2*pi/HFPeriods) ) / cos( 2 * pi / HFPeriods ); 
HP = AMA2( Data - Ref( Data, -1 ), 0.5 * ( 1 + alpha1 ), alpha1 ); 
// 6-tap low-pass FIR filter 
SmoothHP  = ( HP + 2 * Ref( HP, -1 ) + 3 * Ref( HP, -2 ) + 
   3 * Ref( HP, -3 ) + 2 * Ref( HP, -4 ) + Ref( HP, -5 ) )/12; 
SmoothHPDiff = SmoothHP - Ref( SmoothHP, -1 ); 
x = BarIndex(); 
delta = -0.015 * x + 0.5; 
delta = Max( delta, 0.15 ); 
Q  = 0; 
Real = 0; 
Imag = 0; 
Ampl = 0; 
DB =  0; 
I = SmoothHP; 
MaxAmpl = 0; 
for( N = 8; N <= 50; N++ ) 
{ 
  beta = cos( 2 * PI / N ); 
  Q = ( N / ( 2 * PI ) ) * SmoothHPDiff; 
  
  for( bar = 8; bar < BarCount; bar++ ) 
  { 
     gamma = 1 / cos( 4 * PI * delta[ bar ] / N ); 
     alpha = gamma - sqrt( gamma ^ 2 - 1 ); 
  
     Real[ bar ] = 0.5 * ( 1 - alpha ) * ( I[ bar ] - I[ bar - 1 ] ) + 
                   beta * ( 1 + alpha ) * Real[ bar - 1 ] - 
                   alpha * Real[ bar - 2 ]; 
     Imag[ bar ] = 0.5 * ( 1- alpha ) * ( Q[ bar ] - Q[ bar - 1 ] ) + 
                beta * ( 1 + alpha ) * Imag[ bar - 1 ] - 
                alpha * Imag[ bar - 2 ]; 
   } 
   Ampl = Real ^ 2 + Imag ^ 2; 
   MaxAmpl = Max( MaxAmpl, Ampl ); 
   VarSet("Ampl"+N, Ampl ); 
} 
TunedFilterDisplay = ParamToggle("Dom Cycle Tuned Filter", "No|Yes" ); 
// Plot Heat Map ( Spectrogram ) 
// and find dominant cycle 
DcNum = DcDenom = 0; 
for( N = 8; N <= 50; N++ ) 
{ 
   Ampl = VarGet("Ampl"+N); 
   db  = Nz( -10 * log10( 0.01 / ( 1 - 0.99 * Ampl / MaxAmpl ) ) ); 
  
   db = Min( db, 20 ) ; 
   Red = IIf( db <= 10, 255, 255 * ( 2 - db/10 ) ); 
   Green = IIf( db <= 10, 255 * ( 1 - db/10 ), 0 ); 
   if( NOT TunedFilterDisplay  ) 
      PlotOHLC( N, N, N-1, N-1, "", ColorRGB( Red, Green, 0 ), 
                                    styleCloud | styleNoLabel ); 
   DcNum = DcNum + (db < 3 ) * N * ( 20 - db ); 
   DcDenom = DcDenom + ( db < 3 ) * ( 20 - db ); 
} 
DC = DcNum / DcDenom; 
if( ParamToggle("Show Dom. Cycle?", "No|Yes" ) ) 
{ 
  DomCycle = Median( DC, 10 ); 
  Plot( DomCycle, "Dominant Cycle", colorBlue ); 
} 
if( TunedFilterDisplay ) 
{ 
   DomCycle = Median( DC, 10 ); 
   DomCycle = Max( DomCycle, 8 ); 
   Value = 0; 
   for( bar = 10; bar < BarCount; bar++ ) 
   { 
     beta = cos( 2 * PI / domCycle[ bar ] ); 
     gamma = 1 / cos( 4 * PI * delta[ bar ] / DomCycle[ bar ] ); 
     alpha = gamma - sqrt( gamma ^ 2 - 1 ); 
     Value[ bar ] = 0.5 * ( 1 - alpha ) * SmoothHPDiff[ bar ] + 
           beta * ( 1 + alpha ) * Value[ bar - 1 ] - 
           alpha * Value[ bar - 2 ]; 
   } 
   Value2 = ( domCycle / ( 2 * PI ) ) * ( Value - Ref( Value, -1 ) ); 
   Plot( Value, "Sine", colorBlue ); 
   Plot( Value2, "Cosine", colorWhite ); 
} 
GraphZOrder = 1; 
_SECTION_END();