Measuring Cycle Period

/
"Filters are tuned to 8,9,10,...,50 periods. The filter with the highest output represents the dominant cycle. Implementing the idea presented in the article is easy using the AmiBroker Formula Language. ";

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", colorRed );
   Plot( Value2, "Cosine", colorGreen );
}
GraphZOrder = 1;