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//+------------------------------------------------------------------+
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//| Fourier_Series_Calculator.mqh |
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//| Calculation engine for the John Ehlers' Fourier Series. |
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//| Copyright 2025, xxxxxxxx |
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//+------------------------------------------------------------------+
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#property copyright "Copyright 2025, xxxxxxxx"
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#include <MyIncludes\HeikinAshi_Tools.mqh>
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//+==================================================================+
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//| |
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//| CLASS 1: CFourierSeriesCalculator (Base Class) |
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//| |
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//+==================================================================+
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class CFourierSeriesCalculator
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{
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protected:
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int m_period;
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double m_bandwidth;
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double m_price[];
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// Filter coefficients
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double L1, G1, S1;
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double L2, G2, S2;
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double L3, G3, S3;
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virtual bool PreparePriceSeries(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[]);
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public:
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CFourierSeriesCalculator(void) {};
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virtual ~CFourierSeriesCalculator(void) {};
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bool Init(int period, double bandwidth);
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void Calculate(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[],
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double &wave_buffer[], double &roc_buffer[]);
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};
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//+------------------------------------------------------------------+
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bool CFourierSeriesCalculator::Init(int period, double bandwidth)
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{
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m_period = (period < 10) ? 10 : period;
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m_bandwidth = bandwidth;
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// Pre-calculate filter coefficients
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L1 = cos(2 * M_PI / m_period);
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G1 = cos(m_bandwidth * 2 * M_PI / m_period);
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S1 = 1.0 / G1 - sqrt(1.0 / (G1 * G1) - 1.0);
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L2 = cos(2 * M_PI / (m_period / 2.0));
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G2 = cos(m_bandwidth * 2 * M_PI / (m_period / 2.0));
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S2 = 1.0 / G2 - sqrt(1.0 / (G2 * G2) - 1.0);
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L3 = cos(2 * M_PI / (m_period / 3.0));
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G3 = cos(m_bandwidth * 2 * M_PI / (m_period / 3.0));
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S3 = 1.0 / G3 - sqrt(1.0 / (G3 * G3) - 1.0);
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return true;
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}
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//+------------------------------------------------------------------+
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void CFourierSeriesCalculator::Calculate(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[],
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double &wave_buffer[], double &roc_buffer[])
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{
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if(rates_total < m_period * 2)
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return;
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if(!PreparePriceSeries(rates_total, price_type, open, high, low, close))
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return;
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// Intermediate buffers
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double bp1[], bp2[], bp3[], q1[], q2[], q3[];
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ArrayResize(bp1, rates_total);
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ArrayResize(bp2, rates_total);
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ArrayResize(bp3, rates_total);
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ArrayResize(q1, rates_total);
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ArrayResize(q2, rates_total);
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ArrayResize(q3, rates_total);
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// State variables for recursive filters
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double bp1_p1=0, bp1_p2=0, bp2_p1=0, bp2_p2=0, bp3_p1=0, bp3_p2=0;
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for(int i = 2; i < rates_total; i++)
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{
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// Step 2: Band-Pass Filters
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bp1[i] = 0.5 * (1.0 - S1) * (m_price[i] - m_price[i-2]) + L1 * (1.0 + S1) * bp1_p1 - S1 * bp1_p2;
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bp2[i] = 0.5 * (1.0 - S2) * (m_price[i] - m_price[i-2]) + L2 * (1.0 + S2) * bp2_p1 - S2 * bp2_p2;
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bp3[i] = 0.5 * (1.0 - S3) * (m_price[i] - m_price[i-2]) + L3 * (1.0 + S3) * bp3_p1 - S3 * bp3_p2;
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// Step 3: Quadrature Components
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q1[i] = (m_period / (2.0 * M_PI)) * (bp1[i] - bp1[i-1]);
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q2[i] = (m_period / (2.0 * M_PI)) * (bp2[i] - bp2[i-1]);
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q3[i] = (m_period / (2.0 * M_PI)) * (bp3[i] - bp3[i-1]);
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// Update state variables
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bp1_p2 = bp1_p1;
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bp1_p1 = bp1[i];
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bp2_p2 = bp2_p1;
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bp2_p1 = bp2[i];
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bp3_p2 = bp3_p1;
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bp3_p1 = bp3[i];
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}
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for(int i = m_period * 2 -1; i < rates_total; i++)
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{
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// Step 4: Calculate Power
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double p1=0, p2=0, p3=0;
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for(int j = 0; j < m_period; j++)
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{
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p1 += bp1[i-j]*bp1[i-j] + q1[i-j]*q1[i-j];
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p2 += bp2[i-j]*bp2[i-j] + q2[i-j]*q2[i-j];
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p3 += bp3[i-j]*bp3[i-j] + q3[i-j]*q3[i-j];
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}
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// Step 5: Synthesize Wave
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if(p1 > 0)
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{
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wave_buffer[i] = bp1[i] + sqrt(p2/p1)*bp2[i] + sqrt(p3/p1)*bp3[i];
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}
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// Step 6: Optional ROC
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if(i > 1)
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roc_buffer[i] = (m_period / (4.0 * M_PI)) * (wave_buffer[i] - wave_buffer[i-2]);
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}
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}
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//+------------------------------------------------------------------+
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bool CFourierSeriesCalculator::PreparePriceSeries(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[])
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{
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ArrayResize(m_price, rates_total);
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// Ehlers' example uses Median Price
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for(int i=0; i<rates_total; i++)
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m_price[i] = (high[i]+low[i])/2.0;
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return true;
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}
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//+------------------------------------------------------------------+
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//| |
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//+------------------------------------------------------------------+
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class CFourierSeriesCalculator_HA : public CFourierSeriesCalculator
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{
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private:
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CHeikinAshi_Calculator m_ha_calculator;
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protected:
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virtual bool PreparePriceSeries(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[]) override;
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};
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//+------------------------------------------------------------------+
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//| |
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//+------------------------------------------------------------------+
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bool CFourierSeriesCalculator_HA::PreparePriceSeries(int rates_total, ENUM_APPLIED_PRICE price_type, const double &open[], const double &high[], const double &low[], const double &close[])
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{
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double ha_open[], ha_high[], ha_low[], ha_close[];
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ArrayResize(ha_open, rates_total);
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ArrayResize(ha_high, rates_total);
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ArrayResize(ha_low, rates_total);
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ArrayResize(ha_close, rates_total);
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m_ha_calculator.Calculate(rates_total, open, high, low, close, ha_open, ha_high, ha_low, ha_close);
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ArrayResize(m_price, rates_total);
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for(int i=0; i<rates_total; i++)
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m_price[i] = (ha_high[i]+ha_low[i])/2.0;
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return true;
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}
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//+------------------------------------------------------------------+
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