102 lines
5.1 KiB
MQL5
102 lines
5.1 KiB
MQL5
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//+------------------------------------------------------------------+
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//| FourierTransform.mqh |
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//| MMQ — Muhammad Minhas Qamar |
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//| www.mql5.com/en/articles/23491 |
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//+------------------------------------------------------------------+
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#property copyright "MMQ — Muhammad Minhas Qamar"
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#property link "https://www.mql5.com/en/articles/23491"
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#property version "1.00"
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#property strict
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#include <Math\Alglib\alglib.mqh>
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//+------------------------------------------------------------------+
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//| CDFT - the real-input Fourier front end for SFA. |
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//| |
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//| SFA does not need a full spectrum. For a window of length w it |
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//| keeps only the first 'l' complex Fourier coefficients, whose |
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//| real and imaginary parts become the l real numbers that are |
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//| later binned into letters. Low index = low frequency, so |
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//| keeping the first few coefficients is a low-pass filter: it |
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//| retains the coarse shape of the window and discards the |
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//| high-frequency jitter. That built-in denoising is the whole |
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//| reason SFA tolerates noisy price data. |
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//| |
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//| The transform itself is delegated to ALGLIB's FFTR1D, a real |
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//| FFT that accepts any window length (no power-of-two rule). We |
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//| simply read back the coefficients we want. The class exists to |
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//| give SFA one clean call and to fix the coefficient-ordering |
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//| convention in a single place. |
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//+------------------------------------------------------------------+
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//--- how many real values a request for 'coeff_count' coefficients
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//--- yields once real and imaginary parts are laid out side by side.
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#define DFT_REALS_PER_COEFF 2
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//+------------------------------------------------------------------+
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//| Interleaving convention for the flat output array. |
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//| |
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//| ALGLIB returns coefficients as a complex[] array f[0..w/2]. |
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//| SFA wants a flat double[] of the low coefficients' real and |
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//| imaginary parts. We lay them out as |
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//| out = { Re(f1), Im(f1), Re(f2), Im(f2), ... } |
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//| starting at f[1], because f[0] (the DC term) is the window |
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//| mean and is identically zero after z-normalization — carrying |
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//| it would waste a letter on a constant. 'coeff_count' therefore |
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//| counts non-DC coefficients, and the flat array has |
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//| coeff_count * 2 entries. |
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//+------------------------------------------------------------------+
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class CDFT
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{
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public:
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//--- transform raw[0..len-1] and write the first 'coeff_count'
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//--- non-DC coefficients, interleaved (re,im,re,im,...), into
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//--- out[]. out[] is resized to coeff_count*2. Returns false if
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//--- the window is too short to supply that many coefficients.
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static bool LowCoefficients(const double &raw[],int len,
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int coeff_count,double &out[]);
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//--- largest number of non-DC coefficients a length-'len' window
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//--- can supply. ALGLIB yields floor(len/2)+1 coefficients
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//--- including DC, so the usable non-DC count is floor(len/2).
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static int MaxCoefficients(int len) { return (len>1)?(len/2):0; }
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};
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//+------------------------------------------------------------------+
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//| Compute the low-frequency coefficients of a real window. |
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//| |
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//| 'raw' is expected to be already z-normalized by the caller so |
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//| that the DC term is ~0 and every window is compared on shape, |
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//| not on price level. We still start reading at f[1] regardless, |
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//| so a non-normalized window simply loses its mean here. |
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//+------------------------------------------------------------------+
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bool CDFT::LowCoefficients(const double &raw[],int len,
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int coeff_count,double &out[])
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{
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if(len<2 || coeff_count<1)
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return false;
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if(coeff_count>MaxCoefficients(len))
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return false;
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//--- ALGLIB needs a plain double[] of exactly 'len' samples.
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double sample[];
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ArrayResize(sample,len);
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for(int i=0;i<len;i++)
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sample[i]=raw[i];
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complex spectrum[];
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CAlglib::FFTR1D(sample,len,spectrum);
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if(ArraySize(spectrum)<coeff_count+1) // need f[1..coeff_count]
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return false;
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//--- flatten f[1..coeff_count] into interleaved real/imag pairs.
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ArrayResize(out,coeff_count*DFT_REALS_PER_COEFF);
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for(int k=0;k<coeff_count;k++)
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{
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complex c=spectrum[k+1]; // skip f[0] (DC)
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out[DFT_REALS_PER_COEFF*k] =c.real;
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out[DFT_REALS_PER_COEFF*k+1]=c.imag;
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}
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return true;
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}
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//+------------------------------------------------------------------+
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