Signal To Noise Ratio

The Signal To Noise Ratio was authored by John Ehlers; it is derived from his Hilbert Transform Indicator. Highs, lows, Euler’s logarithms, factors and feedback are applied to Hilbert’s complex number calculations to produce this indicators amplitude value. The user may change the input (midpoint) and Hilbert period length. This indicator’s definition is further expressed in the condensed code given in the calculation below.

Click here for more information on Ehler’s indicators.

Click here for more information on the Hilbert Transform Indicator

How To Trade Using the Signal To Noise Ratio

The Signal To Noise Ratio may be used in conjuction with other indicators. No trading signals are calculated in this study.

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Go to the top menu, choose Study>John Ehlers>Signal To Noise Ratio

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Calculation

//input = price, user defined, default is midpoint price
//Hilbert period = user defined, default is 7
//quad = quadrature = imaginary part of complex number
//inPhase = real part of complex number
//amp = amplitude
//index = current bar number

iMult = .635;
qMult = .338;

priorPrice = price[index-period];
//v1 = detrend price
v1 = price - priorPrice;

high = series.getHigh(index);
low = series.getLow(index);
prevRange = range[index-1];
range = (.2 * (high - low)) + (.8 * prevRange);

v2 = v1[index-2];      
v4 = v1[index-4];      

inPhase3 = inPhase[index-3];      
quad2 = quad[index-2];      

//Hilbert transform complex number components, inPhase (real part), quad (imaginary part)
inPhase = 1.25 * (v4 - (iMult*v2) + (iMult*inPhase3));
quad = v2 - (qMult*v1) + (qMult*quad2);

prevV2 = v2[index-1];
//smoothed signal amplitude
v2 = .2 * (inPhase * inPhase + quad * quad) + .8 * prevV2;
prevAmp = amp[index-1];
//smoothed SNR in decibels 
if (v2 lessThan .001) v2 = .001;
if (range lessThan 0) 
      amp = .25 * (10 * Math.log(v2/(range*range))/Math.log(10) + 1.9) + .75 * prevAmp;
endIf
Plot amp;