Does anyone know how to figure out a workaround to avoid computing overflow/u​nderflow/N​aN/inf in this algorithm?

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Eric Diaz
Eric Diaz 2015-11-15
评论： Eric Diaz 2015-11-22
M14 = Signal.^14;
M12 = Signal.^12 ; M10 = Signal.^10;
M8 = Signal.^8 ; M6 = Signal.^6;
M4 = Signal.^4 ; M2 = Signal.^2;
S14 = Sigma.^14;
S12 = Sigma.^12 ; S10 = Sigma.^10;
S8 = Sigma.^8 ; S6 = Sigma.^6;
S4 = Sigma.^4 ; S2 = Sigma.^2;
nPiD2 = pi/2;
sqrtNpiD2 = sqrt(nPiD2);
n1D2 = 1/2;
n1D4 = 1/4;
n1DM10Sig = 1./(M10.*Sigma);
n1DM12Sig = 1./(M12.*Sigma);
alpha = M2./S2;
nAlphaD4 = n1D4*alpha;
FirstTerm = n1DM10Sig.*(M12 + 9*M10.*S2 - 15*M8.*S4 + 90*M6.*S6 - 495*M4.*S8 + 2160*M2.*S10 - 5760*S12).*besseli(0,nAlphaD4);
SecondTerm = n1DM12Sig.*(M14 + 7*M12.*S2 - 27*M10.*S4 + 150*M8.*S6 - 855*M6.*S8 + 4320*M4.*S10 - 17280*M2.*S12 + 46080*S14).*besseli(1,nAlphaD4);
biasedSignal = n1D2*sqrtNpiD2*exp(-nAlphaD4).*(FirstTerm + SecondTerm);
As you can imagine, because of the powers of these numbers being rather high, I am running into issues with computing inf/NaN where I don't actually want it. Is there a way to avoid computing these values?

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采纳的回答

Jan
Jan 2015-11-15
You can calculate the logarithm of all equations to keep the ranges of the values inside the limits. Replace besseli by its taylor series to build its log.
  2 个评论
Eric Diaz
Eric Diaz 2015-11-22
It turns out that most of the overflow problem was occuring in the besseli function.
I actually was having some problems with overflow of the besseli function two nights ago and I found a solution which works really well without having to use a taylor approximation.
Instead of explaining it, I will give you the link of where I found the solution. As you may know, Cleve Moler, who is the person that is providing the solution, is the person that founded MATLAB.
https://www.mathworks.com/matlabcentral/newsreader/view_thread/101943
I found that solution #2, works really well!

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