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

infMATLABnanoverflowunderflow

        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?

Best Answer

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.
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