Recursive Implementation of the Gaussian Filter

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Royi Avital
Royi Avital 2015-3-14
回答： Royi Avital 2015-3-15
Hello,
I'm trying to implement the article "Recursive Implementation of the Gaussian Filter".
This article suggest an IIR Filter as an approximation of the Gaussian Blur. This is the suggested method:
Namely it is an order 4 IIR Filter.
I tried to reproduce the results for q = 5 as given in the article (See "Example").
Here is my code:
qFactor = 5;
b0Coeff = 1.57825 + (2.44413 * qFactor) + (1.4281 * qFactor * qFactor) + (0.422205 * qFactor * qFactor * qFactor);
b1Coeff = (2.44413 * qFactor) + (2.85619 * qFactor * qFactor) + (1.26661 * qFactor * qFactor * qFactor);
b2Coeff = (-1.4281 * qFactor * qFactor) + (-1.26661 * qFactor * qFactor * qFactor);
b3Coeff = 0.422205 * qFactor * qFactor * qFactor;
normalizationCoeff = 1 - ((b1Coeff + b2Coeff + b3Coeff) / b0Coeff);
vDenCoeff = [b0Coeff, b1Coeff, b2Coeff, b3Coeff] / b0Coeff;
vXSignal = zeros(61, 1);
vXSignal(31) = 10;
vYSignal = filter(normalizationCoeff, vDenCoeff, vXSignal);
vYSignal = filter(normalizationCoeff, vDenCoeff, vYSignal(end:-1:1));
figure();
plot(vYSignal);
I get the correct number for all coefficients, yet the result is:
What am I missing?
Has anyone managed to make it work?
Thank You.

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采纳的回答

Royi Avital
Royi Avital 2015-3-15
he answer was simple, the article uses the coefficients value on one hand where the MATLAB implementation on the other. Namely, a minus sign should be added.
Here's the correct code:
qFactor = 5;
b0Coeff = 1.57825 + (2.44413 * qFactor) + (1.4281 * qFactor * qFactor) + (0.422205 * qFactor * qFactor * qFactor);
b1Coeff = (2.44413 * qFactor) + (2.85619 * qFactor * qFactor) + (1.26661 * qFactor * qFactor * qFactor);
b2Coeff = (-1.4281 * qFactor * qFactor) + (-1.26661 * qFactor * qFactor * qFactor);
b3Coeff = 0.422205 * qFactor * qFactor * qFactor;
normalizationCoeff = 1 - ((b1Coeff + b2Coeff + b3Coeff) / b0Coeff);
vDenCoeff = [b0Coeff, -b1Coeff, -b2Coeff, -b3Coeff] / b0Coeff;
vXSignal = zeros(61, 1);
vXSignal(31) = 10;
vYSignal = filter(normalizationCoeff, vDenCoeff, vXSignal);
vYSignal = filter(normalizationCoeff, vDenCoeff, vYSignal(end:-1:1));
figure();
plot(vYSignal);

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