Deconvolution of two different Gaussians

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Tim
Tim 2025-1-14
评论： Tim 2025-1-20
Hi all
I'm convolving two different Gaussians: straggling and espread. But when I deconvolve the resultant I see either straggling or "nonsense". Is it possible to deconvolve the resultant in such a way that I see espread? My code is attached.
Sorry, bit of a noob question.
Regards
Tim

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Matt J
Matt J 2025-1-16
编辑：Matt J 2025-1-16
Ran in:
If you know a priori that all the signals are Gaussians, then deconvolution would not be the best way to recover espread. You know that the mean and variance of Gaussian signals add under convolution, so just fit a Gaussian (e.g. with this Download) to the output y and subtract its mean and variance from the known mean and variance of 'straggling'.
x1 = linspace(0, 20, 512);
dt=(x1(2)-x1(1));
straggling = GaussianPDF(x1, 7.7, 0.1);
figure; hold on;
plot(x1, straggling);
espread = GaussianPDF(x1, 7.7, 1);
% espread = espread/max(espread);
plot(x1, espread);
y = conv(straggling, espread)*dt;
x2 = (0:numel(y)-1)*dt;
plot(x2, y);
grid on;
legend('Straggling', 'E-Spread', 'Convolution');
p=gaussfitn(x2',y',[],{0,[],[]},{0,[],[]} );
espreadRec=GaussianPDF(x1,p{3}-7.7, sqrt(p{4}-0.1^2));
figure;
plot(x1,espread,'o',x1,espreadRec,'-');
legend Original Recovered
grid on;
  1 个评论
Tim
Tim 2025-1-20
Thanks Matt.
This was the clue I was looking for:
"If you know a priori that all the signals are Gaussians, then deconvolution would not be the best way to recover espread. You know that the mean and variance of Gaussian signals add under convolution, so just fit a Gaussian (e.g. with this Download) to the output y and subtract its mean and variance from the known mean and variance of 'straggling'."
Regards
Tim

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更多回答（1 个）

Catalytic
Catalytic 2025-1-16
编辑：Catalytic 2025-1-16
Is it possible to deconvolve the resultant in such a way that I see espread?
Since you deconvolve y by espread, of course you will get straggling. Presumably you meant to deconvolve by straggling -
a=deconv(y,straggling);

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