Deconvolution of two different Gaussians

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

[Tim]

Attached here is the GaussianPDF function

Answer 1

[Matt J]

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;

[Tim]

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

Answer 2

[Catalytic]

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);

[Tim]

Hi Catalytic,

I tried that and got "nonsense". See attched.

Regards

Tim