Optimizing calculation in for loop for convolution
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Hello everyone,
I'm trying to compute the convolution of a heaviside and a gaussian function. For that purpose i use the following code:
x=-100:0.01:100;
sigma=5;
tzero=10;
Hea=heaviside(x-tzero);
to=min(x)+3*sigma:0.01:max(x)-3*sigma;
for i=1:length(to)
sliding_gaussian=exp(-((x-to(i))/sigma).^2);
S=@(x) Hea.*sliding_gaussian;
q=integral(S,-100,100,'ArrayValued',true);
int(i)=abs(sum(q)*0.01);
end
But it's taking ages. I need to include that into a fit so the complete computation will take even longer.
I tried the matlab function "conv" but i guess i don't know how to use it, since it didn't return what i expected - I appreciate any example that would fit my purpose.
Thank you for your help.
采纳的回答
Bruno Luong
2020-8-26
编辑：Bruno Luong
2020-9-3
Use error function ERF
x = -100:0.01:100;
sigma = 5;
tzero = 10;
to = min(x)+3*sigma:0.01:max(x)-3*sigma;
convfun = @(t) sqrt(pi)*sigma/2*(1+erf((t-tzero)/sigma));
int = convfun(to);
plot(to,int)
xlim([-10,30])
更多回答（1 个）
Bjorn Gustavsson
2020-8-26
This should work:
Hea = heaviside(x-tzero); % your shifted Heaviside
sliding_gaussian=exp(-(x/sigma).^2); % Gaussian
sliding_gaussian = sliding_gaussian/sum(sliding_gaussian); % Normalize it
GHc = conv(Hea,sliding_gaussian,'same'); % use convolution
figure
plot(x,[Hea;GHc])
% The dip at the end is due to implicit zero-padding of Hea in conv
% If you have the image processing toolbox you can use imfilter
% which does pretty much the same convolution-job as conv, but with
% more options of edge-handling:
B = imfilter(Hea,sliding_gaussian,'replicate');
hold on
plot(x,B)
HTH
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