Hello, I am trying to fit something that requires a convolution.
With matlab, the discrete convolution means that it is only valid for the time over which the two functions are defined (matlab evaluates the convolution past this). As such, I am only interested in the part of the convolution that my functions are defined over. When I usually do my convolution, this is how:
x = 1:someNumber; numberOfElements = length(x);
newFunc = conv(func1,func2) newFunc = newFunc(1:numberOfElements)
where func1 and func 2 are defined over x. Using the 'same' property doesn't work.
The problem lies now that I need to do fitting using the convolution i.e.,
model = @(a, b, c, x) conv(func1(a,b,c,x),func2(a,b,c,x))
outputFit = fit(x,y,model) but not I need some way to tell matlab that I only want certain points from the convolution.
Edit: I should mention that I tried to avoid the convolution entirely by changing my convolution to an integral.
If function 2 is exp(a(t-t')/b)
and the convoltuon is
integral from (0 to t) of func1(t)*exp(a(t-t')/b)dt' - you can factor out the t and just have an integral from 0 to t (but its every t in the array i.e., 0 to t1 0 to t2 0 to t3...
I did this using arrayfun
kineticModel = @(ve,Ktrans,shift,x) Ktrans.*exp(-Ktrans.*(x-shift)./ve).*arrayfun(@(x) integral(@(x) Cpt(x,shift).*exp(Ktrans.*(x-shift)./ve),shift,x),x);
but for some reason when I plot the resulting kineticModel fit and then plug those values back into a convolution (to see if they are the same) they aren't, even when I have normalized the convolution by the spacing.