Convolution of a gaussian and an exponential

Hello,

I am trying to get a fitting equation by calculating the integral of a gaussian with an exponential, however, I am unsure why matlab is giving me results with complex numbers. Any help would be appreciated.

Thanks :)

syms I0 E E0 s N0 a Emax

A = I0*exp(-(E-E0)^2/(2*s^2*pi))

A = 

B = N0*exp(-a*E0)

B = 

int(A*B,E0,-inf,Emax)

ans = 

Answer 1

[Paul]

Are all of the parameters in the problem real? If so, then asserting them as such yields a simpler result.

syms I0 E E0 s N0 a Emax real
A = I0*exp(-(E-E0)^2/(2*s^2*pi))

A = 

B = N0*exp(-a*E0)

B = 

int(A*B,E0,-inf,Emax)

ans = 

Why does the Question refer to convolution? Asking because this integral is not a convolution integral, if convolution is really what is desired.

[Lamees Alkiyumi]

Yes all the parameters are real.

Thanks Paul appreciate it.

I was trying to replicate the following convultion but under different limits:

http://www.np.ph.bham.ac.uk/research_resources/programs/halflife/gauss_exp_conv.pdf

What should I add for it to be a convolution integral?

Many thanks.

[Paul]

Hi Lamees,

Using the notation in the linked reference, specifically in equation (3), the definition of convolution is:

given functions a(x) and b(x), their convolution is

c(y) = int(a(x)*b(y-x),x,0,inf) = int(a(y-x)*b(x),x,0,inf)

Note the argument of b in the first instance and of a in the second, and the lmits of integration, which implicitly assume that a(x) = b(x) = 0 for x < 0.

In your case, with x = E0, I think you just did

c(y) = int(a(x)*b(x),x,-inf,Emax)

That is, your equation doesn't do the "flip and slide" of b(x) (or alternatively a(x) ). Not sure what you're assuming for those limits of integration.