Find value of variable in a equality

Hi, i have to estimate the sigma from here,

(dB) = (1/sqrt(2*pi*sigma))*exp(-(BW-m)²/2(sigma)²)

as you see is the gaussian densitiy function.

I know the value of (dB), and the (BW-m)² polynomial, so my question is,

How can I get the sigma value?

Thank you all, my first time here, it's an honor.

Answer 1

[José-Luis]

This is not really a Matlab question. You could explicitely solve this equation using some arithmetic. That said, you could always use the symbolic toolbox to do that for you:

 syms x dB val
 solve(1/sqrt(2*pi*x)*exp(-(val/(2*x)))-dB)
 ans =

 -val/lambertw(0, -2*pi*dB^2*val)

You just need to replace val (BW-m)^2 and dB in that expression.

[Lucas]

That's what I needed, thank you so much José-Luis.