In electric engineering (my field) we use Fourier Transform to represent an arbitrary signal as a sum of sinusoidal signals.
I've stumbled upon a statistics problem where I want to decompose a distribution function as a sum of normal curves. Like the drawing bellow:
I think there is an analog to Fourier transform to this but, instead of frequency, the coefficients to be determined would be the mean and the standard deviation of each normal component. In the college we see a lot of links between exponentials and sinusoidals functions, which makes me think there is a missing link here that wasn't presented to me.
I don't want a lecture, just someone to point me the right direction.
You're probably looking for the Weierstrass transform, defined by $$ W[f](x) \frac{1}{\sqrt{4\pi}}\int_{-\infty}^{\infty} f(y) e^{(x-y)^2/4} \, dy. $$