I've arrived at the following equation involving the convolution of two functions:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

f(x) = \int_{-\infty}^{\infty} f(t) g(t-x) dt = f(x) \ast g(x)

[/itex]

Where:

[itex]

g(z) = e^{-z^2/2}

[/itex]

In other words, a function convoluted with a Gaussian pdf results in the same function.

I've tried taking fourier transforms, realizing that the FT of a gaussian results in another Gaussian:

[itex]

F[f(x)] = F[f(x) \ast g(x)] = F[f(x)] \cdot F[g(x)]

[/itex]

But this results in the [itex] F[f(x)] [/itex] cancelling out, leaving me with just:

[itex]

1 = F[g(x)] = e^{-w^2/2}

[/itex]

Any suggestions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Strange convolution equation

**Physics Forums | Science Articles, Homework Help, Discussion**