Hi,
Gaussian filters have a property that their support in the time domain, is equal to their support in the frequency domain.
This comes about from the Gaussian being its own Fourier Transform.
Here gaussian filter is used as low pass filter to remove high frequency component and band limit the signals.
When we use gauusian filter in receivers we would have obtain the Gaussian optical receiver’s eigenmodes exactly in frequency domain. Their eigenfunctions are Hermite functions multiplied by a common phase factor. Using these eigenmodes, we investigate the probability distribution functions of the electrical filter’s output before the decision circuit. We derive a bit-error rate (BER) expression in a closed form using the lowest-order eigenmode. It is valid when the optical filter bandwidth is comparable to the modulation bandwidth as in conventional high capacity optical wavelength-division multiplexing transmission systems. The BER expression can be applied also to non-Gaussian optical receivers.
thanks