matched filter's output: gaussian?

[neoflash]

when I was reading "Digital Communications", I was confused by one assumption in matched filter design chapter.

The book stated that the matched filter should maxmize the signal-to-noise power ratio at its output. And the relationship between BER and SNR is derived based on one assumption: the noise after the matched filter is still gaussian distributed.

How we ensure that? How to prove it?

 

[zorro]

Hi neoflash,

any gaussian stationary stochastic process filtered by a linear time-invariant system is gaussian at the ouput.
This can be seen from the convolution integral that relates the output with the input, and by the fact that the linear combination of gaussian random variables is another gaussian RV.
Regards

Z

 

[ceaser]

look

in the majority in any noise calculations in Digital Communications we use gausian

destribution to indicate the statistics of noise

for LTI system if the input is gausian destripution the output also will be gausian

destripution

 

[neoflash]

Hi neoflash,

any gaussian stationary stochastic process filtered by a linear time-invariant system is gaussian at the ouput.
This can be seen from the convolution integral that relates the output with the input, and by the fact that the linear combination of gaussian random variables is another gaussian RV.
Regards

Z

that's exactly what I wanted, thanks