Is the noise output of a mached filter white?

[carpa]

digital matched filter

For a matched filter, although the input noise is white, the output of it is not. However, many papers talking about communication signal processing assume that n(t) at the output of the matched filter is Gaussion and WHITE. Is that right? Or just for simplicity?

 

[darock]

The output of a matched filter is definitely Gaussian if the input is Gaussian.
Firstly, linear operations on Gaussian is always Gaussian.
Regarding the whiteness of noise..

original signal n(t) E[ n(t) n(t+k)]= N0 when k=0; otherwise

Now we have n(k)=Output of matched filter.

Consider E( n(k) n(k+m)] = E[ integral n(t) from kT to (k+1)T * integral n(t) from (k+m)T to (k+m+1)T]


Take both integrals outside and expectation inside, then we have two integrals E[ n(t) n(t+k)]= N= when m=0; 0 otherwise

Thus it is Gaussian and white..hope it helps

 

[m_llaa]

Hi Carpa
You are right. MF output is absolutly gaussian, but it is not white. Its shape is equal to matched filter shape.
But common matched filters are flat in their bandwidth, then output noise is white in bandwidth of filter.

 

[Sal]

HI

AWGN is present at any point of an electronic circuit, which means tha it is present at the input as well as the output of a matched filter, that is why the assumption.

Sal

 

[kastantin]

For a matched filter, although the input noise is white, the output of it is not. However, many papers talking about communication signal processing assume that n(t) at the output of the matched filter is Gaussion and WHITE. Is that right? Or just for simplicity?

when the white noise pass through any filter (except all pass filter) becom not white noise