Mixing correlated, band-limited Noise

If a band-limited white noise source is mixed with a non-delayed version of
itself in a down-conversion process, is the noise cancelled?  If the noise
is mixed with a version of itself, which is time delayed by greater than a
1/BW, is the noise power out of the mixer 2x one of the noise sources? I
modelled this process in matalb and dont get the expected result.  
Thanks.
		
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JohnnyM wrote:
> If a band-limited white noise source is mixed with a non-delayed
version of
> itself in a down-conversion process, is the noise cancelled?  If the
noise
> is mixed with a version of itself, which is time delayed by greater
than a
> 1/BW, is the noise power out of the mixer 2x one of the noise
sources? I
> modelled this process in matalb and dont get the expected result.
> Thanks.
>
> This message was sent using the Comp.DSP web interface on
> www.DSPRelated.com

Are you using the term "mix" like the audio guys as in ADD or like the
RF guys as in MULTIPLY?

Mark

>
>JohnnyM wrote:
>> If a band-limited white noise source is mixed with a non-delayed
>version of
>> itself in a down-conversion process, is the noise cancelled?  If the
>noise
>> is mixed with a version of itself, which is time delayed by greater
>than a
>> 1/BW, is the noise power out of the mixer 2x one of the noise
>sources? I
>> modelled this process in matalb and dont get the expected result.
>> Thanks.
>>
>> This message was sent using the Comp.DSP web interface on
>> www.DSPRelated.com
>
>Are you using the term "mix" like the audio guys as in ADD or like the
>RF guys as in MULTIPLY?
>
>Mark
>
Multiply-like the RF guys.  My signals are complex and I am modelling the
mixer as the sum of the straight product and the product of the signal
times its complex conjugate.
John
>


		
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>
>JohnnyM wrote:
>> If a band-limited white noise source is mixed with a non-delayed
>version of
>> itself in a down-conversion process, is the noise cancelled?  If the
>noise
>> is mixed with a version of itself, which is time delayed by greater
>than a
>> 1/BW, is the noise power out of the mixer 2x one of the noise
>sources? I
>> modelled this process in matalb and dont get the expected result.
>> Thanks.
>>
>> This message was sent using the Comp.DSP web interface on
>> www.DSPRelated.com
>
>Are you using the term "mix" like the audio guys as in ADD or like the
>RF guys as in MULTIPLY?
>
>Mark
>
Multiply-like the RF guys.  My signals are complex and I am modelling the
mixer as the sum of the straight product and the product of the signal
times its complex conjugate.
John
>


		
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JohnnyM wrote:

>>JohnnyM wrote:
>>
>>>If a band-limited white noise source is mixed with a non-delayed
>>>version of itself in a down-conversion process, is the noise 
>>>cancelled?  If the noise is mixed with a version of itself, which 
>>>is time delayed by greater than a 1/BW, is the noise power out of  
>>>the mixer 2x one of the noise sources? I
>>
>>>modelled this process in matalb and dont get the expected result.
>>>Thanks.
>>>
>>>This message was sent using the Comp.DSP web interface on
>>>www.DSPRelated.com
>>
>>Are you using the term "mix" like the audio guys as in ADD or like the
>>RF guys as in MULTIPLY?
>>
>>Mark
>>
> 
> Multiply-like the RF guys.  My signals are complex and I am modelling the
> mixer as the sum of the straight product and the product of the signal
> times its complex conjugate.
> John
> 
No.  Study up on random processes, on what happens when you square a 
zero-mean random process (i.e. your noise times itself) and what happens 
when you multiply two zero-mean random processes (i.e. your noise times 
its complex conjugate).

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

>JohnnyM wrote:
>
>>>JohnnyM wrote:
>>>
>>>>If a band-limited white noise source is mixed with a non-delayed
>>>>version of itself in a down-conversion process, is the noise 
>>>>cancelled?  If the noise is mixed with a version of itself, which 
>>>>is time delayed by greater than a 1/BW, is the noise power out of  
>>>>the mixer 2x one of the noise sources? I
>>>
>>>>modelled this process in matalb and dont get the expected result.
>>>>Thanks.
>>>>
>>>>This message was sent using the Comp.DSP web interface on
>>>>www.DSPRelated.com
>>>
>>>Are you using the term "mix" like the audio guys as in ADD or like the
>>>RF guys as in MULTIPLY?
>>>
>>>Mark
>>>
>> 
>> Multiply-like the RF guys.  My signals are complex and I am modelling
the
>> mixer as the sum of the straight product and the product of the signal
>> times its complex conjugate.
>> John
>> 
>No.  Study up on random processes, on what happens when you square a 
>zero-mean random process (i.e. your noise times itself) and what happens

>when you multiply two zero-mean random processes (i.e. your noise times 
>its complex conjugate).
>
>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>


		
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>JohnnyM wrote:
>
>>>JohnnyM wrote:
>>>
>>>>If a band-limited white noise source is mixed with a non-delayed
>>>>version of itself in a down-conversion process, is the noise 
>>>>cancelled?  If the noise is mixed with a version of itself, which 
>>>>is time delayed by greater than a 1/BW, is the noise power out of  
>>>>the mixer 2x one of the noise sources? I
>>>
>>>>modelled this process in matalb and dont get the expected result.
>>>>Thanks.
>>>>
>>>>This message was sent using the Comp.DSP web interface on
>>>>www.DSPRelated.com
>>>
>>>Are you using the term "mix" like the audio guys as in ADD or like the
>>>RF guys as in MULTIPLY?
>>>
>>>Mark
>>>
>> 
>> Multiply-like the RF guys.  My signals are complex and I am modelling
the
>> mixer as the sum of the straight product and the product of the signal
>> times its complex conjugate.
>> John
>> 
>No.  Study up on random processes, on what happens when you square a 
>zero-mean random process (i.e. your noise times itself) and what happens

>when you multiply two zero-mean random processes (i.e. your noise times 
>its complex conjugate).
>
>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com

I'll have to think about it.  I took the above products to get the sum and
difference frequencies produced by the mixing process - this works for
detrministic signals, e.g., sin cos.  If I think about this stochasically,
the two products certainly dont give the same thing - you get x(n)=
e^j(s(n)-s(n))+e^j(s(n)+s(n)), but is it incorrect?  I would guess the
autocorrelations of the two terms of x(n) should be the same if this is
correct.  For zero lag, the first term will gives what I expect (=1 for
correlated signals), but the second term doesn't, so it seems something is
wrong.  What I am trying to to must have been done a thousand times before.
 Can anyone suggest a reference or approach?
Thanks,
John M.


		
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