Reply by Jerry Avins March 30, 20052005-03-30
Randy Yates wrote:

   ...

> OK Jerry, I understand what you meant now - thanks for the > clarification. Since "amplitude" is clearly a time-domain phenomenom, > it seemed confusing that you were speaking of a frequency-domain > phenomenom in the same sentence without clarifying.
You were right to call me on it. My original post was very poorly expressed. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by Mike Yarwood March 30, 20052005-03-30
"Jerry Avins" <jya@ieee.org> wrote in message 
news:SrudnUDeeKjEedffRVn-tg@rcn.net...
> Mike Yarwood wrote: > > ... > >> Hi Jerry! I intended to say uniform phase distribution and rayleigh >> magnitude is the polar representation alternative to the two orthogonal >> gaussian distributions (left out all the identical variance and zero mean >> stuff that you need to be sure you get the uniform phase distribution). >> I assume you were talking about a zero-mean , >> 2_Dimensional gaussian distribution in your earlier post so the uniform >> phase distribution made sense but I'm used to generating I and Q >> components so this representation is less confusing for me at any rate. > > Mike, > > I hope I didn't offend you. I certainly didn't mean to. I just wanted to > be sure that nobody was misled. Noise is so confusing precisely because > it's so noisy. There's a beautiful general distribution of which Gaussian > and Rayleigh are two extreme cases. Since the tails of a Gaussian extend > to infinity in both directions, no positive-only quantity (such as radius) > can have a Gaussian distribution. If the mean is high enough compared to > the variance, the distribution can be very close to Gaussian. As the ratio > shrinks, the closest to Gaussian becomes increasingly distorted. A > Rayleigh distribution can be viewed as the limit of that process. What was > Gaussian noise at the input to an FM detector becomes Rayleigh at the > output. > > FM detectors were my first exposure to Rayleigh distributions. After a > while I realized that Rayleigh is related to Poisson the same way that > Gaussian is to Binomial. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Hey - no offence at all - I enjoy reading _all_ your posts (by that I mean all the ones I've seen on this backwater of a news server I'm using ). Keep it up ! and I'll carry on mostly lurking.... it's less stress. Best of Luck - Mike
Reply by March 30, 20052005-03-30
Jerry Avins <jya@ieee.org> writes:

> Randy Yates wrote: > > Jerry Avins <jya@ieee.org> writes: > > > > >>Your Name Heres wrote: > >> > >>>When we talk about an AWGN signal, n(t), which parameter(s) has the > >>>Gaussian distribution? ... > >> > >> > >>Amplitude distribution is Gaussian. Phase distribution is uniform. > > Jerry, I'll jump in as at least one other has and ask about this > > phase thing. > > > If we're talking about a real signal, then what do you mean by "phase"? > > Take the FT of the AWGN (if the FT aliases, how would you > know?). Express the result in magnitude/phase form. That's the phase I > meant. (The spectrum amplitude should be flat. If it isn't and you > really started with AWGN, you know you aliased.)
OK Jerry, I understand what you meant now - thanks for the clarification. Since "amplitude" is clearly a time-domain phenomenom, it seemed confusing that you were speaking of a frequency-domain phenomenom in the same sentence without clarifying. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Reply by Jerry Avins March 30, 20052005-03-30
Randy Yates wrote:
> Jerry Avins <jya@ieee.org> writes: > > >>Your Name Heres wrote: >> >>>When we talk about an AWGN signal, n(t), which parameter(s) has the >>>Gaussian distribution? ... >> >> >>Amplitude distribution is Gaussian. Phase distribution is uniform. > > > Jerry, > > I'll jump in as at least one other has and ask about this phase thing. > If we're talking about a real signal, then what do you mean by "phase"?
Take the FT of the AWGN (if the FT aliases, how would you know?). Express the result in magnitude/phase form. That's the phase I meant. (The spectrum amplitude should be flat. If it isn't and you really started with AWGN, you know you aliased.) Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by Jerry Avins March 30, 20052005-03-30
Mike Yarwood wrote:

   ...

> Hi Jerry! I intended to say uniform phase distribution and rayleigh > magnitude is the polar representation alternative to the two orthogonal > gaussian distributions (left out all the identical variance and zero mean > stuff that you need to be sure you get the uniform phase distribution). I > assume you were talking about a zero-mean , > 2_Dimensional gaussian distribution in your earlier post so the uniform > phase distribution made sense but I'm used to generating I and Q components > so this representation is less confusing for me at any rate.
Mike, I hope I didn't offend you. I certainly didn't mean to. I just wanted to be sure that nobody was misled. Noise is so confusing precisely because it's so noisy. There's a beautiful general distribution of which Gaussian and Rayleigh are two extreme cases. Since the tails of a Gaussian extend to infinity in both directions, no positive-only quantity (such as radius) can have a Gaussian distribution. If the mean is high enough compared to the variance, the distribution can be very close to Gaussian. As the ratio shrinks, the closest to Gaussian becomes increasingly distorted. A Rayleigh distribution can be viewed as the limit of that process. What was Gaussian noise at the input to an FM detector becomes Rayleigh at the output. FM detectors were my first exposure to Rayleigh distributions. After a while I realized that Rayleigh is related to Poisson the same way that Gaussian is to Binomial. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by Your Name Heres March 30, 20052005-03-30
In article <R7Y1e.4233$yq2.984@newssvr12.news.prodigy.com>, 
pleaserespondhere@ok.com says...
> >When we talk about an AWGN signal, n(t), which parameter(s) has the Gaussian >distribution? Is it the amplitude, power, or phase of the signal?? Also is
the
>parameter linear or logarithmic under the Gaussian distribution? For >example, are we to assume that AWGN describes a power signal with a >mean and variance on a logarithmic scale versus time? Any help >understanding this will be appreciated. > >Thanks. > >-Please respond to this forum. >
thanks to everyone for their input.
Reply by Your Name Heres March 30, 20052005-03-30
Ravi,

Thanks for the detailed explanation. Things are starting to come back to me 
now...
>>
Reply by Peter K. March 29, 20052005-03-29
Mark wrote:

> Is the amplitude distribution of AWGN still Gaussian after it > has been band limited?
Definitely! Other distributions than Gaussian will also tend to be Gaussian after filtering (like band-limiting). [Vague wave of the hands towards the central limit theorem].
> Is clipped AWGN still white?
Definitely not Gaussian... I believe it will still be white (think of quantizing AWGN to 1 bit).
> Is a random signal with a uniform amplitude distribution white?
It certainly can be. The distribution (Gaussian or Uniform) says what the likelihood is of a paricular measurement value (e.g. 34.123791823 knuths). The whiteness says how much influence one measurement has over the next measurement.
> Are the amplitude distribution and frequency shape of a random signal > independent?
The amplitude distribution says what the "distribution" is. The "frequency shape" says how much influence one measurement has over the next measurement. So, yes, the two can be independent.
> Can I create a random signal of any amplitude distribution and any > frequency distribution independently or are there some > interdependencies?
If you start with uniformly distrubuted white noise and filter it (to change the "frequency shape"), then the filtering will mean [if it's LTI] that you will no longer have a uniform distribution. The distribution will tend to Gaussian, because you're adding lots of random variables together (assuming filtering with a long impulse response, where long is greater than ~ 12 samples). I'm not sure how you'd go about assigning a Uniform distribution independently of the "frequency shape" though. Ciao, Peter K.
Reply by Mark March 29, 20052005-03-29
A few questions..

robert bristow-johnson wrote:
> one of the nasty things about white noise is that it has INfinite
power (the
> area under the power spectrum curve is infinite). the concept exists
only
> for this white noise to be processed with a system of finite
bandwidth.
> then the noise in the pass band is finite power but isn't really
white. it
> might be viewed as white within the context of that pass band. >
Is the amplitude distribution of AWGN still Gaussian after it has been band limited? Is clipped AWGN still white? Is a random signal with a uniform amplitude distribution white? Are the amplitude distribution and frequency shape of a random signal independent? Can I create a random signal of any amplitude distribution and any frequency distribution independently or are there some interdependencies? thanks Mark
Reply by March 29, 20052005-03-29
Jerry Avins <jya@ieee.org> writes:

> Your Name Heres wrote: > > When we talk about an AWGN signal, n(t), which parameter(s) has the > > Gaussian distribution? ... > > > Amplitude distribution is Gaussian. Phase distribution is uniform.
Jerry, I'll jump in as at least one other has and ask about this phase thing. If we're talking about a real signal, then what do you mean by "phase"? -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124