> On Apr 23, 10:39 am, Jerry Avins <j...@ieee.org> wrote:
...
>> "Bandwidth of Gaussian noise" just doesn't figure. Watts/Hz doesn't
>> really constrain the bandwidth. It's just that you don't care about what
>> it is outside the band of interest.
> Yes and no.
>
> The yes part is the fact that I agree that you can create white noise
> and then just look at what is going in the BW of interest to you.
>
> The no part is that I need to have a noise source whose power is
> uniform within a given BW. The problem I see with WGN is that I wanted
> to make a signal with unform power over all freqs, from which I would
> then just come in and observe the BW I want, I would need to have a
> signal with infinite power.
>
> Regardless of my model then, is there some way to create a continuous
> signal (not a pulse) that (at least in a statistical sense) behaves
> like WGN and has a uniform PSD within a given BW.
In short, no. It would, as you point out, have infinite power, and
probably be a radiation hazard (X- and gamma rays and all that). More to
the point I assume (but which is only implied by your including a DSP
forum), you want a digital signal. By its nature, that can't be continuous.
Why is it not enough for you that the noise behave like WGN in the
frequency band that interests you?
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by junoexpress●April 25, 20072007-04-25
On Apr 23, 10:39 am, Jerry Avins <j...@ieee.org> wrote:
> junoexpress wrote:
> > Hi,
>
> > In part of modeling a communications system, I need to incorporate a
> > broadband interference source. The model of interest is a source which
> > generates Gaussian noise whose bandwidth and total power are
> > specified. I am thinking of doing this by using the following model
> > for a discrete signal by letting:
>
> > n =3D time index at which signal is sampled
> > dt =3D uniform time between samples
> > w =3D 2*pi*f*dt
> > BW =3D bandwidth
>
> > then the signal at nth time pt is:
> > X(t) =3D Integral over BW of { A(w,n)*exp[i*(wn + phi(n,w)] } dw
>
> > where
> > phi[n,w] ~ i.i.d. wrt both w and n and is distributed unif(0,2*pi)
> > A(w,n) =3D amplitude at time point n and freq w ~ Normal(0,Power/BW)
>
> > Does this seem like a reasonable model? Essentially, all I am doing is
> > making sure that the amplitudes are normally distributed such that
> > their average power integrated over the BW =3D total specified power.
> > The phase portion of the model is of a little more concern to me: what
> > I am doing here is assigning a phase so that the (time-averaged)
> > correlation between any two fixed frequencies is zero and also the
> > correlation of the phases for a fixed frequency over time is also
> > zero.
>
> "Bandwidth of Gaussian noise" just doesn't figure. Watts/Hz doesn't
> really constrain the bandwidth. It's just that you don't care about what
> it is outside the band of interest.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
Yes and no.
The yes part is the fact that I agree that you can create white noise
and then just look at what is going in the BW of interest to you.
The no part is that I need to have a noise source whose power is
uniform within a given BW. The problem I see with WGN is that I wanted
to make a signal with unform power over all freqs, from which I would
then just come in and observe the BW I want, I would need to have a
signal with infinite power.
Regardless of my model then, is there some way to create a continuous
signal (not a pulse) that (at least in a statistical sense) behaves
like WGN and has a uniform PSD within a given BW.
TIAA,
M
Reply by Jerry Avins●April 23, 20072007-04-23
junoexpress wrote:
> Hi,
>
> In part of modeling a communications system, I need to incorporate a
> broadband interference source. The model of interest is a source which
> generates Gaussian noise whose bandwidth and total power are
> specified. I am thinking of doing this by using the following model
> for a discrete signal by letting:
>
> n = time index at which signal is sampled
> dt = uniform time between samples
> w = 2*pi*f*dt
> BW = bandwidth
>
> then the signal at nth time pt is:
> X(t) = Integral over BW of { A(w,n)*exp[i*(wn + phi(n,w)] } dw
>
> where
> phi[n,w] ~ i.i.d. wrt both w and n and is distributed unif(0,2*pi)
> A(w,n) = amplitude at time point n and freq w ~ Normal(0,Power/BW)
>
> Does this seem like a reasonable model? Essentially, all I am doing is
> making sure that the amplitudes are normally distributed such that
> their average power integrated over the BW = total specified power.
> The phase portion of the model is of a little more concern to me: what
> I am doing here is assigning a phase so that the (time-averaged)
> correlation between any two fixed frequencies is zero and also the
> correlation of the phases for a fixed frequency over time is also
> zero.
"Bandwidth of Gaussian noise" just doesn't figure. Watts/Hz doesn't
really constrain the bandwidth. It's just that you don't care about what
it is outside the band of interest.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by julius●April 23, 20072007-04-23
On Apr 23, 8:30 am, junoexpress <MTBrenne...@gmail.com> wrote:
> Hi,
>
> In part of modeling a communications system, I need to incorporate a
> broadband interference source. The model of interest is a source which
> generates Gaussian noise whose bandwidth and total power are
> specified. I am thinking of doing this by using the following model
> for a discrete signal by letting:
>
> n = time index at which signal is sampled
> dt = uniform time between samples
> w = 2*pi*f*dt
> BW = bandwidth
>
> then the signal at nth time pt is:
> X(t) = Integral over BW of { A(w,n)*exp[i*(wn + phi(n,w)] } dw
>
> where
> phi[n,w] ~ i.i.d. wrt both w and n and is distributed unif(0,2*pi)
> A(w,n) = amplitude at time point n and freq w ~ Normal(0,Power/BW)
>
> Does this seem like a reasonable model? Essentially, all I am doing is
> making sure that the amplitudes are normally distributed such that
> their average power integrated over the BW = total specified power.
> The phase portion of the model is of a little more concern to me: what
> I am doing here is assigning a phase so that the (time-averaged)
> correlation between any two fixed frequencies is zero and also the
> correlation of the phases for a fixed frequency over time is also
> zero.
>
> TIA,
>
> Matt B.
Sure. Assuming that A is white in both w and n (you didn't specify).
Julius
Reply by junoexpress●April 23, 20072007-04-23
Hi,
In part of modeling a communications system, I need to incorporate a
broadband interference source. The model of interest is a source which
generates Gaussian noise whose bandwidth and total power are
specified. I am thinking of doing this by using the following model
for a discrete signal by letting:
n = time index at which signal is sampled
dt = uniform time between samples
w = 2*pi*f*dt
BW = bandwidth
then the signal at nth time pt is:
X(t) = Integral over BW of { A(w,n)*exp[i*(wn + phi(n,w)] } dw
where
phi[n,w] ~ i.i.d. wrt both w and n and is distributed unif(0,2*pi)
A(w,n) = amplitude at time point n and freq w ~ Normal(0,Power/BW)
Does this seem like a reasonable model? Essentially, all I am doing is
making sure that the amplitudes are normally distributed such that
their average power integrated over the BW = total specified power.
The phase portion of the model is of a little more concern to me: what
I am doing here is assigning a phase so that the (time-averaged)
correlation between any two fixed frequencies is zero and also the
correlation of the phases for a fixed frequency over time is also
zero.
TIA,
Matt B.