# Constant for white Noise Question

Started by March 6, 2010
```I see in alot of communcations books the constant No used for white noise
and and in other texts some authors use No/2 when doing calculations for
white noise.

Many times there are no derivations given, so i cannot see where the
distincion between No vs No/2 is comming from.

```
```On Mar 7, 10:31=A0am, "westocl" <cwest...@hotmail.com> wrote:
> I see in alot of communcations books the constant No used for white noise
> and and in other texts some authors use No/2 when doing calculations for
> white noise. =A0
>
> Many times there are no derivations given, so i cannot see where the
> distincion between No vs No/2 is comming from.
>

They split the power bewteen the positive and negative frequencies.
This is in analogy with say a sinusoid where the amplitude is A.
The Fourier TF is two delta functions of amplitude A/2. One in
positive and one in negative frequencies. Not everybody does this for
white noise however. Comms people do.
In stochastic control systems theory they leave it as No.

Hardy
```
```On Mar 6, 3:31&#2013266080;pm, "westocl" <cwest...@hotmail.com> wrote:
> I see in alot of communcations books the constant No used for white noise
> and and in other texts some authors use No/2 when doing calculations for
> white noise. &#2013266080;
>
> Many times there are no derivations given, so i cannot see where the
> distincion between No vs No/2 is comming from.
>

The noise power in a frequency band of bandwidth W Hz
is WN0 watts (or volts^2).

If you believe in negative frequencies (so that the transfer
function of an ideal low-pass filter with cut-off W Hz is
nonzero from f = -W to f = +W), then use N0/2; if you don't
believe in negative frequencies and the transfer function
of your ideal LPF is nonzero only from f = 0 to f = W Hz,
use N0.  If you believe that Hertzian frequencies are the
invention of the devil and radians/second is the only unit
that God intended us to use, then you might think that
your mileage may vary, but it won't.  You still use N0/2 or
N0 depending on whether you believe in negative radian
frequencies or not.  Finally, if you are, God forbid, a
physicist who's strayed into this forum and all your
Fourier transforms have a 1/sqrt(2 pi) in front of them,
then you are on your own....

--Dilip Sarwate
```
```On Mar 6, 5:43&#2013266080;pm, dvsarwate <dvsarw...@gmail.com> wrote:
> On Mar 6, 3:31&#2013266080;pm, "westocl" <cwest...@hotmail.com> wrote:
>
> > I see in alot of communcations books the constant No used for white noise
> > and and in other texts some authors use No/2 when doing calculations for
> > white noise. &#2013266080;
>
> > Many times there are no derivations given, so i cannot see where the
> > distincion between No vs No/2 is comming from.
>
> > Can somewone please explain?
>
> The noise power in a frequency band of bandwidth W Hz
> is WN0 watts (or volts^2).
>
> If you believe in negative frequencies (so that the transfer
> function of an ideal low-pass filter with cut-off W Hz is
> nonzero from f = -W to f = +W), then use N0/2; if you don't
> believe in negative frequencies and the transfer function
> of your ideal LPF is nonzero only from f = 0 to f = W Hz,
> use N0. &#2013266080;If you believe that Hertzian frequencies are the
> invention of the devil and radians/second is the only unit
> that God intended us to use, then you might think that
> your mileage may vary, but it won't. &#2013266080;You still use N0/2 or
> N0 depending on whether you believe in negative radian
> frequencies or not. &#2013266080;Finally, if you are, God forbid, a
> physicist who's strayed into this forum and all your
> Fourier transforms have a 1/sqrt(2 pi) in front of them,
> then you are on your own....
>
> --Dilip Sarwate

Actually we physicists are quite familiar with different scalings used
for fourier transforms. So we don't get hung up on with that
detail ;-)

Clay
```