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Constant for white Noise Question

Started by westocl 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. 

Can somewone please explain?
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. > > Can somewone please explain?
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. > > 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. 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