relationship between power spectral density and variance

[pdcom]

variance psd

can anyone please help me by telling what is the relationship between power spectral density and variance of complex white noise in AWGN.
suppose power spectral density of noise is No then what will be its variance and why?
thanks

 

[bulx]

power spectral density

PSD gives you the power of a random signal as a function of frequency ie with it, you can find how much power the signal has a given frequency.

Variance is a measure of the average power of a signal.

For white noise, the power is the same at all frequencies, thus you can simply say the PSD is No, because it is No at all frequencies.

variance of a WSS signal = 2 * PSD integrated from 0 Hz to ∞ hertz.

for WGN bandlimited to B Hz
variance = 2 * B * No
-b

 

[carpa]

variance spectral density

Acturely AWGN does not exist in reality because AWGN should have constant PSD and infinity bandwidth, which will lead to an ridiculous result that AWGN has infinity power.

When we consider white noise we always constrain it into some specific bandwidth B (SSB supposed), although it is not real white in all band. Variance of the noise is the same as the power, therefore the above conclusion of "variance = integral of PSD over 2*B" is correct.

 

[senaydud]

relation between power and variance

So you all say that;
PSD = No
variance = 2*B*No

So what is No/2?

 

[bulx]

power spectral density variance

It is usual to assume white noise PSD in No/2, so that total noise power in a given bandwisth B is No* B; half of it from negative and rest half from positive frequency range
-b

 

[pdcom]

white noise power variance

HI!
normally it is written PSD is No and variance is No/2, and Bandwidth is not mentioned,What does this means, from your point of view B=1/2 in this case.Is it true reason.
Regards

 

[bulx]

variance power spectral density

If you can point out where (in any standard book) such an assumption is made, can try to explain.

When the nature of the randomness alone is relevant (ie, whether it is gaussian, uniform etc), BW wont be mentioned. These are two separate characteristics of random signals (BW and distribution).
-b