White noise ? Is it really a nuisance?
The following just occurred to me:
If theorical white noise is defined as a psd diagram of constant intensity (i.e -100dBm/Hz) throughout the infinite spectrum of frequencies,
then,
according to the duality principle of Fourier transforms, its equivalent time-function will be a dirac at t=0 (of amplitude proportionnal to the constant intensity mentionned above).
This does NOT make any sense! :(
This implies that white noise will have avery strong impact on a signal at t=0, but will leave it unpertubed a t>0.
I know I must be doing something wrong because this means that theoretical white noise is not much of a bother at t>0.
Can someone explain to me why is my reasonning wrong?
Regards
-Frank
Well white noise does not really extend to infinite frequency. It falls off at around Tera Hertz frequency range. So it can not be modelled as a delta function at t = 0.
regards
Ramgopal
Mathematically, the noise exists for the duration of the impulse. You are extrapolating a mathematical ideal the wrong way to the physical world. Noise in electron devices is partially caused by the electrons flowing. Each one produces a triangular shaped current pulse. There are so many electrons flowing that these triangles of current add up to a constant average plus a variation. It is the variation that is the noise.
You have to look at noise as a statistical process, not a real signal. It is described in dBm/Hz also, so for integrated noise you have to add signal bandwidth. Moreover, this is only spectral density of vn^2, which is always positive. Whereas vn itself is a statistical process and can be both positive and negative.
You misunderstood what PSD means. PSD is the frequency domain representation of autocorrelation function of stochastic signal--not the signal itself. The dirac function in time domain only indicate that signal at differect time instant are uncorrelated or C(ti,tj) = 0 when ti != tj where C(.,.) is autocovariance.
Actually white noise si the worst case scenario. If your design beats in simulation maximum white noise expected then go for it, build it.
when y do duality,donot ignore the phase influence,the psd phase coresspond the time delay in the time domain