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?
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.
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.