HdrChopper wrote on Oct 12th, 2008, 9:07am:Hi,
The PSD of x[n] must be scaled by 1/Ts^2, not 1/Ts. The reason being that you have to consider the modulus of the square of the "transfer function" of your system. Ideal sampling can be modeled by a train of impulses equally spaced in time.
Squaring the Fourier transform of the impulses (the same way you square the reconstruction filter transfer function) gives you the sampled PSD scaled by 1/Ts^2.
Therefore the scale factor cancells out after reconstruction
Regards
Tosei
A lot of thanks to your input! Tosei.
For the scaling in sampling the continuous-time noise into discrete-time noise sequence using ideal impulse sampling, you can look at eq. 10.50, pp731, A.V Oppenheim's "Discrete-time signal processing" 2nd edition.
There is only
1/Ts scaling between the two domain's PSD not
1/Ts^2.
The reason is that discrete-time PSD can be regard as DTFT of the
sampling of the autocorrelation function of continuous-time noise.