On 12 Okt, 12:04, "Qian.S...@[EMAIL PROTECTED]
" <Qian.S...@[EMAIL PROTECTED]
> wrote:
> a bandlimit white noise x(t) with PSD of S0 is sampled (no aliasing)
> to produce x[n]. The PSD of x[n] is calculated to be S0/Ts (Ts is the
> sample period).
> Now I just reconstruct the continuous noise xr(t) by passing x[n]
> impulses to the ideal reconstruction filter (gain=Ts, -fs<f<fs). The
> output PSD is calculated to be S0/Ts*Ts^2=S0*Ts. There is an offset
> from the input noise PSD by a ratio of Ts!
> There must be some scaling error in above statement because ideal
> sampling and reconstructing a bandlimit white noise should produce
> itself. Please correct me!! Thanks!!
First, if the missing scaling factor is 1/Ts I would check
out the definitions of the Fourier transforms. With the discrete-
domain DFT there is a 'skewness' between the forward and inverse
transforms. The scale factor is 1 in the forward transform and
1/N in the inverse tranform.
So check the definitions of the FTs to see if there are more
issues like that around, and what effects they might have.
That said, scaling factors are usually ignored unless there
are very good reasons for keeping them. Which is done only in
calibrated systems. So if the missing 1/Ts factor is associated
with the ADC or DAC, chances are that it is just dropped.
Rune
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