Rune Allnor wrote:
> 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.
Or 1 in the inverse direction and 1/n forward. Or 1/sqrt(N) in each
direction. Think of it as different dialects.
>
> 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
Jerry
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