Filtering Problems

I've the answer I think.

Imagine to have a analogue signal that can be seen as white noise (I mean a sort of flat spectrum in all frequencies) and to sample it at a Fs=10Mhz.

You know that when you sample an analogue signal to "transform" it in a digital one, you've spectral replicates at k*Fs (where k= 0,+-1,+-2,..)

After that you have some digital sample at Fs rate.

When you oversampling it you do 2 things:

1) zero padding

2) filtering

When you zero padding the initial signal, the thing that changes is that between the initial samples you put (N-1) zeroes. This increase the "spectral resolution" of the signal without changing anything else.1

Consequence of it is that your Fs(final) increase to N*Fs(start).

At this point you filter this resulting signal in order to keep it in the bandwith you need and "kill" the spectral replicates at Fs(start) among the true one at Fs(final).

Hope this help someone else.

For do an example let Fs(start) = 10 MHz

This mean that you've the replication of your base spectrum at 0MHz, 10MHz, 20MHz, 30MHz, 40MHz, and so on

Now let N = 2.

So we insert between each original sample a 0.

In frequencies we also have our Fs(Final)= 2*10Mhz = 20Mhz.

If we've sampled the initial signal at Fs=20Mhz we expect the spectral replication af 0MHz, 20Mhz, 40Mhz, 60Mhz, and so on.

So we need to filter the replication at 10MHz, 30Mhz, 50Mhz, etc..

And that's what we do.

Try to make a picture of it is very simpler than writing it.