Re: [Leica] Nyquist again (was scanning)

[Adam Bridge <abridge@mac.com>]

on 7/26/01 9:49 AM, Mxsmanic at mxsmanic@hotmail.com thoughtfully wrote:

>> Can't 20kHz be sampled by a 44.1kHz sampling
>> rate?
> 
> Of course, but you seemed to be implying that the extra 4.1 kHz was required
> to
> resolve 20 kHz, and that is not the case.  Even 40.001 kHz would have
> sufficed.

Um......NO....this is NOT the case.

There are is a major assumption which is not stated and which is vital to
understand:

The bandwidth of the audio signal must be limited by a low-pass filter with
infinite steepness at half the sampling rate.


Without a filter serious aliasing occurs and all sort of artifact appear.


You will note, however, that the filter is impossible to achieve. There are
no infinitely steep low pass filters. That being the case the designer does
put in a real limiting filter and then pushes the sampling rate higher to
account for the point where the high frequencies disappear into the noise
(which had better be low or you're back into problems with aliasing again.)


I'm going to have to wander over to the UCD image processing lab and get a
prof to discuss how digital signal processing theory interacts with sampling
of images which are themselves sampled.

As I write this I'm thinking that film grain is essentially the noise of an
audio signal. This is TOTALLY an uneducated opinion. Nevertheless the folks
who derive data from, say, satellite sensors or other high resolution
imaging systems must know and understand quite clearly the relationships
that exist.

Perhaps there is someone from the NRO who would care to comment???

Adam Bridge