Quadrature Sampling Question

My understanding is that you phase shift one signal by 90 degrees with a
hilbert tranformer than sample - is that right? With a carrier based system
you need only use sin and cos and then sample giving I and Q.

The advantage appears to be that you can sample at B (bandwidth) rather than
2BHz.

Can we extend this and phase shift by pi/4 and sample with 4 ADCs? In
general we would get a sampling freq of

(2/n).B where n is the number of samplers. Would this work or does it only
work for the quadrature case.

Also where is the proof of quadraure sampling? I understand the standard
theory, it begins by multiplication of f(t) the signal by an impulse train
which you then take a FT of and do convolution in the freq domain. With the
quadrature case do we take f(t) and jf(t) and do the same thing?

The otehr thing is, if you need a Hilbert transform before you sample then
the signal would need to be in digital form before you sample unless you can
do it analogue.

Thanks

Tom

Entropy wrote:
> My understanding is that you phase shift one signal by 90 degrees with a
> hilbert tranformer than sample - is that right? With a carrier based system
> you need only use sin and cos and then sample giving I and Q.
> 
> The advantage appears to be that you can sample at B (bandwidth) rather than
> 2BHz.
> 
> Can we extend this and phase shift by pi/4 and sample with 4 ADCs? In
> general we would get a sampling freq of
> 
> (2/n).B where n is the number of samplers. Would this work or does it only
> work for the quadrature case.
> 
> Also where is the proof of quadraure sampling? I understand the standard
> theory, it begins by multiplication of f(t) the signal by an impulse train
> which you then take a FT of and do convolution in the freq domain. With the
> quadrature case do we take f(t) and jf(t) and do the same thing?
> 
> The otehr thing is, if you need a Hilbert transform before you sample then
> the signal would need to be in digital form before you sample unless you can
> do it analogue.

You need two samples per cycle of the highest frequency with all the 
schemes you cite. They all work in theory. The more converters in your 
system, the harder it is to match their offsets, non-linearities, and 
gains. The more sampling channels, the harder it is to keep them all 
properly phased.

There is usually a reason for common practice, but don't let that stop 
you from looking for better ways. Every so often, you will find one.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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