question about non-uniform sampling?

glen herrmannsfeldt wrote:
> Jerry Avins wrote:
>
> > Steve Underwood wrote:
>
> (snip)
> >>  There is nothing wrong with any
> >> extreme of non-uniformity in a purely mathematical sense. That is in a
> >> world with infinite sampling precision and no noise due to the
> >> converter itself.
>
> > It's also a world where signals exist for all time. I doesn't matter how
> > precisely one can sample and how often, nothing can be known about a
> > speech yet to be given, even if the mathematics of nonuniform and highly
> > clumped sampling shows that it can.
>
> I am not so sure what quantum mechanics says about this.

   The only thing quantum mechanics says about anything
   that is not quantum mechanics is the scattering strength of
   100,000 GeV particles. Which is why the only people who
   even use QM are mathematicians, since both Giga's and eV's
   are stastical propertites, not physical properties.

    Since there is no conversion from an eV to any other
    observalble macroscopic  property that isn't first filtered through

    General Relavity, Protons, and The Eiffel Tower, rather than
sampling theory.

    Much can even said about speeches yet t be given,
    since the only people who even listen to them
    are the speaker's speahwriter rather than the  speaker.
    Which is why blow-up barbie dolls still confuse
    Behaviourists, more than they do Barbie.

JohnCreighton_@hotmail.com wrote:
> David Tweed at dtweed@acm.org wrote on 11/12/2005 09:32:
> > lucy wrote:
> > > What is the Nyquist sampling rate in the non-uniform case?
> >
> > Believe it or not, it's the same as the uniform case ... the number
> > of samples over the time interval must exceed twice the bandwidth
> > of the signal.
>
> That sounds like a sensible conclusion but how do we define bandwidth?
> For instance, if you have one peak in the frequency domain, you can
> measure the bandwidth as the width of the peak.  But what if you have
> more then one peek? If they were the same amplitude I would assume you
> could add the peaks up. If they were we different amplitudes I would
> think you would want to weight them somehow.

The bandwidth is defined as the bandwidth of the perfect brick-wall
low-pass or band-pass antialias filter you ran the signal through
*prior* to sampling it. The impulse response of this filter is the
interpolation function used in the system of equations you have to
solve as shown in my writeup.

-- Dave Tweed

David Tweed wrote:
> JohnCreighton_@hotmail.com wrote:
> > David Tweed at dtweed@acm.org wrote on 11/12/2005 09:32:
> > > lucy wrote:
> > > > What is the Nyquist sampling rate in the non-uniform case?
> > >
> > > Believe it or not, it's the same as the uniform case ... the number
> > > of samples over the time interval must exceed twice the bandwidth
> > > of the signal.
> >
> > That sounds like a sensible conclusion but how do we define bandwidth?
> > For instance, if you have one peak in the frequency domain, you can
> > measure the bandwidth as the width of the peak.  But what if you have
> > more then one peek? If they were the same amplitude I would assume you
> > could add the peaks up. If they were we different amplitudes I would
> > think you would want to weight them somehow.
>
> The bandwidth is defined as the bandwidth of the perfect brick-wall
> low-pass or band-pass antialias filter you ran the signal through
> *prior* to sampling it. The impulse response of this filter is the
> interpolation function used in the system of equations you have to
> solve as shown in my writeup.

   But, what mathematicians don't seem to understand about sampling
   theory is that the perfect brickwall low-pass filter isn't made of
bricks.
   Its a forest  made of  trees,  leaves, and lakes, rather than bricks
and mrrors.
   Since the rocks in the forest need no interpolation,
    the lake surface needs no idiiot QM chemists and thermostats,
   and they automatically generate generalized sampling theory,
   both non-uniform sampling theory, uniform sampling,
   and non-Gaussian interpolation functions.

   

    



> 
> -- Dave Tweed