Sampling and Nyquist/Antialiasing filters

[Harvey Devoe Thornburg]

> 
> >>>>> "DRB" == Duane R Balvage <dbalvage at ptdcs2.ra.intel.com> writes:
> 
> Is this the reason people have considered oversampling? Certainly.
> 
>  DRB> They are using 4 pole input filters (I think - have to check the schems)
>  DRB> so the slopes are a bit gradual, taking off some of the "sparkle" of
>  DRB> the samples because they have to have their corner frequency set low 
>  DRB> enough to avoid aliasing. Any suggestions???
> 
> The benefit of 48 db extra per octave allows us to move the cutoff
> upwards. I made some quick calculations and assuming that we require
> the same damping at the nyquist point, we can move it to
> 
> 41 kHz	18.85 kHz
> 32 kHz	14.4 kHz
> 12 kHz	10.6 kHz
> 
> This using a very crude method (basically using a Bode-plot fashion of
> view and let the nyquist frequency be the common intersection point) .
>

This assumes that all of the poles are at the same frequency, right?
Maybe it is possible to distribute them somehow such that the slope
is steeper at the Nyquist frequency, or such that the response is
an even better approximation to a "brickwall" lowpass.  Elliptic
filters give you the best approximation, in the sense of minimizing
the maximum of the difference between your filter's response and the
desired "brickwall" response.

Unfortunately, elliptic filters as well as cascaded one poles have 
a highly nonlinear phase response.  This means certain frequencies
will be delayed relative to others. I would guess this becomes a 
bad problem near the Nyquist frequency. There is another type of filter
(called Bessel filter) which has approximately linear phase, but a more
gradual cutoff.  IMHO, nonlinear phase is not so important for a sampler,
but for "high-end" or mixing applications, recording engineers swear by
it.  Also in communications it is important not to distort the shape of 
the waveform; most of the "shape" information is contained in the pahse. for 
these reasons all of the DAC's I've seen employ Bessel filters, something 
like 6-8th order(*).  if this were my project I would try elliptic filters.

--Harvey