interpolation accuracy, oversampling and fractional interpolation

robert bristow-johnson wrote:
> Ron N. wrote:
> > robert bristow-johnson wrote:
> > > dspunrelated wrote:
> > > > Have anyone tried to implement the polynomial based interpolator proposed
> > > > by Vesma Jussi?
> > >
> > > after Googling and looking at the papers i could get for free online, i
> > > don't see what particular new idea Jussi, et. al. is offering.  the
> > > concept of interpolating using a variety of fitted polynomials is not
> > > new (i personally like Hermite, but B-spline might attenuate the images
> > > even better).  and interpolating over-sampled input using polynomials
> > > (this is what you do if you want to use Parks-McClellan or similar to
> > > optimally design your interpolation LPF, but are left with a bunch of
> > > finite phases or fractional sample delays).
> >
> > My impression was that this interpolator was based on polynomial
> > interpolation of segments of your Parks-McClellan kernel (instead
> > of simple table-look-up, or a single-difference table-look-up
> > approximation).
>
> but that is precisely what Duane and I and Olli were doing.  what are
> these "segments" of the interpolation kernal, if not a table lookup.
> how is that different?

I wasn't sure from your prior post whether you were interpolating
the input data or the filter kernel, and/or whether you were
building an interpolation polynomial to replace almost all of the
table entries, or just for between table entries.  One Farrow
kernel interpolation version looked like it used one polynomial
per windowed sinc lobe, which means only one polynomial per tap
for some types of resampling FIR filters.  I suppose you could
call one polynomial (or one constant) a one-entry table, but you
wouldn't need any table lookups in a per-tap parallel hardware
implementation if you use one polynomial per sinc lobe (or the
entire range of phase between two taps for other types of
kernels).

> still don't see what the big deel is.

No big deal.   They all seem to be slightly different optimizations
of a just a few basic ideas.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M