interpolation accuracy, oversampling and fractional interpolation

Started by renaudin October 9, 2006
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