[music-dsp] hermite vs lagrange interpolation
yaakov_s at rad.com
Tue Feb 17 02:44:56 EST 2004
> For a fractionally addressed delay line is there any reason
> hermite interpolation might be better than lagrange
Lagrange interpolation can be seen as a special case of Hermite
interpolation. Lagrange interpolation finds a polynomial that
goes throught given data points, while Hermite interpolation
finds a polynomial that goes through points and additionally
matches derivative data at these points. If no derivatives
are specified and the interpolations are carried out to the same
order and using the same end constraints, then they Hermite
reduces to Lagrange.
> Or is there a better method I should know about?
There are various computation schemes to compute polynomial
interpolation (e.g. Aitken's recursion, Vandermonde's deteminant)
that may help.
Have you tried B-splines? There has been a re-awakening
regarding splines in the DSP world in recent years
(see the excellent review article in IEEE signal processing
magazine a few years ago).
Of course, all pure polynomial methods are not technically correct
from a DSP point of view, since they are not band-limited
Interpolation should match spectral shapes as well as time behavior,
and this can be done using sinc functions
or directly in the frequency domain using FFTs.
The modern spline approach is also "correct" from the DSP viewpoint.
Jonathan (Y) Stein
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