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Lagrange Interpolation in Faust, Fixed Delay $ d$

Fast time-invariant-delay algorithm fdelaylti -- derived by truncated Taylor series expansion above -- in Faust's filter.lib

import("music.lib");

fdelaylti(N,n,d,x)
  = delay(n,id,x) <: seq(i,N,section(i)) : !,_
with {
  o = (N-1.00001)/2;  // ~center FIR interpolator
  dmo = d - o; // assumed >=0 [d > (N-1)/2]
  id = int(dmo);
  fd = o + frac(dmo);
  section(i,x,y) = (x-x') * c(i) <: _,+(y);
  c(i) = (i - fd)/(i+1);
};

process = fdelayl(5,1024,5.4); // 5th-order ex.


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``Bandlimited Interpolation, Fractional Delay Filtering, and Optimal FIR Filter Design'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2017-05-12 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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