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Thiran Allpass Interpolation in Matlab

function [A,B] = thiran(D,N)
%  [A,B] = thiran(D,N)
%  returns the order N Thiran allpass interpolation filter 
%  for delay D (samples).

A = zeros(1,N+1);
for k=0:N
    Ak = 1;
    for n=0:N
        Ak = Ak * (D-N+n)/(D-N+k+n);
    end
    A(k+1) = (-1)^k * nchoosek(N,k) * Ak;
end

B = A(N+1:-1:1);


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA