# Frequency response of allpass thiran Filter without inbuilt 'thiran' syntax

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Gayani on 18 May 2023
Commented: Gayani on 24 May 2023
Hi team,
I am trying to get the frequency response (H(z)) for the thiran filter using below. But I am stuck after getting the 'ak' value how to proceed to get the frequency response without inbuilt syntax ? Can you please help?
I used below code for calculating ak.
function [b,a] = thiran_1(D,N)
% [b,a] = thiran_1(D,N)
% b and a are numerator and denominator of H, respectively
% 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
if(D == N && k==0 && n==0)
ak=1;
else
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);
end
Ref:
[1] T. Laakso, V. Valimaki, “Splitting the Unit Delay”, IEEE Signal Processing Magazine, Vol. 13, No. 1, p.30-60, 1996.

Gokul Nath S J on 22 May 2023
Hi Gayani,
It seems that you would like to compute the thiran filter. However note that MATLAB already has an inbuild function which could compute the filter response.
with regards,
Gokul Nath S J
Gayani on 24 May 2023
Thank you so much
Gayani on 24 May 2023
But what I need is to implement Thiran filter without default syntax.Then get th z transform. Next to get the inverse z transform in matlab.

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