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

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.

Answer 1

[Gokul Nath S J]

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.

For more information about the function, kindly go through the following links.

https://in.mathworks.com/help/control/ref/thiran.html

with regards,

Gokul Nath S J

[Gayani]

Thank you so much

[Gayani]

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.