So this coding is based on computation of coefficients of the 
the filter structure formula as given in the img:
d is the bandwidth tuning factor :
N is the polynomial order and M is subfilter order N =M-1
this is the fractional delay of Farrow Rate Converter d is fractional delay of Newton used for bandwidth tuning
My code :
function coeffMatrix = computeNewtonCoeff(N, d)
% Compute the Newton Coefficient matrix
% N: Order of the interpolator
% d: Bandwidth tuning parameter
N =M-1;
% Pre-allocate the coefficient matrix
coeffMatrix = zeros(N + 1, 1);
% Loop to compute coefficients using the equation
for k = 0:N
mu =linspace(-0.5,0.5);
d= compute_d_in_steady_state(mu, N);
% Compute the factorial term
numerator = prod(d:(d + k - 1)); % d * (d+1) * ... * (d+k-1)
denominator = factorial(k); % k!
coeffMatrix(k + 1) = numerator / denominator; % Coefficients
end
end
function d = compute_d_in_steady_state(~, N)
% Computes d in steady-state given mu and N
% mu: Fractional part of accum, should be in [-1, 0)
% N: Interpolator order
% Ensure mu is within the valid range
mu = linspace(-0.5,0.5);
% Compute d using the steady-state expression
d = mu - N / 2;
end
N= 4;
mu = linspace(-0.5,0.5);% Order of the interpolator
d =compute_d_in_steady_state(mu,N); % Example value of the bandwidth tuning parameter
coeffMatrix = computeNewtonCoeff(N, d);
disp('Newton Coefficient Matrix:');
disp(coeffMatrix);
Solution is showing after running :
Newton Coefficient Matrix:
1.0000
-2.5000
1.8750
-0.3125
-0.0391
The solution mentioned in the paper is different :
I have attached the pdf - Design_of_Low_Complexity_Arbitrary_Pass-band_Filter_Hardware_using_Newton_Structure-based_Lagrange_Interpolators (3).pdf
for further reference you can read through .
