I am trying to solve the Newton Coefficeint matrix for Newton sample rate converter please could you suggest for modifications?

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 .