Is the code for calculation of Vandermonde matrix correct along with codes to calculate filter matrix and coefficient polynomials for order N ?

The code for Vandermonde matrix V

for N = 10
    x = 0:N; % D values from 0 to 10
    V =fliplr(vander(x)) ;
end% Vandermonde matrix with powers increasing from left to right
disp('The Vandermonde Matrix V:')
disp(V);

Calculating Z

Q = inv(V);
%% 
disp('Filter Coefficient Matrix Q:');
disp(Q);

Calculating C

% Step 4: Calculate the Coefficient Polynomials C_k(z) for each k by multiplying Q and z
c = Q .* z;
% Display the coefficients
disp('Coefficient Polynomials C_k(z) for each k:');
for k = 0:N
    fprintf('C_%d(z): %f\n', k, c(k+1));
end
for Z:
    syms z 
    Z = [1 z^-1 z^-2 z^-3 z^-4 z^-5 z^-6 z^-7 z^-8 z^-9 ].';
    t = iztrans(Z);

Please could you suggest alternatives to correct or modify this code ? Is it possible to develop them as functions in MATLAB?

[Walter Roberson]

I think it likely that you are intended to calculate the vandermode matrix yourself, instead of calling vander()

Answer 1

[Umang Pandey]

Hi Rohitashya,

From what I understand, you want to generate the Vandermode matrix as mentioned in the image and abstract out all the calculations within matlab functions.

1) You don't need to run a loop to obtain the Vnadermode matrix, "vander" itself generates the entire matrix. You can refer to this documentation for details : https://www.mathworks.com/help/matlab/ref/vander.html#bubf_mp-2

x = 0:N;
V = fliplr(vander(x));

2) Yes, you can create functions for obtaining these matrices, passing the other required matrices/values as parameters. Here are a few examples:

function V = generateVandermonde(N)
    x = 0:N; % Values from 0 to N
    V = fliplr(vander(x)); % Vandermonde matrix with powers increasing from left to right
end

% ---------------------------------------------------------

function Q = calculateInverse(V)
    Q = inv(V);
end

% ---------------------------------------------------------

function c = calculateCoefficients(Q, z)
    z = zeros(N+1, 1);
    for k = 0:N
        z(k+1) = 1 / (1^k); % z = [1, z^-1, z^-2, ..., z^-N]
    end
    c = Q * z; % Matrix multiplication
end

Best,

Umang