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

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Rohitashya
Rohitashya 2024-10-21，14:24
回答： Umang Pandey 2024-10-29，5:00
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?

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回答（1 个）

Umang Pandey
Umang Pandey 2024-10-29，5:00
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

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