How to solve the problem of noise using weighted values?

I have a voltage signal for 11 cycles. Each cycles has 32 samples of data. I was trying to reconstruct the signal using the following equation.I have to find the coefficients .

where is the time of the downsampled data. I tried to solve the problem by using the follwoing equation.

Where, X is the array of the coefficinets, A is the matrix at follwoing form . Y is the values of the voltage samples. is the transpose of matrix A and W is the weighted values. I tried to use the backslash command which results in x=A\Y. The results are accurate. However, I need to implement the weighted equation given in equation (2) to solve for X. I tried every command but it did not work.

[Ashutosh]

Hey, have you tried something like:

mat = A' * W * A;
X = inv(mat) * A' * W * Y;

That is, using the inv() function of MATLAB to find the inverse?