Newbie: ploting Rectangular Signals and apply Grahm-Schmidt procedure??

Dear Experts, I would like to work on Gram-Schmidt Orthognolization Procedure for given signals in matlab

. steps are 1. define and plot the above signals. 2. Obtain Signal Energies 3. find set of orthonormal functions 4. vector representation of the signals

I have obtained the analytical solution for it but would any one be kind enough to help me write the code for it in matlab??

I shall be very much thankful

Answer 1

[Wayne King]

Presumably you have these as N-dimensional vectors in the MATLAB workspace. Place those vectors as columns of a matrix and us qr().

A = [1 1 0; 1 0 1; 0 1 1];
% columns of A are your signals
[Q,R] = qr(A);

Look at the matrix, Q.

norm(Q(:,1),2) % for example
dot(Q(:,1),Q(:,2)) % for example

[Usman Ali]

Hi King, thanks alot for your response. I would like to know what are Q and R in this case. shall I consider Q as the basis function and R ans the signal vectors? if yes isn't Q the basis function supposed to be a column or row vector but not a matrix??? or am i confusing things.

[Wayne King]

The columns of Q are the basis functions. They constitute the Gram-Schmidt procedure applied to the columns of A.

[Usman Ali]

what confuses me is that from analytic solution I find 3 basis that are scalar values. in this case Q is a 3x3 matrix. I am confused which values to consider for basis function.

[Matt J]

They constitute the Gram-Schmidt procedure applied to the columns of A.

Or rather, a numerically stable alternative to Gram-Schmidt.