Matlab function to calculate coeffiecients of projection of a function on orthogonal set

I want to write a function in matlab, that would do the following:

Given linear space of periodic functions, and given an orthogonal set in this space, I want to write a function that accepts as an argument a periodic function and the orthogonal set, and calculates the projection of the periodic function on each of the functions in the orthogonal set.

i.e, the arguments of the function are:

1)Vector which contains values of a periodic function

2)Matrix with N columns such that each column contains values of one of the orthogonal functions

3)Scalar - T which represents the period.

And the function should return a vector which contains the projections of the periodic function on each of the orthogonal functions. Meaning, the vector should return the coefficients .

Here's what I have tried:

function [coeff] = mekadmim_bekef(xt, M, T)
    Size = size(M); %Get dimensions of M
    num_of_samples=Size(2); %get the number of samples of each function
    N=Size(2); %Get number of columns of M
    coeff = zeros(1,N); %Initialize vector of length N
    time_vector = 0:num_of_samples:T;
 
    for k=1:N
        curr_column = M(:,k);
        conj_column=conj(curr_column)
        num_to_int = xt.*conj_column;
        deno_to_int = curr_column.*conj_column;
        numerator = trapz(time_vector,num_to_int);
        denominator = trapz(time_vector,deno_to_int);
        coeff(k)=numerator./denominator;
end
    

But when I try to test it with the following code:

clc;
clear all;
close all;

t=0:2*pi/1000:2*pi;
f1 = sin(t);
f2=sin(2*t);
f3=sin(3*t);
f4=sin(4*t);

M=[f1;f2;f3;f4]';
T=2*pi;

a=mekadmim_bekef(f1',M,T);
disp(a);

It dosent work.

What went wrong?

Thanks in advance.

Answer 1

[Binaya]

Hi Itzik, 

As per my understanding, you would like to understand why your code is not working for the required task.

While going through the code, I found following 2 errors in the given code:

1. The function code snippet needs one more “end” command at the function.
2. At line number 6 of the function, “time_vector” array is not correct. There are two methods to generate an array between two points with a fixed step:

a. time_vector = 0:step_size:T; where step_size = 2*pi/1000;

b. time_vector = linspace(0,T,1001);

Please refer to the below documentation for more details:

1. Linspace: https://www.mathworks.com/help/matlab/ref/linspace.html
2. Colon,”:”: https://www.mathworks.com/help/matlab/ref/colon.html
3. Trapz: https://www.mathworks.com/help/matlab/ref/trapz.html

I hope this solves your query.

Regards 

Binaya