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

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Itzik Waizman
Itzik Waizman 2021-11-25
回答： Binaya 2023-10-11
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.

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回答（1 个）

Binaya
Binaya 2023-10-11
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 

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