How to Calculate Relative Power Using Fourier Coefficients in Matlab?

[Kipster1203]

I have the following code

dt = 0.01;                                % Set the time increment to 0.02 second.

t = (0:1:199)*dt;                      % Create a time array.

x1 = 0.5*square(pi*t);               % Use MATLAB to create the signal

                                              % amplitude +/- 0.5 and period 2.

subplot(2,1,1),plot(t,x1), axis([0,2.1,-0.6,0.6]);

x2 = zeros(1,length(x1));            % Define an empty column vector for the

                                              % triangle function.

                                              % Use a discrete approximation to the integral of the square

                                              % wave to create the triangular signal.

x2(1) = -0.25;

for i = 2:200; x2(i) = x2(i-1) + x1(i)*dt; end

subplot(2,1,2),plot(t,x2), axis([0,2.1,-0.6,0.6]);

I need to calculate the sums of the power (by evaluating the Fourier coefficients) in harmonics 1 - 3, 1 - 9, and 1 - 29 for signal x1 relative to the total power in the original signal x1.
Can anyone help me out??

 

[Jhero]

The sum of the power in harmonics 1-3 is given by:P1_3 = (1/length(x1))*sum((abs(fft(x1)).^2).*(abs(fft(x1))>0.5));The sum of the power in harmonics 1-9 is given by:P1_9 = (1/length(x1))*sum((abs(fft(x1)).^2).*(abs(fft(x1))>1.5));The sum of the power in harmonics 1-29 is given by:P1_29 = (1/length(x1))*sum((abs(fft(x1)).^2).*(abs(fft(x1))>4.5));The total power in the original signal x1 is given by:Ptotal = (1/length(x1))*sum(abs(fft(x1)).^2);The relative power in harmonics 1-3, 1-9 and 1-29 is then given by: RelP1_3 = P1_3/Ptotal;RelP1_9 = P1_9/Ptotal;RelP1_29 = P1_29/Ptotal;

 

[oswaler]

Sure, I can help you out with calculating the relative power using Matlab. First, let's define the Fourier coefficients for the signal x1. We can use the fft function in Matlab to calculate the discrete Fourier transform:

X1 = fft(x1);

Next, we need to calculate the power for each harmonic using the formula P = |c|^2, where c is the Fourier coefficient for that harmonic. We can do this using a for loop:

% Initialize an empty vector for storing the power values
power = zeros(1,29);

% Loop through each harmonic
for n = 1:29
% Calculate the power for the nth harmonic
power(n) = abs(X1(n))^2;
end

Now, we can calculate the total power in the original signal x1 by summing up all the power values:

total_power = sum(power);

To calculate the relative power for each harmonic, we can divide the power value for that harmonic by the total power:

% Initialize an empty vector for storing the relative power values
relative_power = zeros(1,29);

% Loop through each harmonic
for n = 1:29
% Calculate the relative power for the nth harmonic
relative_power(n) = power(n) / total_power;
end

To calculate the sums of the power for harmonics 1-3, 1-9, and 1-29, we can simply sum up the corresponding values in the relative_power vector:

% Sum of the power for harmonics 1-3
sum_power_1_3 = sum(relative_power(1:3));

% Sum of the power for harmonics 1-9
sum_power_1_9 = sum(relative_power(1:9));

% Sum of the power for harmonics 1-29
sum_power_1_29 = sum(relative_power(1:29));

I hope this helps! Let me know if you have any further questions.