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I have some problems on 'for' and 'while' loop so I could not write a MATLAB program for this question;
.
Well, how can I start?
Well, how can I start?
function y = f(x)
%%The loop would look like:
y=0.0;
for n = 1:50
y = y + 2(-1)^(n+1) ( (pi^2)/n - (6/(n^3)) sin(n x);
end
%%After which you could write
x = 1.0 : 0.1 : 2*pi
y = f(x);
plot(y,x)
L = 8;
syms n x;
a_n = sqrt(2/L)*( (2*L)/(n*pi) )*( (sin((n*pi)/2))^2 )*sin(n*pi); %fourier coefficient a_n
b_n = -sqrt(2/L)*( (2*L)/(n*pi) )*( (sin((n*pi)/2))^2 )*cos(n*pi); %fourier coefficient b_n
x = 0:0.2:8; %range
V_x = symsum( a_n*sqrt(2/L)*cos( (n*2*pi*x)/L ) + b_n*sqrt(2/L)*sin( (n*2*pi*x)/L ), n, 1, 9 ); %fourier series
plot(x, V_x);
grid on;
axis([ 0 8 -1.4 1.4]);
hold on;
The Fourier Series in Matlab is a mathematical tool used to represent a periodic function as a sum of sine and cosine functions. It is based on the principle that any periodic function can be represented as an infinite sum of sinusoidal functions with different amplitudes, frequencies, and phases.
To calculate the Fourier Series in Matlab, you first need to define the periodic function and its period. Then, you can use the built-in function fft
to compute the coefficients of the Fourier Series. These coefficients can then be used to plot the Fourier Series in the time or frequency domain.
The Fourier Series in Matlab is used to represent a periodic function, while the Fourier Transform is used to represent a non-periodic function. The Fourier Transform also provides a continuous representation in the frequency domain, while the Fourier Series is a discrete representation in the frequency domain.
The Fourier Series is a powerful tool in signal processing as it allows us to analyze and manipulate signals in the frequency domain. This can be useful for filtering out unwanted frequencies, detecting periodicity in a signal, and extracting important features from a signal.
One limitation of using the Fourier Series in Matlab is that it assumes the input signal is periodic, which is not always the case in real-world applications. Additionally, the accuracy of the Fourier Series is limited by the number of terms used in the summation. Using a larger number of terms may result in longer computation times and may not always provide significant improvements in accuracy.