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EXERCISE #1: FOURIER SERIES - I The Fourier series for a square wave $f(x) = \begin{cases} 1 & 0 \le x < \pi \\ 0 & \pi \le x < 2\pi \\ f(x + 2\pi) & \text{elsewhere} \end{cases}$ is given by $f(x) = \frac{1}{2} + \frac{2}{\pi} \sum_{n=1, n \text{ odd}}^{\infty} \frac{\sin nx}{n}$ First, write a user-defined function in MATLAB to accept the number of harmonics, $n$, as input and produce the Fourier series waveform up to and including the $n$ harmonics using the following code segment. function [x,f] = FS_sq(N) x = linspace(0,10); f = 0.5; for i = 1:2:N b = 2/(pii); f = f + bsin(i*x); end Next, write a script in MATLAB to test this function by generating and plotting (on the same figure using subplot commands) the following cases: (1) N = 5 (2) N = 10 (3) N = 20 (4) N = 50 Label all the axes and assign a title to each subplot.

          EXERCISE #1: FOURIER SERIES - I

The Fourier series for a square wave $f(x) = \begin{cases} 1 & 0 \le x < \pi \\ 0 & \pi \le x < 2\pi \\ f(x + 2\pi) & \text{elsewhere} \end{cases}$ is given by

$f(x) = \frac{1}{2} + \frac{2}{\pi} \sum_{n=1, n \text{ odd}}^{\infty} \frac{\sin nx}{n}$

First, write a user-defined function in MATLAB to accept the number of harmonics, $n$, as
input and produce the Fourier series waveform up to and including the $n$ harmonics using the
following code segment.
function [x,f] = FS_sq(N)
x = linspace(0,10);
f = 0.5;
for i = 1:2:N
    b = 2/(pi*i);
    f = f + b*sin(i*x);
end

Next, write a script in MATLAB to test this function by generating and plotting
(on the same figure using subplot commands) the following cases:
(1) N = 5 (2) N = 10 (3) N = 20 (4) N = 50

Label all the axes and assign a title to each subplot.

EXERCISE #1: FOURIER SERIES - I

The Fourier series for a square wave f(x) = 1 0 ≤ x < π
0 π≤ x < 2π
f(x + 2π) elsewhere is given by

f(x) = (1)/(2) + (2)/(π)∑n=1, n odd^∞(sin nx)/(n)

First, write a user-defined function in MATLAB to accept the number of harmonics, n, as
input and produce the Fourier series waveform up to and including the n harmonics using the
following code segment.
function [x,f] = FSsq(N)
x = linspace(0,10);
f = 0.5;
for i = 1:2:N
b = 2/(pi*i);
f = f + b*sin(i*x);
end

Next, write a script in MATLAB to test this function by generating and plotting
(on the same figure using subplot commands) the following cases:
(1) N = 5 (2) N = 10 (3) N = 20 (4) N = 50

Label all the axes and assign a title to each subplot.

Added by James C.

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