Fourier Series Example

MATLAB Code


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%FOURIER_SERIES_01_MAT

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fig_size = [232 84 774 624];

x = [0.1 0.9 0.1]; % 1 period of x(t)

x = [x x x x]; % 4 periods of x(t)

tx = [-2 -1 0 0 1 2 2 3 4 4 5 6]; % time points for x(t)

figure(1),plot(tx,x),grid,xlabel('Time (s)'),ylabel('Amplitude'),...

title('Periodic Signal x(t)'),axis([-2 6 0 1]),...

set(gcf,'Position',fig_size)

%

a0 = 0.5; % DC component of Fourier Series

ph0 = 0;

n = [1 3 5 7 9]; % Values of n to be evaluated

an = -3.2 ./ (pi * n).^2; % Fourier Series coefficients

mag_an = abs(an);

ph_an = -180 * ones(1,length(n));

%

n = [0 n];

mag_an = [a0 mag_an]; % Including a0 with a_n

ph_an = [ph0 ph_an];

%

figure(2),clf,subplot(211),plot(n,mag_an,'o'),grid,xlabel('Harmonic Number'),...

ylabel('Magnitude'),title('Fourier Series Magnitude'),axis([0 10 0 0.6]),...

set(gcf,'Position',fig_size)

%

subplot(212),plot(n,ph_an,'o'),grid,xlabel('Harmonic Number'),...

ylabel('Phase (deg)'),title('Fourier Series Phase'),axis([0 10 -200 0]),...

set(gcf,'Position',fig_size)

%

w0 = pi; % Fundamental Frequency

t = [-2:0.002:6]; % time vector for approximations

%

x1 = 0; % approximation with DC + 1 term

for i = 1:2

x1 = x1 + mag_an(i)*cos(n(i)*w0*t + ph_an(i)*pi/180);

end

%

x2 = x1; % approximation with DC + 2 terms

i = 3;

x2 = x2 + mag_an(i)*cos(n(i)*w0*t + ph_an(i)*pi/180);

%

x3 = x2; % approximation with DC + 3 terms

i = 4;

x3 = x3 + mag_an(i)*cos(n(i)*w0*t + ph_an(i)*pi/180);

%

x4 = x3; % approximation with DC + 5 terms

for i = 5:6

x4 = x4 + mag_an(i)*cos(n(i)*w0*t + ph_an(i)*pi/180);

end

%

figure(3),subplot(221),plot(t,x1),grid,xlabel('Time (s)'),...

ylabel('Amplitude'),title('DC + 1 Term'),axis([-2 6 0 1]),...

subplot(222),plot(t,x2),grid,xlabel('Time (s)'),...

ylabel('Amplitude'),title('DC + 2 Terms'),axis([-2 6 0 1]),...

subplot(223),plot(t,x3),grid,xlabel('Time (s)'),...

ylabel('Amplitude'),title('DC + 3 Terms'),axis([-2 6 0 1]),...

subplot(224),plot(t,x4),grid,xlabel('Time (s)'),...

ylabel('Amplitude'),title('DC + 5 Terms'),axis([-2 6 0 1]),...

set(gcf,'Position',fig_size)

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%      ***** MATLAB Code Stops Here *****

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Latest revision on Thursday, May 18, 2006 10:54 PM