Triangle Approximation: Sum of Sinusoids Example

The following Matlab code provides an example of the fact that any signal can constructed using a sum of sinusoids.

clear all; %clear all variables

fs = 50; % sample freq

Ts=1/fs; % sample period

n=0:1*fs; % time window (fs=samples per second), 1 second

tn=n*Ts; % sample index

wave_1=sin(2*pi*5*tn);

wave_2=sin(-1/9*sin(6*pi*5*tn));

wave_3=sin(1/25*sin(10*pi*5*tn));

wave_4=sin(-1/49*sin(14*pi*5*tn));

wave_5=sin(1/81*sin(18*pi*5*tn));

wave_6=sin(-1/121*sin(22*pi*5*tn));

wave_7=sin(1/169*sin(26*pi*5*tn));

x = (8/(pi^2))*(wave_1+wave_2+wave_3+wave_4+wave_5+wave_6+wave_7);

% Time domain plot of x(t)=cos(2*pi*5*tn)

figure('Color',[1 1 1]);

h=plot(tn,wave_1,'--r',tn,wave_2,'--k',tn,x,'g','LineWidth',2);box off;hold on;

xlabel('Time(s)');

ylabel('Amplitude');

title('Square Wave Approximation');

axis([0 1 -1.5 1.5]);

## 1 comment:

Why does the above code has

x = ( 8 / (pi^2 ) ??????

Please if you could explain, would really appreciate it.

Thanks in advance,

Yatin

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