This document appears to be a student report describing experiments with trigonometric and complex signal representations. It includes plots of various signals constructed as sums of sinusoidal and complex exponential terms. The student is exploring trigonometric representations of sawtooth waveforms as well as complex exponential representations. Code snippets are provided to generate the signals and plots.

1. qwertyuiopasdfghjklzxcvbnmqwerty
uiopasdfghjklzxcvbnmqwertyuiopasd
fghjklzxcvbnmqwertyuiopasdfghjklzx
cvbnmqwertyuiopasdfghjklzxcvbnmq
wertyuiopasdfghjklzxcvbnmqwertyui
opasdfghjklzxcvbnmqwertyuiopasdfg
hjklzxcvbnmqwertyuiopasdfghjklzxc
vbnmqwertyuiopasdfghjklzxcvbnmq
wertyuiopasdfghjklzxcvbnmqwertyui
opasdfghjklzxcvbnmqwertyuiopasdfg
hjklzxcvbnmqwertyuiopasdfghjklzxc
vbnmqwertyuiopasdfghjklzxcvbnmq
wertyuiopasdfghjklzxcvbnmqwertyui
opasdfghjklzxcvbnmqwertyuiopasdfg
hjklzxcvbnmrtyuiopasdfghjklzxcvbn
mqwertyuiopasdfghjklzxcvbnmqwert
yuiopasdfghjklzxcvbnmqwertyuiopas
Universidad Autónoma de Baja
California
Citec Valle de las Palmas
Ingeniería en Electrónica
Procesamiento Digital de Señales
Reporte 2
Señal Diente de Sierra en función
trigonométrica y compleja
15-Abril/2015
564
Marcos Marcos Fernando
Paul Medina

2. t=0:0.001:4;
a0=(3/2)*ones(1,length(t));
a1=(6/pi)*cos((pi)*t);
plot(t,a0);
hold on;
grid;
plot(t,a1);
plot(t,xt,'r');
t=0:0.001:4;
a0=(3/2)*ones(1,length(t));
a1=(6/pi)*cos((pi)*t);
a3=((-2/pi)*cos((3*pi)*t));
plot(t,a0);
hold on;
grid;
plot(t,a1);
plot(t,a3);
plot(t,xt,'r');
t=0:0.001:4;
a0=(3/2)*ones(1,length(t));
a1=(6/pi)*cos((pi)*t);
a3=((-2/pi)*cos((3*pi)*t));
a5=((6/(5*pi))*cos((5*pi)*t));
a7=((-6/(7*pi))*cos((7*pi)*t));
a9=((6/(9*pi))*cos((9*pi)*t));
a11=((-6/(11*pi))*cos((11*pi)*t));
a13=((6/(13*pi))*cos((13*pi)*t));
a15=((-6/(15*pi))*cos((15*pi)*t));
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4

3. xt=a0+a1+a3+a5+a7+a9+a11+a13+a15;
plot(t,a0);
hold on;
grid;
plot(t,a1);
plot(t,a3);
plot(t,a5);
plot(t,a7);
plot(t,a9);
plot(t,a11);
plot(t,a13);
plot(t,a15);
plot(t,xt,'r');
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4

5. Solución compleja
𝑥( 𝑡) = ∑ 𝑗
5
2𝜋𝑛
−∞
𝑛=∞
𝑒𝑗𝑛𝜔0 𝑡

6. t=0:0.001:4;
a0=(5/2)*ones(1,length(t));
a1=(-5/(1*pi))*sin(1*pi*t);
a2=(-5/(2*pi))*sin((2*pi*t));
xt=a0+a1+a2;
hold on;
grid;
plot(t,a0);
plot(t,a1);
plot(t,a2);
plot(t,xt,'r');
t=0:0.001:4;
a0=(5/2)*ones(1,length(t));
a1=(-5/(1*pi))*sin(1*pi*t);
a2=(-5/(2*pi))*sin((2*pi*t));
a3=(-5/(3*pi))*sin((3*pi*t));
a4=(-5/(4*pi))*sin((4*pi*t));
a5=(-5/(5*pi))*sin((5*pi*t));
a6=(-5/(6*pi))*sin((6*pi*t));
a7=(-5/(7*pi))*sin((7*pi*t));
a8=(-5/(8*pi))*sin((8*pi*t));
a9=(-5/(9*pi))*sin((9*pi*t));
a10=(-5/(10*pi))*sin((10*pi*t));
xt=a0+a1+a2+a3+a4+a5+a6+a7+a8+a9+a10;
hold on;
grid;
plot(t,a0);
plot(t,a1);
plot(t,a2);
plot(t,a3);
plot(t,a4);
plot(t,a5);
plot(t,a6);
plot(t,a7);
plot(t,a8);
plot(t,a9);
plot(t,a10);
plot(t,xt,'r');
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4
5

7. t=0:0.001:4;
a0=(5/2)*ones(1,length(t));
a1=(-5/(1*pi))*sin(1*pi*t);
a2=(-5/(2*pi))*sin((2*pi*t));
a3=(-5/(3*pi))*sin((3*pi*t));
a4=(-5/(4*pi))*sin((4*pi*t));
a5=(-5/(5*pi))*sin((5*pi*t));
a6=(-5/(6*pi))*sin((6*pi*t));
a7=(-5/(7*pi))*sin((7*pi*t));
a8=(-5/(8*pi))*sin((8*pi*t));
a9=(-5/(9*pi))*sin((9*pi*t));
a10=(-5/(10*pi))*sin((10*pi*t));
a11=(-5/(11*pi))*sin((11*pi*t));
a12=(-5/(12*pi))*sin((12*pi*t));
a13=(-5/(13*pi))*sin((13*pi*t));
a14=(-5/(14*pi))*sin((14*pi*t));
a15=(-5/(15*pi))*sin((15*pi*t));
a16=(-5/(16*pi))*sin((16*pi*t));
a17=(-5/(17*pi))*sin(17*pi*t);
a18=(-5/(18*pi))*sin(18*pi*t);
a19=(-5/(19*pi))*sin(19*pi*t);
a20=(-5/(20*pi))*sin(20*pi*t);
xt=a0+a1+a2+a3+a4+a5+a6+a7+a8+a9+a10+a11+a12+a13+a14+a15+a16+a17+a18+a
19+a20;
hold on;
grid;
plot(t,a0);
plot(t,a1);
plot(t,a2);
plot(t,a3);
plot(t,a4);
plot(t,a5);
plot(t,a6);
plot(t,a7);
plot(t,a8);
plot(t,a9);
plot(t,a10);
plot(t,a11);
plot(t,a12);
plot(t,a13);
plot(t,a14);
plot(t,a15);
plot(t,a16);
plot(t,a17);
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4
5
6

8. plot(t,a18);
plot(t,a19);
plot(t,a20);
plot(t,xt,'r');
t=0:0.001:4;
xt=(5/2)*ones(1,length(t));
plot(t,xt);
for i=1:100
t=0:0.001:4;
ai=(-5/(i*pi))*sin(i*pi*t);
xt=xt+ai;
plot(t,xt,'r');
end
t=0:0.001:4;
xt=(5/2)*ones(1,length(t));
plot(t,xt);
for i=1:1000
t=0:0.001:4;
ai=(-5/(i*pi))*sin(i*pi*t);
xt=xt+ai;
plot(t,xt,'r');
end
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3 3.5 4
-1
0
1
2
3
4
5
6

9. 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
0
1
2
3
4
5
6