transformada de fourier - señales en forma trigonometrica y complejas

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Universidad Autónoma de Baja California

Citec Valle de las Palmas

Ingeniería en Electrónica

Procesamiento Digital de SeñalesReporte 2

Señal Diente de Sierra en función trigonométrica y compleja

15-Abril/2015

564

Marcos Marcos Fernando

Paul Medina

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');

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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');

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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));

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');

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Solución compleja

x (t )=∑n=∞

−∞

j 52 πn

e j nω0 t

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');

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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');

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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+a19+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);

plot(t,a18);plot(t,a19);plot(t,a20);plot(t,xt,'r');

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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

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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

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