/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 13.04.2 ] */

/* [wxMaxima: input   start ] */
kill(all)$
N:8$ Ts:1/N$
n:makelist(n,n,0,N-1); t:Ts*n;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
/* PULS Width:a=3/8 Sec PULS  */
x:[1,1,1,0,0,0,0,0];
wxplot2d([discrete,n,x],[y,-0.2,1.2],[style,[points,2,1,1]]);
Xs:sum(exp(-%i*w*Ts*n)*x[n+1],n,0,N-1);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
/* sinc Function */
a:3/8;
wxplot2d([sin(a*w/2)/(w/2)],[w,-100*%pi,100*%pi],[y,-0.2,0.5]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
/* Plot DTFT  */
wxplot2d(abs(Xs),[w,-4*%pi/Ts,4*%pi/Ts]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
xo:Ts*integrate(expand(exp(%i*w*Ts*n)*Xs),w,-%pi/Ts,%pi/Ts)/(2*%pi);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
x:[0,0,1,1,1,0,0,0];
Xs:sum(exp(-%i*w*Ts*(n-3))*x[n+1],n,0,N-1);
wxplot2d([discrete,n-3,x],[y,-0.2,1.2],[style,[points,2,1,1]]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d(realpart(Xs),[w,-4*%pi/Ts,4*%pi/Ts]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
a:3/8;
plot2d([realpart(Xs)*Ts,sin(a*w/2)/(w/2)],[w,-4*%pi/Ts,4*%pi/Ts],[y,-0.2,0.5]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
xo:Ts*integrate(expand(exp(%i*w*Ts*(n-3))*Xs),w,-%pi/Ts,%pi/Ts)/(2*%pi);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
kill(all)$
N:24$ Ts:1/N$
n:makelist(n,n,0,N-1); t:Ts*n;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
x:[0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0];
Xs:sum(exp(-%i*w*Ts*n)*x[n+12],n,-11,12);
wxplot2d([discrete,n-11,x],[y,-0.2,1.2],[style,[points,2,1,1]]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d(realpart(Xs),[w,-1*%pi/Ts,1*%pi/Ts]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
a:9/24;
plot2d([realpart(Xs)*Ts,sin(a*w/2)/(w/2)],[w,-4*%pi/Ts,4*%pi/Ts],[y,-0.2,0.5]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
xo:expand(Ts*integrate(expand(exp(%i*w*Ts*(n-11))*Xs),w,-%pi/Ts,%pi/Ts)/(2*%pi));
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$