% WRITTEN by M.S. Branicky
% Last modified: 10/07/04

figure(1)
clf;
% PROBLEM 3.50(e)
k=-4:4;
Xk=(1/2)*(1-exp(-(j*pi*k+1)))./(1+j*2*pi*k);
subplot(2,1,1), stem(k,abs(Xk),'filled'), ylabel('|X[k]|');
title('Problem 3.50(e)');
subplot(2,1,2), stem(k,angle(Xk),'filled'), ylabel('\angle X[k]'), xlabel('k');
line([-4 4],[0 0])
print -deps 'pr3_50e.eps'


figure(2)
clf;
% PROBLEM 3.51(b)
t=-2:0.011:2;
omega0=4*pi;
x=j*exp(j*1*omega0*t)-j*exp(j*-1*omega0*t)+exp(j*3*omega0*t)+exp(j*-3*omega0*t);
plot(t,x), xlabel('t'), ylabel('x(t)'), grid on;
title('Problem 3.51(b)');
print -deps 'pr3_51b.eps'


figure(3)
clf;
% PROBLEM 3.100(c)(i)
h=1/1000;
t=0:h:1;
x=2*(t>=1/2).*(t<=3/4);
phi0=(t>=0);
phi1=((t<1/2)-(t>1/2));
phi2=(t>=0)-2*(t>=1/4)+2*(t>=3/4);
phi3=phi2.*phi1;
phi4=(t>=0)-2*(t>=1/8)+2*(t>=3/8)-2*(t>=5/8)+2*(t>=7/8);
phi5=phi4.*phi1;

c0=1/2; c1=-1/2; c2=-1/2; c3=1/2; c4=0; c5=0;
% Alternatively: c0=trapz(x.*phi0)*h, c1=trapz(x.*phi1)*h, ...

xhat=c0*phi0+c1*phi1+c2*phi2+c3*phi3+c4*phi4+c5*phi5;

plot(t,x,'-',t,xhat,'--');
xlabel('t'), axis([0 1 -0.1 2.1]);
legend('x(t)','xhat(t)');
title('Problem 3.100(c)(i)');
print -deps 'pr3_100ci.eps'


figure(4)
clf;
% PROBLEM 3.106
T=1;
omega0=2*pi/T;

allJ=[29 59 99];

t=-0.5:0.0001:0.5;
xhat=0*t;
for k=0:max(allJ),
  if     (k==0), Bk=1/2;
  else
    if   (rem(k,2)), Bk=2*(-1)^((k-1)/2)./(k*pi);
    else Bk=0;
    end;
  end;
  xhat=xhat+Bk*cos(k*omega0*t);
  if (find(k==allJ)),
    [k max(xhat)]
    ylabel1=sprintf('B[%d] cos(\\omega_0 t)',k);
    ylabel2=sprintf('x_{%d}(t)',k);
    plotfile=sprintf('pr3_106_%d.eps',k);
    titlestring=sprintf('Problem 3.106, k=%d',k);
    subplot(2,1,1), plot(t,Bk*cos(k*omega0*t)); ylabel(ylabel1);
    title(titlestring);
    subplot(2,1,2), plot(t,xhat); ylabel(ylabel2); xlabel('t');
    print('-deps',plotfile);
    pause
  end;
end;