(1-a)/(1-a*exp(-j*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(0.5,a,%);
H:%;
plot2d(cabs(H),[f,0,10000],[logx]);
plot2d(carg(H),[f,0,10000],[logx]);
(1+exp(-j*omega*T)+exp(-2*j*omega*T))/3;
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(0.5,a,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx]);
plot2d(carg(H(f)),[f,0,500],[logx]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,500]],[x,-1,1],[y,-1,1]);
sum(exp(-(n-1)*j*\omega*T),n,1,N)/N;
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(0.5,a,%);
define(H(f,N),%);
plot2d([cabs(H(f,2)),cabs(H(f,4)),cabs(H(f,8)),cabs(H(f,10))],[f,0,500],[y,0.001,1],[logx],[logy]);
plot2d([carg(H(f,2)),carg(H(f,4)),carg(H(f,8)),carg(H(f,10))],[f,0,500]);
plot2d([[parametric,realpart(H(f,2)),imagpart(H(f,2)),[f,0,500]],
[parametric,realpart(H(f,4)),imagpart(H(f,4)),[f,0,500]],
[parametric,realpart(H(f,8)),imagpart(H(f,8)),[f,0,500]],
[parametric,realpart(H(f,10)),imagpart(H(f,10)),[f,0,500]]],[x,-1,1],[y,-1,1],[nticks,100]);
(1-exp(-5*j*omega*T))/(5*exp(-j*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(0.5,a,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy]);
plot2d(carg(H(f)),[f,0,500]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,500]],[x,-1,1],[y,-1,1]);
(1-exp(-5*j*omega*T))/(5*(1-exp(-j*omega*T)));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(0.5,a,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy]);
plot2d(carg(H(f)),[f,0,500]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,500]],[x,-1,1],[y,-1,1]);
1-exp(-j*M*omega*T);
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(16,M,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy],[y,0.0001,10]);
plot2d(carg(H(f)),[f,0,500]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,500]],[x,-1,1],[y,-1,1]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,60]],[x,-1,1],[y,-1,1]);
1/(1-exp(-j*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy],[y,0.1,1000]);
plot2d(carg(H(f)),[f,0,500]);
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,0,500]],[x,-1,1])
plot2d([parametric,realpart(H(f)),imagpart(H(f)),[f,1,500]],[x,-1,1])
1/(1-exp(-j*M*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(16,M,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy],[y,0.1,1000]);
plot2d(carg(H(f)),[f,0,500]);
(1-exp(-j*M*omega*T))/(1-exp(-j*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
subst(16,M,%);
define(H(f),%);
plot2d(cabs(H(f)),[f,0,500],[logx],[logy],[y,0.01,100]);
plot2d(carg(H(f)),[f,0,500]);
(1+exp(-j*omega*T)+exp(-2*j*omega*T))$
ratsimp(%);
(1-exp(-j*3*omega*T))/(1-exp(-j*omega*T))$
ratsimp(%);
%e^(-2*j*omega*T)*(%e^(2*j*omega*T)+%e^(j*omega*T)+1)
(1+exp(-j*omega*T)+exp(-2*j*omega*T)+exp(-3*j*omega*T))$
ratsimp(%);
(1-exp(-j*4*omega*T))/(1-exp(-j*omega*T))$
ratsimp(%);
%e^(-3*j*omega*T)*(%e^(3*j*omega*T)+%e^(2*j*omega*T)+%e^(j*omega*T)+1)
(1+exp(-j*omega*T)+exp(-2*j*omega*T)+exp(-3*j*omega*T)+exp(-4*j*omega*T)+exp(-5*j*omega*T)+exp(-6*j*omega*T)+exp(-7*j*omega*T))$
ratsimp(%);
(1-exp(-j*8*omega*T))/(1-exp(-j*omega*T))$
ratsimp(%);
%e^(-7*j*omega*T)*(%e^(7*j*omega*T)+%e^(6*j*omega*T)+%e^(5*j*omega*T)+%e^(4*j*omega*T)+%e^(3*j*omega*T)+%e^(2*j*omega*T)+%e^(j*omega*T)+1)
(1+exp(-j*omega*T)+exp(-2*j*omega*T)+exp(-3*j*omega*T)+exp(-4*j*omega*T)+exp(-5*j*omega*T)+exp(-6*j*omega*T)+exp(-7*j*omega*T)+exp(-8*j*omega*T)+exp(-9*j*omega*T)+exp(-10*j*omega*T)+exp(-11*j*omega*T)+exp(-12*j*omega*T)+exp(-13*j*omega*T)+exp(-14*j*omega*T)+exp(-15*j*omega*T))$
ratsimp(%);
(1-exp(-j*16*omega*T))/(1-exp(-j*omega*T))$
ratsimp(%);
%e^(-15*j*omega*T)*(%e^(15*j*omega*T)+%e^(14*j*omega*T)+%e^(13*j*omega*T)+%e^(12*j*omega*T)+%e^(11*j*omega*T)+%e^(10*j*omega*T)+%e^(9*j*omega*T)+%e^(8*j*omega*T)+
%e^(7*j*omega*T)+%e^(6*j*omega*T)+%e^(5*j*omega*T)+%e^(4*j*omega*T)+%e^(3*j*omega*T)+%e^(2*j*omega*T)+%e^(j*omega*T)+1)
(1-a1-a2)/(1-a1*exp(-j*omega*T)-a2*exp(-2*j*omega*T));
subst(2*exp(-%pi*B0*T)*cos(2*%pi*F0*T),a1,%);
subst(-exp(-2*%pi*B0*T),a2,%);
subst(1/(10*T),F0,%);
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
define(H(f,B0),%);
plot2d([cabs(H(f,1)),cabs(H(f,10)),cabs(H(f,20))],[f,0,500],[logx]);
plot2d([carg(H(f,1)),carg(H(f,10)),carg(H(f,20))],[f,0,500],[logx]);
c0*(1+b1*exp(-j*omega*T)+exp(-2*j*omega*T))/(1-a1*exp(-j*omega*T)-a2*exp(-2*j*omega*T));
subst((1-a1-a2)/(2+b1),c0,%);
subst(2*exp(-%pi*B0*T)*cos(2*%pi*F0*T),a1,%);
subst(-exp(-2*%pi*B0*T),a2,%);
subst(-2*cos(2*%pi*F0*T),b1,%);
subst(1/(10*T),F0,%);
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
define(H(f,B0),%);
plot2d([cabs(H(f,1)),cabs(H(f,10)),cabs(H(f,20))],[f,0,500],[logx]);
plot2d([carg(H(f,1)),carg(H(f,10)),carg(H(f,20))],[f,0,500],[logx]);
(exp(-j*omega*T)-a)/(1-a*exp(-j*omega*T));
subst(%i,j,%);
subst(2*%pi*f,omega,%);
subst(0.001,T,%);
define(H(f,a),%);
plot2d([cabs(H(f,-0.9)),cabs(H(f,-0.5)),cabs(H(f,0.5)),cabs(H(f,0.9))],[f,0,500],[logx],[y,0.99999,1.00001]);
plot2d([carg(H(f,-0.9)),carg(H(f,-0.5)),carg(H(f,0.5)),carg(H(f,0.9))],[f,0,500],[logx]);