clear all
close all

[D,x]=cheb(4);
x_hd=-1:0.01:1;

y=sin(pi*x);
y_hd=sin(pi*x_hd);


v=[0 0.8 0 -0.8 0];


T0=1;
T1=x;
T2=2*x.*T1-T0;
T3=2*x.*T2-T1;
T4=2*x.*T3-T2;

fox=v(1)*T0+v(2)*T1+v(3)*T2+v(4)*T3+v(5)*T4;

figure
plot(x,zeros(length(x)),'o')
hold on
plot(x_hd,y_hd,'b','linewidth',2)
plot(x,fox,'r','linewidth',2)

dy=D*y;

plot(x,dy,'g','linewidth',2)