a_ds=3+mod(47411,3)
b_ds=4+mod(47411,5)
x=[-pi:0.01:pi];
y_ds=a_ds*x.^2-b_ds;
m=4+mod(47411,3)
j_ds=[0:1:2*m-1];
xj=-pi+(j_ds/m)*pi
yj=a_ds*xj.^2-b_ds
a0_ds=(1/3)*sum(yj.*cos(0*xj))
a1_ds=(1/3)*sum(yj.*cos(1*xj))
a2_ds=(1/3)*sum(yj.*cos(2*xj))
b1_ds=(1/3)*sum(yj.*sin(xj))
S2_ds=(1/2)*a0_ds+a1_ds*cos(x)+a2_ds*cos(2*x)+b1_ds*sin(x);
plot(x,S2_ds)
hold on
plot(x,y_ds)
scatter(xj,yj)