function [Hr,w,a,L]=Hr_type1(h);
M=length(h);
L=(M-1)/2;
a=[h(L+1) 2*h(L:-1:1)];
n=[0:1:L];
w=[0:1:500]'*pi/500;
Hr=cos(w*n)*a';

function [Hr,w,b,L]=Hr_type2(h);
M=length(h);
L=(M)/2;
a=2*[h(L:-1:1)];
n=[1:1:L];n=n-0.5;
w=[0:1:500]'*pi/500;
Hr=cos(w*n)*b';

function [Hr,w,c,L]=Hr_type3(h);
M=length(h);
L=(M-1)/2;
a=2*[h(L:-1:1)];
n=[1:1:L];n=n-0.5;
w=[0:1:500]'*pi/500;
Hr=sin(w*n)*c';

function [Hr,w,d,L]=Hr_type4(h);
M=length(h);
L=(M)/2;
a=2*[h(L:-1:1)];
n=[1:1:L];n=n-0.5;
w=[0:1:500]'*pi/500;
Hr=sin(w*n)*b';

h=[-4,1,-1,-2,5,6,5,-2,-1,1,-4];
M=length(h);n=0:M-1;
[Hr,w,a,L)=Hr_type1(h);
a,L
amax=max(a)+1;amin=min(a)-1