% DWT pomocou matic - Db2 - 16,8,4,2

% h1 a g1 - koeficienty pre analyzu
% h2 a g2 - koeficienty pre rekonstrukciu

h1 = [-0.1294 0.2241 0.8365 0.4830]*sqrt(2)
g1 = [-0.4830 0.8365 -0.2241 -0.1294]*sqrt(2)
h2 = [0.4830 0.8365 0.2241 -0.1294]*sqrt(2)
g2 = [-0.1294 -0.2241 0.8365 -0.4830]*sqrt(2)


H1_16=[ h1(1:4) zeros(1,12);
   zeros(1,2) h1(1:4) zeros(1,10);
   zeros(1,4) h1(1:4) zeros(1,8);
	zeros(1,6) h1(1:4) zeros(1,6);
   zeros(1,8) h1(1:4) zeros(1,4);
   zeros(1,10) h1(1:4) zeros(1,2);
   zeros(1,12) h1(1:4);
  	h1(3:4) zeros(1,12) h1(1:2)]

G1_16=[ g1(1:4) zeros(1,12);
   zeros(1,2) g1(1:4) zeros(1,10);
   zeros(1,4) g1(1:4) zeros(1,8);
	zeros(1,6) g1(1:4) zeros(1,6);
   zeros(1,8) g1(1:4) zeros(1,4);
   zeros(1,10) g1(1:4) zeros(1,2);
   zeros(1,12) g1(1:4);
  	g1(3:4) zeros(1,12) g1(1:2)]

H1_8=[ h1(1:4) zeros(1,4);
   zeros(1,2) h1(1:4) zeros(1,2);
   zeros(1,4) h1(1:4);
	h1(3:4) zeros(1,4) h1(1:2)]

G1_8=[ g1(1:4) zeros(1,4);
   zeros(1,2) g1(1:4) zeros(1,2);
   zeros(1,4) g1(1:4);
   g1(3:4) zeros(1,4) g1(1:2)]


H1_4=[ h1(1:4);
	    h1(3:4) h1(1:2)]

G1_4=[ g1(1:4);
	    g1(3:4) g1(1:2)]
    

H1_2=[ (h1(1)+h1(3)) (h1(2)+h1(4))]

G1_2=[ (g1(1)+g1(3)) (g1(2)+g1(4))]

% Matice pre rozklad 

T_16 = [H1_16;
   G1_16]

T_8 = [H1_8;
   G1_8]


T_4 = [H1_4;
   G1_4]

T_2 = [H1_2;
   G1_2]

% Ideme rozkladat

c0=[1 5 -2 -1 0 4 3 5 0 1 4 9 4 2 -3 0]'

c1_d1 = T_16*c0

c1=H1_16*c0
d1=G1_16*c0

c2 = H1_8*c1
d2 = G1_8*c1

c3 = H1_4*c2
d3 = G1_4*c2

c4 = H1_2*c3
d4 = G1_2*c3


c = [ c4(1); d4(1); d3(1:2); d2(1:4); d1(1:8)]

sum(c0)

Ts_2 = inv(T_2)
Ts_4 = inv(T_4)
Ts_8 = inv(T_8)
Ts_16 = inv(T_16)
c = Ts_16 * c1_d1
c0-c

% Zobrazujeme bazove koeficienty - potrebujeme matice na rekonstrukciu
H2_16=[ h2(1:4) zeros(1,12);
   zeros(1,2) h2(1:4) zeros(1,10);
   zeros(1,4) h2(1:4) zeros(1,8);
	zeros(1,6) h2(1:4) zeros(1,6);
   zeros(1,8) h2(1:4) zeros(1,4);
   zeros(1,10) h2(1:4) zeros(1,2);
   zeros(1,12) h2(1:4);
   h2(3:4) zeros(1,12) h2(1:2)]'

H2_8=[ h2(1:4) zeros(1,4);
   zeros(1,2) h2(1:4) zeros(1,2);
   zeros(1,4) h2(1:4);
   h2(3:4) zeros(1,4) h2(1:2)]'

H2_4=[ h2(1:4);
	    h2(3:4) h2(1:2)]'   

H2_2=[ (h2(1)+h2(3)) (h2(2)+h2(4))]'

c2=[0 1 0 0 ]'
c3=[1 0]'
c0=H2_16*H2_8*c2
plot(c0)
c0=H2_16*H2_8*H2_4*c3
plot(c0)