n=8;​​​​Cvector[n_]:=Table[Subscript[c,i],{i,0,n-1}]​​​​Cvector[n]
{
c
0
,
c
1
,
c
2
,
c
3
,
c
4
,
c
5
,
c
6
,
c
7
}
H[j_,k_,t_]:=Piecewise
j/2
2
+0*t,
k
j
2
<=t<
k+(1/2)
j
2
,-
j/2
2
+0*t,
k+(1/2)
j
2
<=t<
k+1
j
2
,0
Hscaling[t_]=Piecewise[{{1+0*t,0<=t<1}},0]

1
0≤t<1
0
True
Hwavelet[n_,t_]:=HFloor[Log[2,n]],n-
Floor[Log[2,n]]
2
,t
A=Table[Hwavelet[k+1,t],{k,0,n-2}]

1
0≤t<
1
2
-1
1
2
≤t<1
0
True
,
2
0≤t<
1
4
-
2
1
4
≤t<
1
2
0
True
,
2
1
2
≤t<
3
4
-
2
3
4
≤t<1
0
True
,
2
0≤t<
1
8
-2
1
8
≤t<
1
4
0
True
,
2
1
4
≤t<
3
8
-2
3
8
≤t<
1
2
0
True
,
2
1
2
≤t<
5
8
-2
5
8
≤t<
3
4
0
True
,
2
3
4
≤t<
7
8
-2
7
8
≤t<1
0
True

Hvector[n_,t_]:=Table[If[m1==0,Hscaling[t],Hwavelet[m1,t]],{m1,0,n-1}]
Hvector[4,t]


1
0≤t<1
0
True
,
1
0≤t<
1
2
-1
1
2
≤t<1
0
True
,
2
0≤t<
1
4
-
2
1
4
≤t<
1
2
0
True
,
2
1
2
≤t<
3
4
-
2
3
4
≤t<1
0
True

Plot[Hscaling[t],{t,0,1},PlotStyle{Red}]
0.2
0.4
0.6
0.8
1.0
0.5
1.0
1.5
2.0
Plot[Evaluate@Table[Hwavelet[k,t],{k,1,63}],{t,0,1}]
0.2
0.4
0.6
0.8
1.0
-6
-4
-2
2
4
6
Hmatrix[n_]:=TransposeTableHvectorn,
2*j-1
2*n
,{j,1,n}
Hmatrix[n]//MatrixForm
1
1
1
1
1
1
1
1
1
1
1
1
-1
-1
-1
-1
2
2
-
2
-
2
0
0
0
0
0
0
0
0
2
2
-
2
-
2
2
-2
0
0
0
0
0
0
0
0
2
-2
0
0
0
0
0
0
0
0
2
-2
0
0
0
0
0
0
0
0
2
-2