Scaling Vector

Matrices

G[-2]={{0,0,0.02669163201881291`,0.026188780570349884`},{0,0,-0.03940748766209954`,-0.040769035522339014`},{0,0,0,0},{0,0,0,0}};

G[-1]={{-0.11751247435095598`,-0.10652668959666897`,0.30676124077120465`,0.35964167838854366`},{0.18731879383595215`,0.18181954032277048`,-0.4224381824999862`,-0.433225475337907`},{0,0,0,0},{0,0,0,0}};

G[0]={{0.7071067811865841`,0,0.3067612407712861`,-0.3596416783882024`},{0,0.35355339059336993`,0.42243818250022613`,-0.43322547533688205`},{0,0,0.47106586494422936`,0.23604093395898632`},{0,0,-0.5666158791523569`,-0.2916640296146426`}};

G[1]={{-0.11751247435904282`,0.10652668958949803`,0.026691633234707347`,-0.026188779541901065`},{-0.1873187938600181`,0.18181954030143205`,0.03940749128037211`,-0.040769032461869345`},{0.6669057455800359`,0,0.47106586494422936`,-0.23604093395898632`},{0,0.4333094490577162`,0.5666158791523569`,-0.2916640296146426`}};

Function Values

Clear[phi];

phi[0]={1.7308078457850338`,0,0,0}//N

phi[x_]:=If[x≤-1||x≥1,{0,0,0,0},phi[x]];

phi[3]

fill[j_]:=Do[phi[x]=(Sqrt[2])Sum[G[i].phi[2x-i],{i,-2,1}],{x,-1,1,(2^(-j))}];

fill[1]

fill[2]

fill[3]

fill[4]

fill[5]

fill[6]

fill[7]

pts[i_]:=Table[{x,phi[x][[i]]},{x,-1,1,(2^(-7))}];

phi[-1]

phi[-(3/4)]

phi[-(1/2)]

phi[-(1/4)]

phi[0]

phi[(1/4)]

phi[(1/2)]

phi[(3/4)]

phi[1]

Graphs

Show[Graphics[{Black,Thickness[.012],Line[pts[1]]}],Axes->True,PlotRange->{{-1.1,1.1},{-1.75,1.75}},Ticks->{{-1,-.5,.5,1},{-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.012],Line[pts[2]]}],Axes->True,PlotRange->{{-1.1,1.1},{-1.75,1.75}},Ticks->{{-1,-.5,.5,1},{-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.02],Line[pts[3]]}],Axes->True,PlotRange->{{-0.1,1.1},{-1.75,1.75}},Ticks->{{-1,-.5,.5,1},{-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.02],Line[pts[4]]}],Axes->True,PlotRange->{{-0.1,1.1},{-1.75,1.75}},Ticks->{{-1,-.5,.5,1},{-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Multiwavelet

Matrices

H[-2]={{0,0,0.026691631350082096`,0.026188779914217485`},{0,0,0.043743653006003906`,0.06435982959198171`},{0,0,-0.013410540810749855`,-0.013157895717088848`},{0,0,-0.04006995259666773`,-0.060651857618035654`}};

H[-1]={{-0.11751247140680432`,-0.10652668692775462`,0.30676123308562386`,0.35964166937809905`},{-0.3334538093583894`,-0.4246928494631754`,0.1922977905008767`,-0.4067067810936163`},{0.05904119433180234`,0.053521662417019424`,-0.15412448873935367`,-0.18069293784197155`},{0.31660009019953533`,0.4088238959496059`,-0.15157506646288071`,0.45139832417009795`}};

H[0]={{-0.707106787091808`,0,0.3067612330857053`,-0.35964166937775777`},{0,0,0.1922977905022298`,0.4067067810994858`},{0,-0.9347644627208598`,0.15412448873939458`,-0.18069293784180007`},{0,-0.034862829700229456`,0.15157506646421662`,0.4513983241758947`}};

H[1]={{-0.11751247141489116`,0.10652668692058367`,0.0266916325659765`,-0.02618877888576869`},{-0.3334538094952176`,0.42469284934186313`,0.04374367357717413`,-0.06435981219212035`},{-0.05904119433586537`,0.05352166241341656`,0.013410541421645506`,-0.013157895200370542`},{-0.316600090334654`,0.4088238958298094`,0.04006997291081931`,-0.060651840435570196`}};

Graphs

Do[psi[x]=(Sqrt[2])Sum[H[i].phi[2x-i],{i,-2,1}],{x,-1,1,(2^(-7))}];

pts[i_]:=Table[{x,psi[x][[i]]}//N,{x,-1,1,(2^(-7))}];

Show[Graphics[{Black,Thickness[.012],Line[pts[1]]}],Axes->True,PlotRange->{{-1.1,1.1},{-2,2}},Ticks->{{-1,-.5,.5,1},{-2,-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.012],Line[pts[2]]}],Axes->True,PlotRange->{{-1.1,1.1},{-2,2}},Ticks->{{-1,-.5,.5,1},{-2,-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.012],Line[pts[3]]}],Axes->True,PlotRange->{{-1.1,1.1},{-2,2}},Ticks->{{-1,-.5,.5,1},{-2,-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]

Show[Graphics[{Black,Thickness[.012],Line[pts[4]]}],Axes->True,PlotRange->{{-1.1,1.1},{-2,2}},Ticks->{{-1,-.5,.5,1},{-2,-1.5,-1,-.5,.5,1,1.5,2,2.5,3}}]