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{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Filtering with Matrices" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 20 "F
unction Definitions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "phi_
b:=x->piecewise(x>=0 and x<1,1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "psi_b:=x->piecewise(x>=0 and x<1/2,1,x>=1/2 and x<1,-
1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "psi_b:=x->phi_b(2*x)
-phi_b(2*x-1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "haar_s:=(
j,i,x)->phi_b((2^j)*x-i):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "haar_w:=(j,i,x)->psi_b((2^j)*x-i):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 8 "Matrices" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "low1x2:=(1/2)*matrix(1,2,[1,1]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'low1x2G,$-%'MATRIXG6#7#7$\"\"\"F+#
F+\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "low2x4:=(1/2)*ma
trix(2,4,[1,1,0,0,0,0,1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'low
2x4G,$-%'MATRIXG6#7$7&\"\"\"F+\"\"!F,7&F,F,F+F+#F+\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "low4x8:=(1/2)*matrix(4,8,[1,1,0,0,0
,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1]);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%'low4x8G,$-%'MATRIXG6#7&7*\"\"\"F+\"\"!F,F,F,
F,F,7*F,F,F+F+F,F,F,F,7*F,F,F,F,F+F+F,F,7*F,F,F,F,F,F,F+F+#F+\"\"#" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "high1x2:=(1/2)*matrix(1,2,[1,-1]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%(high1x2G,$-%'MATRIXG6#7#7$\"\"\"!\"\"#F+\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "high2x4:=(1/2)*matrix(2,4,[1
,-1,0,0,0,0,1,-1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(high2x4G,$-%
'MATRIXG6#7$7&\"\"\"!\"\"\"\"!F-7&F-F-F+F,#F+\"\"#" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 97 "high4x8:=(1/2)*matrix(4,8,[1,-1,0,0,0,0,0,0
,0,0,1,-1,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,1,-1]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%(high4x8G,$-%'MATRIXG6#7&7*\"\"\"!\"\"\"\"!F-F-F
-F-F-7*F-F-F+F,F-F-F-F-7*F-F-F-F-F+F,F-F-7*F-F-F-F-F-F-F+F,#F+\"\"#" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 4 "
Data" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "coeffs1:=[9,7,3,5]:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "data1:=[9,7,3,5,1,3,7,5
]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
262 12 "First Filter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "d2:
=multiply(low2x4,coeffs1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d2G-%
'VECTORG6#7$\"\")\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "h
igh1:=multiply(high2x4,coeffs1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
&high1G-%'VECTORG6#7$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "multiply(low1x2,d2);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#-%'VECTORG6#7#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "m
ultiply(high1x2,d2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7#
\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 264 13 "Second Filter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "data1:=[9,7,3,5,1,3,7,5]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "data2:=multiply(low4x8,data1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%&data2G-%'VECTORG6#7&\"\")\"\"%\"\"#\"\"'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "multiply(high4x8,data1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'VECTORG6#7&\"\"\"!\"\"F(F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 30 "data3:=multiply(low2x4,data2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%&data3G-%'VECTORG6#7$\"\"'\"\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "multiply(high2x4,data2);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'VECTORG6#7$\"\"#!\"#" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 30 "data4:=multiply(low1x2,data3);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%&data4G-%'VECTORG6#7#\"\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "multiply(high1x2,data3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'VECTORG6#7#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "data5:=[5,1,2,-2,1,-1,-1,1];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&data5G7*\"\"&\"\"\"\"\"#!\"#F'!\"\"F*F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plot(sum(data1[n]*haar_s(3,n-1,x),n
=1..8),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "plot(dat
a5[1]*haar_s(0,0,x)+sum(data5[n+1]*haar_w(coeffj[n],coeffi[n],x),n=1..
7),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 12 "Downsamp
ling" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "temp:=(1/2)*matrix(
4,4,[1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%tempG,$-%'MATRIXG6#7&7&\"\"\"F+\"\"!F,F*7&F,F,F+F+F-#F+\"\"#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "downs:=matrix(4,2,[1,0,
0,0,0,0,0,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&downsG-%'MATRIXG6
#7&7$\"\"\"\"\"!7$F+F+F,7$F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "c2:=multiply(temp,coeffs1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#c2G-%'VECTORG6#7&\"\")F)\"\"%F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "multiply(c2,downs);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#-%'VECTORG6#7$\"\")\"\"%" }}}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }