Wavelet analysis of the blood pressure and pulse frequency measuements with Maple
\302\251 -2013, Prof. Gennady P. Chuiko and Irina A. Danishewska,
Petro Mohyla BlackSea Satate University, Mykolayiv, Ukraine
gp47@mail.ru
<Text-field style="Heading 2" layout="Heading 2">1. Introduction and measurement details</Text-field>
A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.
The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.
Results of measurments of the blood pressure and the pulse frequency of the patient were obtained by automatic blood pressure monitor "Micrilife BP 3AG1" (Microlife AG, Switzerland, http://www.microlife.com.ua). The technical parameters of this device are presented in table 1 in accordance with the accompanying documentation.
Table 1. Technical parameters of device
The results of observations are presented as data tables and vectors below
restart;
Data_s:=convert(Data_s,Vector[row], datatype=float[8]): whattype(Data_s);# systolic blood pressures (mmHg)
JkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJHJvd0dGJw==
Data_d:=convert(Data_d,Vector[row], datatype=float[8]):# systolic blood pressures (mmHg)
Data_p:=convert(Data_p,Vector[row], datatype=float[8]):# pulse frequences (beats per minute - bpm)
<Text-field style="Heading 2" layout="Heading 2">2. Primary results and their statistical characteristics</Text-field>
Let us show the prymary results grafically (table 2)
gs:=plots[listplot](Data_s,view=[0..80,125..185],thickness=2, gridlines=true,tickmarks=[15,16],color=black, title=`fig.1.Systola`,labeldirections=[horizontal,vertical],labels=[`counts`,`Blood pressure, mmHg.`],font=[helvetica,14]):
gd:=plots[listplot](Data_d,view=[0..80,70..110],thickness=2, gridlines=true,tickmarks=[15,16],color=black, title=`fig.2.Diastola`,labeldirections=[horizontal,vertical],labels=[`counts`,`Blood pressure, mmHg.`],font=[helvetica,14]):
gp:=plots[listplot](Data_p,view=[0..80,65..105],thickness=2, gridlines=true,tickmarks=[15,16],color=black, title=`fig.3.Pilse`,labeldirections=[horizontal,vertical],labels=[`counts`,`Pulse, bpm.`],font=[helvetica,14]):
Table 2
The next table shows the statistical characteristics of results
Table 3
The results of table 3 as for standard deviations and accuracies are in certain disagreements with values declared by table 1.
Other visual characteristics of primary measurements are statistical frequency plots (table 4).
Table 4
The readers can decide themself how convincing look the graphs of table 4 for the solving of question of closeness of these distributions of probabilities to the normal law.
A significant positive correlation coefficient has been observed only between systolic pressure and pulse frequency.
Statistics:-Correlation(Data_d,Data_s);
Statistics:-Correlation(Data_d,Data_p);
Statistics:-Correlation(Data_p,Data_s);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMkITAlPUhcO2otSCEjOzcjXUJGOURCOTEzMjAzREUxNEY=
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMkIjA3WmszKTQnMyIhIzo3I10zRkJCQ0REQTM4Mjc2MkZD
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMkIjBySkA+MkZmJSEjOjcjXTNGREQ2NEIxMDNDMUZCNUQ=
However, this correlation also looks not too compelling (see the scatter plot below).
Statistics:-ScatterPlot(Data_p,Data_s,title = "fig.7 Systola-Pulse correlation", legend = "Point data",view=[76..88,140..170],symbol=solidcircle,symbolsize=18,color=black,gridlines=true,font=[helvetica,16],tickmarks=[12,10],labeldirections=[horizontal,vertical],labels=[`Pulse, bpm`,` Systolic pressure, mmHg`], titlefont=[helvetica,16]);
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
The need to clean up the primary data from input noises is the main conclusion of this section. The package of Discrete Wavelet transforms (DWT) looks as suitable tool for this aim [1,2].
JSFH
<Text-field style="Heading 2" layout="Heading 2">3. VectorDWT and InverseVectorDWT procedures</Text-field>
Write down the two procedures for direct Discrete Wavelet transformation (VectorDWT) and for inverse transforms with recovering of the original signal (InverseVectorDWT), using samples of [1]
with(DiscreteTransforms);
NyhJOURpc2NyZXRlV2F2ZWxldFRyYW5zZm9ybUc2IkkxRm91cmllclRyYW5zZm9ybUdGJElASW52ZXJzZURpc2NyZXRlV2F2ZWxldFRyYW5zZm9ybUdGJEk4SW52ZXJzZUZvdXJpZXJUcmFuc2Zvcm1HRiRJNFdhdmVsZXRDb2VmZmljaWVudHNHRiRJLFdhdmVsZXRQbG90R0Yk
VectorDWT := proc (V, iters, w1, w2) local i, s, temp1, temp2; description `Direct wavelet transformation`;s := LinearAlgebra:-Dimensions(V); if modp(s, 2^iters) <> 0 then error "the length of V is not divisible by enough powers of 2" end if; temp1 := Vector(V); temp2 := Vector(V); for i to iters do DiscreteWaveletTransform(s/2^(i-1), temp1, w2, w1, storagetype = singlearray, temp2); ArrayTools:-Copy(temp2, temp1) end do; return temp1 end proc; # direct Discrete Wavelet transformation (VectorDWT)
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
InverseVectorDWT := proc (V, iters, w1, w2) local s, i, temp1, temp2;description `Inverse Wavelet Transformation`; s := LinearAlgebra:-Dimensions(V); if modp(s, 2^iters) <> 0 then error "the length of V is not divisible by enough powers of 2" end if; temp1 := Vector(V); temp2 := Vector(V); for i from iters by -1 to 1 do InverseDiscreteWaveletTransform(s/2^(i-1), temp1, w2, w1, storagetype = singlearray, temp2); ArrayTools:-Copy(temp2, temp1) end do; return temp1 end proc;# inverse Discrete Wavelet transformation (InverseVectorDWT)
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
The input parameters of both procedures (such as V, iters, w1, w2 etc.) will be explained below.
<Text-field style="Heading 2" layout="Heading 2">4. Wavelet analysis, de-noising , compressin and reconstruction of sygnals</Text-field>
Let us determine the number of scale levels for beginning. This number (SDlevels) does not exceed a maximal power of two, which is the divisor of counts number (80). Because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiRRIjNGJ0YyLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXRjI= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiRRIjRGJ0YyLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXRjI= both are the divisors of counts number (80) we can choose SDlevels=3 or SDlevels=4. If we select SDlevels=4, the highest detail scale, as well as the scale of the approximation would be relatively narrow (only 5 counts, because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIzgwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiUtSSVtc3VwR0YkNiUtRi82JFEiMkYnRjItRiM2JS1GLzYkUSI0RidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRkJGRS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTy8lKWJldmVsbGVkR1EmZmFsc2VGJ0Yy =5). So it looks better to choose one level less
SDlevels:=3;
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlTRGxldmVsc0dGKCIiJDcjRi4=
Now we can choose the wavelet family and the lenght (10) of both digital filters ( SDw1,SDw2) [1]:
SDw1,SDw2:=WaveletCoefficients(Symlet,10);
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
WaveletPlot(SDw1,SDw2,output=both);# wawelet digital filters
-%%PLOTG6'-%'CURVESG6%7d\l7$$""!!""$"0myNT/c_"!#A7$$"%DJ!"&$".ehKSwk"!#?7$$"$D'!"%$!0l9Qw4lO&!#B7$$"%v$*!"&$"0\$*='y)3H"!#@7$$"$D"!"$$"/@E1w:[P!#?7$$"&Dc"!"&$"0$H`jve#o%!#@7$$"%v=!"%$"0'*H!Rx4@e!#@7$$"&v=#!"&$"0/DJT)oXQ!#@7$$"#D!"#$"/3n!>%)*=Y!#@7$$"&D"G!"&$"0(GV"pds7"!#?7$$"%DJ!"%$"0-!*f1\@L$!#?7$$"&vV$!"&$"0B,(*Q'R!G'!#?7$$"$v$!"$$"/:j0/D9**!#>7$$"&D1%!"&$"/MWo&[1>"!#=7$$"%vV!"%$"0UgmKDs?"!#>7$$"&vo%!"&$"0"[Y\m4@8!#>7$$""&!""$"040`(zp*["!#>7$$"&DJ&!"&$"0Yso2V@O"!#>7$$"%Dc!"%$"0F6a.MJ7"!#>7$$"&v$f!"&$"0o/Km'3vq!#?7$$"$D'!"$$"0tu=Na[s#!#?7$$"&Dc'!"&$"06d+s!G%3"!#>7$$"%vo!"%$"0wJ5%y^2J!#>7$$"&v=(!"&$"/#HqI.;s&!#=7$$"#v!"#$"/v=#>Eh(*)!#=7$$"&D"y!"&$"0%z=CX8m7!#=7$$"%D")!"%$"0KBb;[3l"!#=7$$"&vV)!"&$"0C:2ZsG5#!#=7$$"$v)!"$$"0ZvoF<me#!#=7$$"&D1*!"&$"0px]],&>H!#=7$$"%v$*!"%$"0(>u8Y@AJ!#=7$$"&vo*!"&$"0AnAikR>$!#=7$$"#5!""$"04mfkD0:$!#=7$$"'DJ5!"&$"0^],C*pJK!#=7$$"&D1"!"%$"0dBy!f&3S$!#=7$$"'v$4"!"&$"0'[=J:V2O!#=7$$"%D6!"$$"0#Q$eWvH%Q!#=7$$"'Dc6!"&$"08L9&*3T!Q!#=7$$"&v="!"%$"0FSzF_s\$!#=7$$"'v=7!"&$"0nfX[)*)*=$!#=7$$"$D"!"#$"0#)zOP5d'G!#=7$$"'D"G"!"&$"0"RiLN>rB!#=7$$"&DJ"!"%$"0m^oC1!p=!#=7$$"'vV8!"&$"0Y#o!=GgE"!#=7$$"%v8!"$$"0_'=)R@(es!#>7$$"'D19!"&$"0"pE![([c7!#=7$$"&vV"!"%$"00CXt*[GG!#=7$$"'vo9!"&$"0<)o`/&H8&!#=7$$"#:!""$"0)fbXU$o=)!#=7$$"'DJ:!"&$"/"[ZX*z_6!#;7$$"&Dc"!"%$"0/e/mt2^"!#<7$$"'v$f"!"&$"0*Qx-)Q%>>!#<7$$"%D;!"$$"0%z$oZ"GnB!#<7$$"'Dc;!"&$"0B^U99u#G!#<7$$"&vo"!"%$"0;JXH:<I$!#<7$$"'v=<!"&$"0fuNL)\rP!#<7$$"$v"!"#$"0$>TVpWPU!#<7$$"'D"y"!"&$"0(Q+TLvdZ!#<7$$"&D"=!"%$"01$3V!)Q6`!#<7$$"'vV=!"&$"0w]*QWD%)e!#<7$$"%v=!"$$"0<Y[@*)4Y'!#<7$$"'D1>!"&$"0F1H$*p.#p!#<7$$"&v$>!"%$"/%fiC1oD(!#;7$$"'vo>!"&$"/"Q>j$[Sv!#;7$$"#?!""$"0bhVFN&ex!#<7$$"'DJ?!"&$"0YW_')=`(y!#<7$$"&D1#!"%$"0"\F%p;B#z!#<7$$"'v$4#!"&$"0%[H]b;sy!#<7$$"%D@!"$$"0R*R'*o9ax!#<7$$"'Dc@!"&$"0j#>"z2mz(!#<7$$"&v=#!"%$"/"z9Vz[*z!#;7$$"'v=A!"&$"0T#)eR0)H#)!#<7$$"$D#!"#$"0#zd6nF7&)!#<7$$"'D"G#!"&$"0v-g[.E$))!#<7$$"&DJ#!"%$"0BU6x_x8*!#<7$$"'vVB!"&$"0b"zsIT.&*!#<7$$"%vB!"$$"0:q*e6So)*!#<7$$"'D1C!"&$"0l&3`I#p()*!#<7$$"&vV#!"%$"0fTO0-Jb*!#<7$$"'voC!"&$"0dM%f[hw*)!#<7$$"#D!""$"0Arp+_t:)!#<7$$"'DJD!"&$"0=a<xStN(!#<7$$"&Dc#!"%$"0EQX`BDd'!#<7$$"'v$f#!"&$"/J4z'e7r&!#;7$$"%DE!"$$"0ajmL>H![!#<7$$"'DcE!"&$"0M0=RKVu$!#<7$$"&vo#!"%$"0#3&Q#>;TD!#<7$$"'v=F!"&$"0xQL/@')R"!#<7$$"$v#!"#$"/Za7=-GJ!#<7$$"'D"y#!"&$!0Ux?a)\h$*!#=7$$"&D"G!"%$!/Et2A*p>#!#;7$$"'vVG!"&$!0$*)pf*3:[$!#<7$$"%vG!"$$!0H8_l'z]Y!#<7$$"'D1H!"&$!0pXs"oqG[!#<7$$"&v$H!"%$!0rMk_C,,%!#<7$$"'voH!"&$!04$e*)oLHD!#<7$$"#I!""$!0%H(Qid9Q$!#=7$$"'DJI!"&$"0K5\]([#R#!#<7$$"&D1$!"%$"0ZIAaK9d&!#<7$$"'v$4$!"&$"0t"Rkw@7%*!#<7$$"%DJ!"$$"0%p2^AVz8!#;7$$"'DcJ!"&$"0%ps/b51=!#;7$$"&v=$!"%$"097)>%))HA#!#;7$$"'v=K!"&$"0N"GG(=9l#!#;7$$"$D$!"#$"0rjZ>y))3$!#;7$$"'D"G$!"&$"0n^p4j$eN!#;7$$"&DJ$!"%$".-[(34kS!#97$$"'vVL!"&$"0*>!oMw[e%!#;7$$"%vL!"$$"0$=x3q-G^!#;7$$"'D1M!"&$"0>Y&*f&RHd!#;7$$"&vV$!"%$"0=*f1i8$Q'!#;7$$"'voM!"&$"0TZ>ECr3(!#;7$$"#N!""$"0jzd0Xl$y!#;7$$"'DJN!"&$"0C**o)HG$e)!#;7$$"&Dc$!"%$"/8/W(>9L*!#:7$$"'v$f$!"&$"0e")e&)***35!#:7$$"%DO!"$$"0$eidbt&3"!#:7$$"'DcO!"&$"/3-%yM#o6!#97$$"&vo$!"%$"/ed&f%=c7!#97$$"'v=P!"&$"0p*p!>IWM"!#:7$$"$v$!"#$"/=7.C-L9!#97$$"'D"y$!"&$"0m,>]#4D:!#:7$$"&D"Q!"%$"08F2d3th"!#:7$$"'vVQ!"&$"0%pJy=s5<!#:7$$"%vQ!"$$"0pAh#e2-=!#:7$$"'D1R!"&$"0xR5!oFs=!#:7$$"&v$R!"%$"/^Er_K@>!#97$$"'voR!"&$"0*y&*o*yb&>!#:7$$"#S!""$"00+4SST(>!#:7$$"'DJS!"&$"0x@9GyE)>!#:7$$"&D1%!"%$"/W&RnjC)>!#97$$"'v$4%!"&$"0hl!e!>(o>!#:7$$"%DT!"$$"/.dKubV>!#97$$"'DcT!"&$"0(4:yw^;>!#:7$$"&v=%!"%$"0-(zcjB()=!#:7$$"'v=U!"&$"0;$pM]%R&=!#:7$$"$D%!"#$"0%\cT-)o"=!#:7$$"'D"G%!"&$"0_5_wP/x"!#:7$$"&DJ%!"%$"/1'zuR^r"!#97$$"'vVV!"&$"0Q*=`Z"Rl"!#:7$$"%vV!"$$"0A8&*)ew'e"!#:7$$"'D1W!"&$"0.Kcz`c^"!#:7$$"&vV%!"%$"0[H3b47W"!#:7$$"'voW!"&$"0`&o$Hn:O"!#:7$$"#X!""$"0k(>Gr_x7!#:7$$"'DJX!"&$"0P1<#zk#>"!#:7$$"&Dc%!"%$"0)3C&Q%316!#:7$$"'v$f%!"&$"0mt3,.$=5!#:7$$"%DY!"$$"0BqC,y$)G*!#;7$$"'DcY!"&$"0)yIQ*QYH)!#;7$$"&vo%!"%$"0d.w$zo1s!#;7$$"'v=Z!"&$"0E<"[%H^3'!#;7$$"$v%!"#$"0>AOFv#H\!#;7$$"'D"y%!"&$"0ul]*pADP!#;7$$"&D"[!"%$"0>r!HQ-2D!#;7$$"'vV[!"&$"0C0P=S_D"!#;7$$"%v[!"$$"0(=m.-@f\!#>7$$"'D1\!"&$!0*yE6`L\5!#;7$$"&v$\!"%$!0i!*\;)H3>!#;7$$"'vo\!"&$!08B<"e]JE!#;7$$"#]!""$!0\I/$**e5K!#;7$$"'DJ]!"&$!0n@&e,G8P!#;7$$"&D1&!"%$!0$*\W)G%)[T!#;7$$"'v$4&!"&$!/t#ooYxY%!#:7$$"%D^!"$$!0XWIs/))o%!#;7$$"'Dc^!"&$!0-bqOw`)[!#;7$$"&v=&!"%$!0%=I#4IP0&!#;7$$"'v=_!"&$!0mDT.=%*=&!#;7$$"$D&!"#$!0F7^o)>$H&!#;7$$"'D"G&!"&$!0rn2ihfI&!#;7$$"&DJ&!"%$!0:WkYO%R_!#;7$$"'vV`!"&$!0\[!R(G]6&!#;7$$"%v`!"$$!0_AO)G(*R\!#;7$$"'D1a!"&$!0>he@W)yZ!#;7$$"&vV&!"%$!0B*R"=9[j%!#;7$$"'voa!"&$!0sN">$o$yW!#;7$$"#b!""$!0v"\"GfhJ%!#;7$$"'DJb!"&$!0&4"e*)*\^T!#;7$$"&Dc&!"%$!0,,[#4/wR!#;7$$"'v$f&!"&$!0y6oB<`!Q!#;7$$"%Dc!"$$!03*y([k2j$!#;7$$"'Dcc!"&$!0-Xrju=Q$!#;7$$"&vo&!"%$!0Hl%RiBiI!#;7$$"'v=d!"&$!0CJKJ<&3F!#;7$$"$v&!"#$!0;PSqj)>B!#;7$$"'D"y&!"&$!0pbu-'[0>!#;7$$"&D"e!"%$!0z^a%4k"["!#;7$$"'vVe!"&$!0,&p$yL4."!#;7$$"%ve!"$$!0eY.LEgr&!#<7$$"'D1f!"&$!0))>NT[X(>!#<7$$"&v$f!"%$"0s**eqmrB*!#=7$$"'vof!"&$"04G5_vJC$!#<7$$"#g!""$"08poTU([\!#<7$$"'DJg!"&$"0@U7"Hc7k!#<7$$"&D1'!"%$".P0nMim(!#:7$$"'v$4'!"&$"0m8w&[lm%)!#<7$$"%Dh!"$$"0^_Jq2a*))!#<7$$"'Dch!"&$"0$)osINh@*!#<7$$"&v='!"%$"0>/jiz>T*!#<7$$"'v=i!"&$"088.6$p6&*!#<7$$"$D'!"#$"0=ZsV.T^*!#<7$$"'D"G'!"&$"07h%*4'zK"*!#<7$$"&DJ'!"%$"0*=bV(>oW)!#<7$$"'vVj!"&$"0x2t?)fIv!#<7$$"%vj!"$$"0rn"f'GVW'!#<7$$"'D1k!"&$"0Zl)z<**[c!#<7$$"&vV'!"%$"0x+fH32:&!#<7$$"'vok!"&$"0-k<rL7x%!#<7$$"#l!""$"0)f)f`!\RX!#<7$$"'DJl!"&$"0o&)o4]%pV!#<7$$"&Dc'!"%$"0ZceZY5A%!#<7$$"'v$f'!"&$"0n)="**)[0U!#<7$$"%Dm!"$$"034`f%**oU!#<7$$"'Dcm!"&$"0mIplHK5%!#<7$$"&vo'!"%$"0[6OA$y@P!#<7$$"'v=n!"&$"0<<4<>7B$!#<7$$"$v'!"#$"0BqF=Uni#!#<7$$"'D"y'!"&$"07#>#oD=-#!#<7$$"&D"o!"%$"0V'*fAn>W"!#<7$$"'vVo!"&$"0,r#\T]#4)!#=7$$"%vo!"$$"0RYPqw:h"!#=7$$"'D1p!"&$!0iZ)e@L)[$!#=7$$"&v$p!"%$!0<cxWE-D(!#=7$$"'vop!"&$!0knqzX6+"!#<7$$"#q!""$!0,P=LPS<"!#<7$$"'DJq!"&$!03/">6bA8!#<7$$"&D1(!"%$!0_H(H_%yW"!#<7$$"'v$4(!"&$!0bpYx]"3:!#<7$$"%Dr!"$$!/tl<BD9:!#;7$$"'Dcr!"&$!0tj*ePN!["!#<7$$"&v=(!"%$!0U0F5<XS"!#<7$$"'v=s!"&$!0$z\t%[oI"!#<7$$"$D(!"#$!04Pr7Bi="!#<7$$"'D"G(!"&$!0A!>Gi]")**!#=7$$"&DJ(!"%$!0)4Ijam=w!#=7$$"'vVt!"&$!/Np8SA@[!#<7$$"%vt!"$$!0m=Z))\'e<!#=7$$"'D1u!"&$"0*4G$Q\GJ%!#>7$$"&vV(!"%$"/,AB+K\<!#<7$$"'vou!"&$"0HV)o2o*e#!#=7$$"#v!""$"0Ny3&)=&)*G!#=7$$"'DJv!"&$"0$pWKbo1I!#=7$$"&Dc(!"%$"09$f(G)f()H!#=7$$"'v$f(!"&$"0<Teg!GiD!#=7$$"%Dw!"$$"0&HOGGy]=!#=7$$"'Dcw!"&$"0J^w6NyR"!#=7$$"&vo(!"%$"0CUz7i)z6!#=7$$"'v=x!"&$"0K#y"\u**3"!#=7$$"$v(!"#$"0d![#>ne8"!#=7$$"'D"y(!"&$"0-cj*3G****!#>7$$"&D"y!"%$"0-vI)4:cq!#>7$$"'vVy!"&$"0AU!fB.;R!#>7$$"%vy!"$$"0.=J)\&\`&!#?7$$"'D1z!"&$!0#yYUJL'y"!#>7$$"&v$z!"%$!0hX!)pQZ/$!#>7$$"'voz!"&$!0Jdi/T;(Q!#>7$$"#!)!""$!03S5n!zgT!#>7$$"'DJ!)!"&$!0/&[.BeLR!#>7$$"&D1)!"%$!0ew*)e:iM$!#>7$$"'v$4)!"&$!0:J'="=.:#!#>7$$"%D")!"$$!0:0s&H)yH&!#?7$$"'Dc")!"&$"06*=B9hnV!#?7$$"&v=)!"%$"08*o&=\q#y!#?7$$"'v=#)!"&$"0W-(odVg")!#?7$$"$D)!"#$"0nm3t%z,^!#?7$$"'D"G)!"&$"0@4m/S%3M!#?7$$"&DJ)!"%$"07eG)[nPK!#?7$$"'vV$)!"&$"0$z(e(p!=(>!#?7$$"%v$)!"$$"0_R(zw*z)>!#@7$$"'D1%)!"&$!0OHn6Rm'z!#@7$$"&vV)!"%$!0J#=%*ohV6!#?7$$"'vo%)!"&$!0dK))y*fh"*!#@7$$"#&)!""$!0=;+g$)4]"!#@7$$"'DJ&)!"&$"0s82;x!>>!#@7$$"&Dc)!"%$"0Pd!*z,uL"!#@7$$"'v$f)!"&$"0l75p#*o8*!#A7$$"%D')!"$$"0*='f&QCTd!#B7$$"'Dc')!"&$!0W(QwC!H'G!#A7$$"&vo)!"%$!0H7f"R_vI!#B7$$"'v=()!"&$"0Jg6$)Gx%G!#B-%'LEGENDG6#-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q/Father~Wavelet6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%'CURVESG6%7d\l7$$""!!""$"0WB#>$p04"!#A7$$"%DJ!"&$"0FQ<(f!y<"!#A7$$"$D'!"%$!0V(pgy@OQ!#B7$$"%v$*!"&$"0QBFwNyA*!#A7$$"$D"!"$$"0@(ej$[$zE!#@7$$"&Dc"!"&$"/nh3,KZL!#?7$$"%v=!"%$"0CtURx6;%!#@7$$"&v=#!"&$"0fwdon!\F!#@7$$"#D!"#$"0anDh`=I$!#A7$$"&D"G!"&$"0^Ux8N"e!)!#@7$$"%DJ!"%$"0[%f6r'>Q#!#?7$$"&vV$!"&$"0%>UEV]*[%!#?7$$"$v$!"$$"0#)eCWVr3(!#?7$$"&D1%!"&$"0**oT3"G6&)!#?7$$"%vV!"%$"0KCG1z(H')!#?7$$"&vo%!"&$"0i'R*\"yV%*!#?7$$""&!""$"0<[N"=!\1"!#>7$$"&DJ&!"&$"0e"Rl%*>P(*!#?7$$"%Dc!"%$"/h#eUd'G!)!#>7$$"&v$f!"&$"0C%\#)Red]!#?7$$"$D'!"$$".hh1Yy%>!#=7$$"&Dc'!"&$"0LF?z;4v(!#?7$$"%vo!"%$"0M&)\!3R@A!#>7$$"&v=(!"&$"0tKiQa+4%!#>7$$"#v!"#$"0O(=!)3`;k!#>7$$"&D"y!"&$"0cJx)z)30*!#>7$$"%D")!"%$"0N$zw!*4!="!#=7$$"&vV)!"&$"0ypf)fA.:!#=7$$"$v)!"$$"0Z@#3"G!\=!#=7$$"&D1*!"&$"0%)yeV))p3#!#=7$$"%v$*!"%$"0y'H1n*=B#!#=7$$"&vo*!"&$"0e7ox'=$G#!#=7$$"#5!""$"0^#)QA78D#!#=7$$"'DJ5!"&$"0v(>**GF4B!#=7$$"&D1"!"%$"/a7-6PJC!#<7$$"'v$4"!"&$"0>\B&>zrD!#=7$$"%D6!"$$"/w!H$>#ps#!#<7$$"'Dc6!"&$"0&*)3:45%p#!#=7$$"&v="!"%$"0#))z'\3'oC!#=7$$"'v=7!"&$"/)=s#zafA!#<7$$"$D"!"#$"0uRx0Yg/#!#=7$$"'D"G"!"&$"0u&>$*HEM;!#=7$$"&DJ"!"%$"0PF$p6Tc6!#=7$$"'vV8!"&$"//r-;Nkc!#=7$$"%v8!"$$!0Nv4&4Tf:!#?7$$"'D19!"&$"0Ut#RF6jD!#>7$$"&vV"!"%$"0XUtC66P"!#=7$$"'vo9!"&$"0=#*46`q&H!#=7$$"#:!""$"/&Q"o0@\]!#<7$$"'DJ:!"&$"0On)[WQ1v!#=7$$"&Dc"!"%$"0xJwA>%>5!#<7$$"'v$f"!"&$"0P4XbdRL"!#<7$$"%D;!"$$"0"f;_uax;!#<7$$"'Dc;!"&$"0))=]]1F'>!#<7$$"&vo"!"%$"0r/_q%o#>#!#<7$$"'v=<!"&$"0(4^*Q!e(Q#!#<7$$"$v"!"#$"08pb#*3_a#!#<7$$"'D"y"!"&$"0P/g(eZ=F!#<7$$"&D"=!"%$"07>fOQo!H!#<7$$"'vV=!"&$"0POW=hE2$!#<7$$"%v=!"$$"0b$H'p[TA$!#<7$$"'D1>!"&$"/zzPc2tL!#;7$$"&v$>!"%$"06Zw/#H/N!#<7$$"'vo>!"&$"0V:)elRoO!#<7$$"#?!""$"/lc4]jZQ!#;7$$"'DJ?!"&$"0zlm*>N()Q!#<7$$"&D1#!"%$"0Rk6eI)HQ!#<7$$"'v$4#!"&$"0TLT&>:#o$!#<7$$"%D@!"$$"0@yLhe*pM!#<7$$"'Dc@!"&$"0<"*)*yU4_$!#<7$$"&v=#!"%$"0/E1@6x#Q!#<7$$"'v=A!"&$"0ul5+A?;%!#<7$$"$D#!"#$"0Lt_o!))RX!#<7$$"'D"G#!"&$"0cnP-P<.&!#<7$$"&DJ#!"%$"0btp@4I^&!#<7$$"'vVB!"&$"0Ni8B9$*3'!#<7$$"%vB!"$$"0:?nS5*Gm!#<7$$"'D1C!"&$"0\%GNi3Uj!#<7$$"&vV#!"%$"0X')f&Qci_!#<7$$"'voC!"&$"0d*ycU?/O!#<7$$"#D!""$"0['zLwRm8!#<7$$"'DJD!"&$!0iK<q?B+"!#<7$$"&Dc#!"%$!0rKA()f\[$!#<7$$"'v$f#!"&$!0UmMfT%*G'!#<7$$"%DE!"$$!0RU%oK6Q$*!#<7$$"'DcE!"&$!0Qf6qP.E"!#;7$$"&vo#!"%$!0jp7F4!4;!#;7$$"'v=F!"&$!0"y%ycXH&>!#;7$$"$v#!"#$!0==-DlHH#!#;7$$"'D"y#!"&$!0<C[(QVvE!#;7$$"&D"G!"%$!0PaAQxs2$!#;7$$"'vVG!"&$!0[T*e))\$\$!#;7$$"%vG!"$$!0oru'4m/R!#;7$$"'D1H!"&$!0H!ywW\wT!#;7$$"&v$H!"%$!0:,'*RKjI%!#;7$$"'voH!"&$!04&RM4)eN%!#;7$$"#I!""$!0)*e"z13:V!#;7$$"'DJI!"&$!0s[)[(=c=%!#;7$$"&D1$!"%$!0_iD(4&)*)R!#;7$$"'v$4$!"&$!0E9r$pU$p$!#;7$$"%DJ!"$$!0335#y5@L!#;7$$"'DcJ!"&$!/kr2TIOI!#:7$$"&v=$!"%$!0$HFBQ(H$G!#;7$$"'v=K!"&$!0R&3f`jXE!#;7$$"$D$!"#$!0FSfFJ*yC!#;7$$"'D"G$!"&$!/j(R,]LG#!#:7$$"&DJ$!"%$!0^]]fir.#!#;7$$"'vVL!"&$!/'e<[7')z"!#:7$$"%vL!"$$!04h.)3'f`"!#;7$$"'D1M!"&$!0*zz_88+6!#;7$$"&vV$!"%$!/_"\_!p*4&!#;7$$"'voM!"&$"0TR*z!Q<T#!#<7$$"#N!""$"02@w&RyP6!#;7$$"'DJN!"&$"0'ywpzPp>!#;7$$"&Dc$!"%$"/#[y#zWpF!#:7$$"'v$f$!"&$"09'fd(*>vN!#;7$$"%DO!"$$"/dj*34jR%!#:7$$"'DcO!"&$"0F%RX,p:b!#;7$$"&vo$!"%$"./ml*GAp!#97$$"'v=P!"&$"0w_1Q<`Q)!#;7$$"$v$!"#$"0XSJ-zT"**!#;7$$"'D"y$!"&$"0w=AQT*f6!#:7$$"&D"Q!"%$"0.m'4TSI8!#:7$$"'vVQ!"&$"/Q#*e127:!#97$$"%vQ!"$$"/#eb,20p"!#97$$"'D1R!"&$"0EM$[;g#y"!#:7$$"&v$R!"%$"0Ni:ej7z"!#:7$$"'voR!"&$"0.r'3y_O<!#:7$$"#S!""$"00^^![#zh"!#:7$$"'DJS!"&$"0.'yG+a%["!#:7$$"&D1%!"%$"0#H5wkyN8!#:7$$"'v$4%!"&$"0J.cG64:"!#:7$$"%DT!"$$"0XE)=Rbb$*!#;7$$"'DcT!"&$"0h,c;iSz'!#;7$$"&v=%!"%$"/f01#[(GQ!#:7$$"'v=U!"&$"/&*G]PQ(\(!#;7$$"$D%!"#$!04nT02*\C!#;7$$"'D"G%!"&$!07TPumb5'!#;7$$"&DJ%!"%$!0*='RB?<***!#;7$$"'vVV!"&$!02q_+[XT"!#:7$$"%vV!"$$!0mRr!)H]$=!#:7$$"'D1W!"&$!0Z_"\]eF@!#:7$$"&vV%!"%$!0d7#=8D%H#!#:7$$"'voW!"&$!0<G;g]TP#!#:7$$"#X!""$!0Y-j!p\jB!#:7$$"'DJX!"&$!0E))yI/*>B!#:7$$"&Dc%!"%$!0(R.l1OZA!#:7$$"'v$f%!"&$!0N*G3Y#G6#!#:7$$"%DY!"$$!0<(=Ec-G>!#:7$$"'DcY!"&$!0>N[o1'=<!#:7$$"&vo%!"%$!/"Rk[%R$["!#97$$"'v=Z!"&$!0xOcrC(Q7!#:7$$"$v%!"#$!0;1/vsd%)*!#;7$$"'D"y%!"&$!0>Ge^[Mu'!#;7$$"&D"[!"%$!0N*Ga9SuK!#;7$$"'vV[!"&$"0h.)[?uo\!#<7$$"%v[!"$$"0zyG%*z3S%!#;7$$"'D1\!"&$"0Jj1'4R4t!#;7$$"&v$\!"%$"048t[fnA*!#;7$$"'vo\!"&$"/^!psh?0"!#97$$"#]!""$"0:75GZW6"!#:7$$"'DJ]!"&$"0MU*[P**[6!#:7$$"&D1&!"%$"0&=,QG?h6!#:7$$"'v$4&!"&$"/vDZsMB6!#97$$"%D^!"$$"0V3/1ek/"!#:7$$"'Dc^!"&$"0R!z9O*Rq*!#;7$$"&v=&!"%$"0%G7<'yN$*)!#;7$$"'v=_!"&$"0)ff%*)[8;)!#;7$$"$D&!"#$"0>p%G6."R(!#;7$$"'D"G&!"&$"/'>)*>r*ei!#:7$$"&DJ&!"%$"0'[R&[,w&[!#;7$$"'vV`!"&$"/j)3F\*)G$!#:7$$"%v`!"$$"0M>$oSE@;!#;7$$"'D1a!"&$"09xTLRn'Q!#<7$$"&vV&!"%$!0"3p\*z27%!#<7$$"'voa!"&$!0KdS^:Nl*!#<7$$"#b!""$!0LD?f#QY7!#;7$$"'DJb!"&$!/$>s7-]S"!#:7$$"&Dc&!"%$!0<b&f1)\Z"!#;7$$"'v$f&!"&$!0wg]!ocG8!#;7$$"%Dc!"$$!0mW.*H8A5!#;7$$"'Dcc!"&$!0EcQT))3.)!#<7$$"&vo&!"%$!0cs&Gpn2m!#<7$$"'v=d!"&$!0VL.c5sg&!#<7$$"$v&!"#$!/O(Q'G!=1&!#;7$$"'D"y&!"&$!0^<;pzNI$!#<7$$"&D"e!"%$!0"=!RKUPv&!#=7$$"'vVe!"&$"0KfDm4Z]#!#<7$$"%ve!"$$"0)eY'z:$=e!#<7$$"'D1f!"&$"045#y'))R)z!#<7$$"&v$f!"%$"0LZ3)fO%)*)!#<7$$"'vof!"&$"0y9N&yNm$*!#<7$$"#g!""$"0yOZ]dR0*!#<7$$"'DJg!"&$"0Jl%pF$pP)!#<7$$"&D1'!"%$"/8A_35Qu!#;7$$"'v$4'!"&$"0t"HQU`Af!#<7$$"%Dh!"$$"075s['e))R!#<7$$"'Dch!"&$"/7:r-:[B!#;7$$"&v='!"%$"0@N.F+cv*!#=7$$"'v=i!"&$!0T7Oug4B#!#=7$$"$D'!"#$!08fl(**3N7!#<7$$"'D"G'!"&$!0w)=(R&oRD!#<7$$"&DJ'!"%$!0"[HGe5eS!#<7$$"'vVj!"&$!0JV<!fU=c!#<7$$"%vj!"$$!0N11`5o<(!#<7$$"'D1k!"&$!/Xp6%f')G)!#;7$$"&vV'!"%$!/a#RWz@&*)!#;7$$"'vok!"&$!0%>&QIKvK*!#<7$$"#l!""$!/ZH%Qy_R*!#;7$$"'DJl!"&$!013,+Q5I*!#<7$$"&Dc'!"%$!0%e`Y%y#o!*!#<7$$"'v$f'!"&$!06"*HA_Tf)!#<7$$"%Dm!"$$!0<)oIv(\#z!#<7$$"'Dcm!"&$!/l>9iE7s!#;7$$"&vo'!"%$!09Q0B/4X'!#<7$$"'v=n!"&$!08N(>;Lqc!#<7$$"$v'!"#$!0K)\#[&*G([!#<7$$"'D"y'!"&$!/;fg%fK)Q!#;7$$"&D"o!"%$!/XVjVfhF!#;7$$"'vVo!"&$!0Y_XD._a"!#<7$$"%vo!"$$!0`7'HuPQG!#=7$$"'D1p!"&$"0G7nc9Ww'!#=7$$"&v$p!"%$"0&>xSeXN8!#<7$$"'vop!"&$"0e[Tpj*3=!#<7$$"#q!""$"0$)*)*yxK"3#!#<7$$"'DJq!"&$"0G8LS9^E#!#<7$$"&D1(!"%$"0HIF^A%yB!#<7$$"'v$4(!"&$"0>v%*G=mL#!#<7$$"%Dr!"$$"02rTV*=u@!#<7$$"'Dcr!"&$"0c]Q[)zC?!#<7$$"&v=(!"%$"0r_BO8A)=!#<7$$"'v=s!"&$"0H$>%*o1U<!#<7$$"$D(!"#$"/NX$p"f0;!#;7$$"'D"G(!"&$"0m23fg.O"!#<7$$"&DJ(!"%$"0"=APGiJ5!#<7$$"'vVt!"&$"0BV9W<k`'!#=7$$"%vt!"$$"0\SbT8#RC!#=7$$"'D1u!"&$!0#[#o')*z#>&!#>7$$"&vV(!"%$!0$3L6X[EB!#=7$$"'vou!"&$!0$*[M.ng_$!#=7$$"#v!""$!00$>t8#*QS!#=7$$"'DJv!"&$!0,43v<jA%!#=7$$"&Dc(!"%$!0(\Gi)zM>%!#=7$$"'v$f(!"&$!0^(\.,.%f$!#=7$$"%Dw!"$$!0Lc=mx'*e#!#=7$$"'Dcw!"&$!/3du,U_>!#<7$$"&vo(!"%$!0;J9B#>];!#=7$$"'v=x!"&$!02>$QF2D:!#=7$$"$v(!"#$!0yN*)*=(*)e"!#=7$$"'D"y(!"&$!0<,j"e!))R"!#=7$$"&D"y!"%$!0aqa&[*3()*!#>7$$"'vVy!"&$!/MLxF;ya!#=7$$"%vy!"$$!/='p,%)Gu(!#>7$$"'D1z!"&$"0'=F()G"*)\#!#>7$$"&v$z!"%$"0F"3)[/$fU!#>7$$"'voz!"&$"0*QB&[jgT&!#>7$$"#!)!""$"0O>%\nb?e!#>7$$"'DJ!)!"&$"/x92Nr-b!#=7$$"&D1)!"%$"0*f#RWU5o%!#>7$$"'v$4)!"&$"0mgV!Q43I!#>7$$"%D")!"$$"0*ewRCC6u!#?7$$"'Dc")!"&$!0oqdiz)4h!#?7$$"&v=)!"%$!0&QUH4$\4"!#>7$$"'v=#)!"&$!0x%H#fo:9"!#>7$$"$D)!"#$!0u*eiL$p8(!#?7$$"'D"G)!"&$!09-nj)3oZ!#?7$$"&DJ)!"%$!/`:aT?HX!#>7$$"'vV$)!"&$!/#>@Ut$eF!#>7$$"%v$)!"$$!0uo:qA5y#!#@7$$"'D1%)!"&$"0_%Qa#eW6"!#?7$$"&vV)!"%$"0uQj+8)*f"!#?7$$"'vo%)!"&$"0EM!p?i"G"!#?7$$"#&)!""$"0>EEeN(*4#!#@7$$"'DJ&)!"&$!0RtbM4Yo#!#@7$$"&Dc)!"%$!0U]B&***3(=!#@7$$"'v$f)!"&$!0ixsxl"y7!#@7$$"%D')!"$$!0hUR%GYJ!)!#B7$$"'Dc')!"&$"/(Q;jK\+%!#@7$$"&vo)!"%$"0/bn7qBI%!#B7$$"'v=()!"&$!0YM?71P)R!#B-%'LEGENDG6#-%)_TYPESETG6#-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q/Mother~Wavelet6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-&%&_AXISG6#"""6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%%ROOTG6'-%)BOUNDS_XG6#$"$q$!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%!e$!""-%.BOUNDS_HEIGHTG6#$"%+O!""-%)CHILDRENG6"
Let us transform all primary data by choosed wavelets:
SData_d := VectorDWT(Data_d, SDlevels, SDw1, SDw2):
SData_s := VectorDWT(Data_s, SDlevels, SDw1, SDw2):
SData_p := VectorDWT(Data_p, SDlevels, SDw1, SDw2):
Table 5.
plots[listplot](SData_s,thickness=3,color=red,gridlines=true,title=`fig.9 Wavelet transformation of Systola (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
plots[listplot](SData_d,thickness=3,color=red,gridlines=true,title=`fig.10 Wavelet transformation of Diastola (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
plots[listplot](SData_p,thickness=3,color=red,gridlines=true,title=`fig.11 Wavelet transformation of Pulse (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
It is noticeable from the graphs of table 5, that thewavelet coefficients (w-coeffs) differ significantly from zero only on a scale of approximation (first 10 counts). At the same time for all three scales of detail (11-20, 21-40, and 41-80 counts) the w-coeffs fluctuate around zero. We can then clear the images of signals from high-frequency noises, using the method of so-called "hard" threshold [3,4]. Let us find t first the noise levels at different scale counts, according to the recommendations of [3,4].
sigma1s:=(Statistics[Median](map(abs,(LinearAlgebra:-SubVector(SData_s,41..80))))-Statistics[Mean](LinearAlgebra:-SubVector(SData_s,41..80)))/0.6745;
sigma2s:=(Statistics[Median](map(abs,(LinearAlgebra:-SubVector(SData_s,21..40))))-Statistics[Mean](LinearAlgebra:-SubVector(SData_s,21..40)))/0.6745;
sigma3s:=(Statistics[Median](map(abs,(LinearAlgebra:-SubVector(SData_s,11..20))))-Statistics[Mean](LinearAlgebra:-SubVector(SData_s,11..20)))/0.6745;
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShzaWdtYTFzR0YoJCIwLiFvKmUnNDk1ISM4NyNdNDAyNDQ4MkNBRTk5Mzc5Qg==
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShzaWdtYTJzR0YoJCIwNmkjbzMmR1AqISM5NyNdNDAyMkJFRTY0RjFBRjEyMg==
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShzaWdtYTNzR0YoJCIwaj4pR2ljMj0hIzg3I100MDMyMTM1RTlBOEQ1N0VD
Now these values would be corrected by numbers of counts [3,4]
SDthresh1s:=evalf(sigma1s*sqrt(2*ln(40))):
SDthresh2s:=evalf(sigma2s*sqrt(2*ln(20))):
SDthresh3s:=evalf(sigma3s*sqrt(2*ln(10))):
T:=[SDthresh1s,SDthresh2s,SDthresh3s];
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJUR0YoNyUkIjBtOjFCI1xhRiEjOCQiMFVBNWdPVUgjRjEkIjBIJSlccnYqeVFGMTcjNyVdNDAzQjhCODAwNzNCQ0RCNV00MDM2RjEzRUU2MUFDNjVCXTQwNDM2NTE2QzMyNTJEQzM=
One can see that the thresholds (4,.4) are slightly differ for different scales. We are guaranteed to get zero w-coeffs on all three scales, choosing the highest of these thresholds
SDthresh_s:=max(T);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStTRHRocmVzaF9zR0YoJCIwSCUpXHJ2KnlRISM4NyNdNDA0MzY1MTZDMzI1MkRDMw==
Thresholds for diastolic pressure an pulse frequencies were obtained in the same way
SDthresh_d := 22.2790061630243;
SDthresh_p := %:
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStTRHRocmVzaF9kR0YoJCIwVi1qaCt6QSMhIzg3I0Yu
Previous cleaning from fluctuations with \302\253hard threshold\302\273 method uses the obtained thresholds SDRaf_1s:= Vector(map( z -> `if`(abs(z) <= SDthresh_s, 0, z),SData_s),datatype = float[8]):
SDRaf_1d:= Vector(map( z -> `if`(abs(z) <= SDthresh_d, 0, z),SData_d),datatype = float[8]):
SDRaf_1p:= Vector(map( z -> `if`(abs(z) <= SDthresh_p, 0, z),SData_p),datatype = float[8]):
About the same way we can de-noise w-coeffs on the approximation scale, using the statistical standard deviation as threshold and the mathematical expectation as a level for the w-coefficients on these scales (1-10 counts)
avs:=Statistics[Mean](LinearAlgebra:-SubVector(SDRaf_1s,1..10));
var_s:=sqrt(Statistics[Variance](LinearAlgebra:-SubVector(SDRaf_1s,1..10)));
avd:=Statistics[Mean](LinearAlgebra:-SubVector(SDRaf_1d,1..10));
var_d:=sqrt(Statistics[Variance](LinearAlgebra:-SubVector(SDRaf_1d,1..10)));
avp:=Statistics[Mean](LinearAlgebra:-SubVector(SDRaf_1p,1..10));
var_p:=sqrt(Statistics[Variance](LinearAlgebra:-SubVector(SDRaf_1p,1..10)));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRhdnNHRigkIjAiZksjMylweFYhIzc3I100MDdCNUM1MTIyNkZGMkMw
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ2YXJfc0dGKCQiMGRQXkcuLysjISM4NyNdNDAzNDAxMDg0QzA0QzRBMw==
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRhdmRHRigkIjBBKCpHXzZVTyMhIzc3I100MDZEOEQ3QTE0NURERkJF
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ2YXJfZEdGKCQiMHREIzM3JG9lKCEjOTcjXTQwMUU1OEVBNDdCRTY4MjA=
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRhdnBHRigkIjBJWi9qLSZHQiEjNzcjXTQwNkQxQjM1NUFEODQzOUQ=
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ2YXJfcEdGKCQiMDBNN0xfcl4pISM5NyNdNDAyMTA4QzgzMEJCNjY5Qg==
SDRaf_s:= Vector(map( z -> `if`(abs(z-avs) <= var_s, avs, z),SDRaf_1s),datatype = float[8]):
SDRaf_d:= Vector(map( z -> `if`(abs(z-avd) <= var_d, avd, z),SDRaf_1d),datatype = float[8]):
SDRaf_p:= Vector(map( z -> `if`(abs(z-avp) <= var_p, avp, z),SDRaf_1p),datatype = float[8]):
Table 6 shows the de-noised wavelet-images of sygnals for a comparicon with table 5
Table 6
plots[listplot](SDRaf_s,thickness=3,color=red,gridlines=true,title=`fig.12 Wavelet transformation of Systola (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
plots[listplot](SDRaf_d,thickness=3,color=red,gridlines=true,title=`fig.13 Wavelet transformation of Diastola (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
plots[listplot](SDRaf_p,thickness=3,color=red,gridlines=true,title=`fig.14 Wavelet transformation of Pulse (Symlet,10)`,font=[helvetica,14],titlefont=[Arial,14],view=[0..80,-50..500],tickmarks=[8,20],labeldirections=[horizontal,vertical],labels=[`counts`,`w-coeffs`]);
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
Wavelet-images now are describing literally a few different from zero coefficients, i.e. they are effectively compressed and de-niised. Now we can reconstruct all sygnals by inverse transformations
SDataNew_s := InverseVectorDWT(SDRaf_s, SDlevels, SDw1, SDw2):
SDataNew_d := InverseVectorDWT(SDRaf_d, SDlevels, SDw1, SDw2):
SDataNew_p := InverseVectorDWT(SDRaf_p, SDlevels, SDw1, SDw2):
Let us present the results graphically
g2s:=plots[listplot](SDataNew_s,thickness=5,color=[red],gridlines=true,title=`\320\240\320\270\321\201.15 Systolic pressure`,font=[helvetica,14],titlef ont=[Arial,14],view=[0..80,125..185],tickmarks=[15,16],labeldirections=[horizontal,vertical],labels=[`counts`,`pressure, mm Hg`]):
g2d:=plots[listplot](SDataNew_d,thickness=5,color=[red],gridlines=true,title=`\320\240\320\270\321\201.15 Diastolic pressure`,font=[helvetica,14],titlef ont=[Arial,14],view=[0..80,65..105],tickmarks=[15,16],labeldirections=[horizontal,vertical],labels=[`counts`,`pressure, mm Hg`]):
g2p:=plots[listplot](SDataNew_p,thickness=5,color=[red],gridlines=true,title=`\320\240\320\270\321\201.15 Pulse`,font=[helvetica,14],titlef ont=[Arial,14],view=[0..80,65..105],tickmarks=[15,16],labeldirections=[horizontal,vertical],labels=[`counts`,`pulse, bpm`]):
Table 7
All curves are characterized by minimum about count\342\211\210(46-52). This feature is associated with the course of treatment of the patient in a sanatorium (Truskvavec\342\200\262, Ukraine). The effect looks quite short-living.
Comparison with the data of table 2 shows the efficiency of cleaning of small-scale fluctuations with high frequencies. De-noised and compressed sygnals of Table 7 include only changes with relative long periods. Such long periodical cyclical nature usually presents itself from autocorrelation functions (Table 8).
Statistics:-AutoCorrelation(SDataNew_s):
acfs:=plots[listplot](%,gridlines=true,thickness=3,title=`fig17. Systolic pressure autocorrelation `, font=[helvetica,14],color=red):
Statistics:-AutoCorrelation(SDataNew_d):
acfd:=plots[listplot](%,gridlines=true,thickness=3,title=`fig.18 Diastolic pressure autocorrelation`, font=[helvetica,14],color=red):
Statistics:-AutoCorrelation(SDataNew_p):
acfp:=plots[listplot](%,gridlines=true,thickness=3,title=`fig.19 Pulse autocorrelation`, font=[helvetica,14],color=red):
Table 8
These autocorrelations are quite expressive, very similar and demonstrating the main period about 12 counts.
<Text-field style="Heading 2" layout="Heading 2">5. Some comparisons and conclusions</Text-field>
Let us recalculate some statistical characteristics of de-noised sygnals
Table 9
It is easy to see that de-noising of primary signals has no influence on the mathematical expectations, but markedly increases the accuracy of the results, comparing the characteristics of table 3 and table 4.
The correlation coefficient between systolic pressure and the pulse frequency, which was essentially masked by noises within primary signals, also increased noticeably (almost twice)
Statistics:-Correlation(SDataNew_p,SDataNew_s);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMkIjA2Jm9XPiZwJykpISM6NyNdM0ZFQzVGQ0U5OUI4Njc1Ng==
Correlation between reconstructed data also looks much more convincing visually, as is demonstrated in table 10
Table 10
Statistics:-ScatterPlot(Data_p,Data_s,title = "fig. 20 Systola-Pulse correlation (primary data)", legend = "Point data",view=[76..88,140..170],symbol=solidcircle,symbolsize=18,color=black,gridlines=true,font=[helvetica,16],tickmarks=[12,10],labeldirections=[horizontal,vertical],labels=[`pulse, bpm`,`pressure, mmHg`]);
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
Statistics:-ScatterPlot(SDataNew_p,SDataNew_s,title = "fig. 21 Systola-Pulse correlation (reconstructed data)", legend = "Point data",view=[76..88,140..170],symbol=solidcircle,symbolsize=18,color=red,gridlines=true,font=[helvetica,16],tickmarks=[12,10],labeldirections=[horizontal,vertical],labels=[`pulse, bpm`,`pressure, mmHg`]);
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
The readers may experiment with different lengths of digital filters in the expression (4.2) and make sure that the selected length=10 is optimal in certain sense. Someone could even change the family of wavelets, since Maple offers a choice of four such families: Daubechies, Symlet, Coiflet, and Battle-Lemarie [1].
The general conclusion that we do here, this is the statement that the Maple package Discrete Wavelet Transforms (DWT) is a perfect tool for analyzing, cleaning and compression of medical signals, if you know how and where to use it.
Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities.
<Text-field style="Heading 2" layout="Heading 2">6. References</Text-field>
[1] Wavelets Examples and Applications. \302\251 - 2012, Maplesoft
[2] Y. Jin, E. Angelini , and A. Laine. "Wavelets in Medical Image Processing: Denoising, Segmentation, and Registration," in Handbook of Biomedical Image Analysis Vol 1- Segmentation Models - Part a, Ed.: D. L. W. Jasjit Suri, Swamy Laximinarayan Kluwer Academic Plenum Publishers, pp. 305-358, (2005).
[3] D.Donoho, and I. Johnstone. Adapting to Unknown Smoothness via Wavelet Shrinkage., Journal of American Statistics Association, Vol. 90, No. 432, pp. 200-1224, (1995).
[4] R. Coifman and D. Donoho.Translation-invariant De-noising. in Wavelets and Statistics, Antoniadis, A. and Oppenheim, G., Eds. New York NY: Springer-Verlag, 1995.
JSFH 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 TTdSMApJN1JUQUJMRV9TQVZFLzQ0MjkyMDczNzhYKiUpYW55dGhpbmdHNiI2IltnbCcjJSEhISIrIiszRjk0MDIwMDM5NjRBMkJDM0Y5NTlCQjgxQzE2MkRFOEJGQzY3MTI2OUUxQ0Q0RjdCRjkxMDAyNDc1MzY5NjI4M0ZFNDQ5OEU0MDRDQzNDQ0JGRTcyNjI3RTI3RUJBNUEzRkM5ODVEQkJGQUFCNEQ1M0ZBNDA5Njc4MUQwNUI5NzNGOUUzQTVCODA3QjVFNURCRjlCRkQzMzJBOTA3RDMwRiU= TTdSMApJN1JUQUJMRV9TQVZFLzQ0MjkyMjA2MDJYKiUpYW55dGhpbmdHNiI2IltnbCcjJSEhISIrIiszRjlCRkQzMzJBOTA3RDMwM0Y5RTNBNUI4MDdCNUU1REJGQTQwOTY3ODFEMDVCOTczRkM5ODVEQkJGQUFCNEQ1M0ZFNzI2MjdFMjdFQkE1QTNGRTQ0OThFNDA0Q0MzQ0MzRjkxMDAyNDc1MzY5NjI4QkZDNjcxMjY5RTFDRDRGN0JGOTU5QkI4MUMxNjJERTgzRjk0MDIwMDM5NjRBMkJDRiU=