Initial import of schiltknecht.fr

16 files changed, 1173 insertions, 0 deletions

diff --git a/TIPE_2007/C/Sauv/TFD - C.tar.bz2 b/TIPE_2007/C/Sauv/TFD - C.tar.bz2
new file mode 100644
index 0000000..d8ca9fc
--- /dev/null
+++ b/TIPE_2007/C/Sauv/TFD - C.tar.bz2
diff --git a/TIPE_2007/C/Sauv/TFD - C.zip b/TIPE_2007/C/Sauv/TFD - C.zip
new file mode 100644
index 0000000..bb60997
--- /dev/null
+++ b/TIPE_2007/C/Sauv/TFD - C.zip
diff --git a/TIPE_2007/C/TFD - C.tar.bz2 b/TIPE_2007/C/TFD - C.tar.bz2
new file mode 100644
index 0000000..9b207b7
--- /dev/null
+++ b/TIPE_2007/C/TFD - C.tar.bz2
diff --git a/TIPE_2007/C/TFD - C.zip b/TIPE_2007/C/TFD - C.zip
new file mode 100644
index 0000000..1e4a38f
--- /dev/null
+++ b/TIPE_2007/C/TFD - C.zip
diff --git a/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf b/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf
new file mode 100644
index 0000000..d6d5f29
--- /dev/null
+++ b/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf
diff --git a/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf.sansTOC b/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf.sansTOC
new file mode 100644
index 0000000..d8a7a47
--- /dev/null
+++ b/TIPE_2007/Dossier/Dossier_TIPE_2007_TF.pdf.sansTOC
diff --git a/TIPE_2007/Dossier/Transparents_TIPE_2007_TF.pdf b/TIPE_2007/Dossier/Transparents_TIPE_2007_TF.pdf
new file mode 100644
index 0000000..25434b7
--- /dev/null
+++ b/TIPE_2007/Dossier/Transparents_TIPE_2007_TF.pdf
diff --git a/TIPE_2007/Maple/TFD - Old.mw b/TIPE_2007/Maple/TFD - Old.mw
new file mode 100644
index 0000000..950dcc2
--- /dev/null
+++ b/TIPE_2007/Maple/TFD - Old.mw
@@ -0,0 +1,496 @@
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+<Layout name="Fixed Width" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
+<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0"/>
+<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0"/>
+<Layout name="Ordered List 2" alignment="left" bullet="none" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0"/>
+<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
+<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
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+<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
+</Styles>
+<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
+<Task-table>
+    <Task-category name="&lt;default&gt;">
+    </Task-category>
+</Task-table>
+<Group labelreference="L3" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
+</Input>
+</Group>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure &quot;na\303\257ve&quot;</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure calcule les coefficients de Fourier par une m\303\251thode dite &quot;naive&quot;.</Font></Text-field>
+<Group labelreference="L4" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDSimple:=proc(x)
+
+local n,X:
+n:=nops(x):
+
+X:=[seq(sum(x[j]*exp(-2*I*(j-1)*(k-1)*Pi/n),j=1..n),k=1..n)];
+
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure prend en entr\303\251e une liste repr\303\251sentant les coefficients d'un polyn\303\264me dont on cherche \303\240 calculer les coefficients de Fourier.</Font></Text-field>
+<Group labelreference="L5" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDRecur:=proc(x)
+
+local N,CoefFFT,xp,xi,u,v,omega:
+N:=nops(x):
+
+if N=1 then CoefFFT:=x:
+else
+
+xp:=[seq(x[2*i],i=1..N/2)]:
+xi:=[seq(x[2*i-1],i=1..N/2)]:
+u:=TFDRecur(xp):
+v:=TFDRecur(xi):
+
+omega:=exp(-2*I*Pi/N):
+      
+CoefFFT:=[seq(omega^(k-1)*u[k]+v[k],k=1..N/2),seq(-omega^(k-1)*u[k]+v[k],k=1..N/2)];
+end if:
+CoefFFT;
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par it\303\251ration</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va utiliser l'\303\251criture des divers coefficients en binaire.</Font></Text-field>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L20" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIter:=proc(x)
+local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
+n:=nops(x):
+l:=x;
+<Font encoding="UTF-8">p:=n/2; #p: puissance max dans d\303\251composition.
+</Font>
+while p&gt;=1 do
+#On fait les signaux jusqu'a 2^p
+<Font encoding="UTF-8">   z:=1; #premi\303\250re valeur de omega.
+</Font>   w:=exp(-I*Pi/p); #c'est omega.
+
+<Font encoding="UTF-8">   for h from 1 to p do #Variable servant \303\240 la d\303\251composition
+</Font>      for m from 1 to n/(2*p) do 
+   #On va calculer le signal xm
+   #prendre l'exemple du Butterfly pour illustrer
+         a:=h+2*(m-1)*p:#indice du signal pour j_(r-1)
+         b:=a+p;
+         tmp:=(l[a]-l[b])*z:
+         l[a]:=l[a]+l[b]:
+         l[b]:=tmp:
+      end do:
+      #On passe au signal m+1 -&gt; w&lt;-w^(m+1)
+      z:=z*w:
+   end do:
+   p:=p/2:
+end do:
+
+#On a maintenant notre liste contenant les signaux x_r
+<Font encoding="UTF-8">#Il reste \303\240 remettre les signaux dans le bon ordre.
+</Font>
+j:=1:
+for i from 1 to n do 
+   if j&gt;i then tmp:=l[j]:
+      l[j]:=l[i]:
+      l[i]:=tmp:
+   end if:
+   p:=n/2:
+   while p&gt;=2 and j&gt;p do
+      j:=j-p:
+      p:=p/2:
+   end do:
+   j:=j+p:
+end do:
+return l;
+
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la Transform\303\251e Inverse.</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">De m\303\252me, il est possible d'effectuer deux m\303\251thodes pour calculer la transform\303\251e inverse de Fourier :</Font></Text-field>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode na\303\257ve</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">En utilisant le m\303\252me algorithme, on obtient : </Font></Text-field>
+<Group labelreference="L6" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDISimple:=proc(X)
+
+local n,F:
+n:=nops(X):
+
+F:=[seq((1/n)*sum(X[i]*exp(2*I*(j-1)*(i-1)*Pi/(n)),i=1..n),j=1..n)];
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal">Attention : Pour que l'on puisse retrouver les valeurs initiales, </Text-field>
+<Text-field style="Text" layout="Normal">il ne faut pas oublier de diviser par le nombre de valeurs.</Text-field>
+<Group labelreference="L16" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIRecur:=proc(X)
+local Coef,N,Xi,Xp,U,V,Omega,k;
+N:=nops(X);
+
+if N=1 then Coef:=X:
+else
+   Xi:=[seq(X[2*k-1],k=1..N/2)];
+   Xp:=[seq(X[2*k],k=1..N/2)]; 
+   U:=TFDIRecur(Xi);
+   V:=TFDIRecur(Xp);
+   Omega:=exp(2*I*Pi/N);
+   Coef:=[seq(U[k]+Omega^(k-1)*V[k],k=1..N/2),seq(U[k]-Omega^(k-1)*V[k],k=1..N/2)]:
+ end if;
+Coef;
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode it\303\251rative</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L25" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIIter:=proc(x)
+local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
+n:=nops(x):
+l:=x;
+p:=n/2;
+
+while p&gt;=1 do
+   z:=1; 
+<Font encoding="UTF-8">   w:=exp(I*Pi/p); #C'est la diff\303\251rence
+</Font>
+   for h from 1 to p do
+      for m from 1 to n/(2*p) do 
+         a:=h+2*(m-1)*p:
+         b:=a+p;
+         tmp:=(l[a]-l[b])*z:
+         l[a]:=l[a]+l[b]:
+         l[b]:=tmp:
+      end do:
+      z:=z*w:
+   end do:
+   p:=p/2:
+end do:
+
+j:=1:
+for i from 1 to n do 
+   if j&gt;i then tmp:=l[j]:
+      l[j]:=l[i]:
+      l[i]:=tmp:
+   end if:
+   p:=n/2:
+   while p&gt;=2 and j&gt;p do
+      j:=j-p:
+      p:=p/2:
+   end do:
+   j:=j+p:
+end do:
+return l/n;
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1">Mesure du temps de calcul</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va ici s'inter\303\251sser \303\240 la mesure du temps pris pour calculer les coefficients de Fourier (Transform\303\251e Directe) par la m\303\251thode na\303\257ve et la m\303\251thode r\303\251cursive pour n grand, par exemple n=2^5, n=2^10, n=2^20.
+Pour cela, on va d\303\251finir la liste de nos coefficients, entiers compris entre -50 et 50 par exemple, par une m\303\251thode &quot;pseudo-al\303\251atoire&quot; : </Font></Text-field>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L7" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(RandomTools[MersenneTwister]);
+A:=[seq(GenerateInteger32(),i=1..2^5)]:</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQtSShtZmVuY2VkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiwtSSNtaUdGJTY5US5HZW5lcmF0ZUZsb2F0RigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y1LUYtNjlRMEdlbmVyYXRlRmxvYXQ2NEYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUYtNjlRMEdlbmVyYXRlSW50ZWdlckYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUYtNjlRMkdlbmVyYXRlSW50ZWdlcjMyRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRi02OVE2R2VuZXJhdGVVbnNpZ25lZEludDMyRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRi02OVEpR2V0U3RhdGVGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GLTY5US1OZXdHZW5lcmF0b3JGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GLTY5USlTZXRTdGF0ZUYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLyUlb3BlbkdRJyZsc3FiO0YoLyUmY2xvc2VHUScmcnNxYjtGKDcjNypJLkdlbmVyYXRlRmxvYXRHRihJMEdlbmVyYXRlRmxvYXQ2NEdGKEkwR2VuZXJhdGVJbnRlZ2VyR0YoSTJHZW5lcmF0ZUludGVnZXIzMkdGKEk2R2VuZXJhdGVVbnNpZ25lZEludDMyR0YoSSlHZXRTdGF0ZUdGKEktTmV3R2VuZXJhdG9yR0YoSSlTZXRTdGF0ZUdGKA==</Equation></Text-field>
+</Output>
+</Group>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode na\303\257ve</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On effectue le calcul pour la m\303\251thode it\303\251rative : </Font></Text-field>
+<Group labelreference="L8" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+N:=TFDSimple(A):
+Temps := time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Calcul pour la m\303\251thode r\303\251cursive : </Font></Text-field>
+<Group labelreference="L9" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+R:=TFDRecur(A):
+Temps := time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+</Section>
+<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode it\303\251rative</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L24" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+I:=TFDIter(A):
+Temps:= time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="Error" layout="Error">Error, illegal use of an object as a name</Text-field>
+</Output>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L26" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
+</Input>
+</Group>
+</Section>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Multiplication de polyn\303\264mes</Font></Text-field></Title>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2">Algorithme</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va prendre en entr\303\251e deux listes contenant les coefficients des deux polyn\303\264mes dont on cherche \303\240 calculer le produit.</Font></Text-field>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Utilise la m\303\251thode simple, car sinon impose en plus une condition sur le degr\303\251 des polyn\303\264mes.</Font></Text-field>
+<Group labelreference="L28" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Multiplication:=proc(P,Q)
+
+local n,N,R,A,B,i,j,k:
+
+n:=nops(P):
+
+<Font encoding="UTF-8">#On cr\303\251e la liste des coefficients \303\251tendus \303\240 2n \303\251l\303\251ments.
+</Font>A:=[seq(P[k],k=1..n),seq(0,k=n+1..2*n)];
+B:=[seq(Q[k],k=1..n),seq(0,k=n+1..2*n)];
+
+#On calcule la TFD de chacune de ces listes.
+A:=TFDIter(A):
+B:=TFDIter(B):
+
+#On effectue les produits
+R:=[seq(A[k]*B[k],k=1..2*n)]:
+
+<Font encoding="UTF-8">#On r\303\251cup\303\250re les coefficients.
+</Font>TFDIIter(R);
+
+end proc:</Text-field>
+</Input>
+</Group>
+<Group labelreference="L27" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2">Exemple</Text-field></Title>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 3" layout="Heading 3">Maple</Text-field></Title>
+<Text-field style="Text" layout="Normal">On va poser <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;P&quot;), Typesetting:-mo(&quot;:=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-munderover(Typesetting:-mo(&quot;\342\210\221&quot;, form = &quot;prefix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;thinmathspace&quot;, stretchy = &quot;true&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;true&quot;, movablelimits = &quot;true&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;i&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mn(&quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mrow(Typesetting:-mn(&quot;10&quot;)), accent = &quot;false&quot;, accentunder = &quot;false&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;iX&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;))">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</Equation> et <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;Q&quot;), Typesetting:-mo(&quot;:=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-munderover(Typesetting:-mo(&quot;\342\210\221&quot;, form = &quot;prefix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;thinmathspace&quot;, stretchy = &quot;true&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;true&quot;, movablelimits = &quot;true&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;i&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mn(&quot;0&quot;)), Typesetting:-mn(&quot;10&quot;), accent = &quot;false&quot;, accentunder = &quot;false&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;i&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;X&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;))">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</Equation></Text-field>
+<Group labelreference="L29" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=sum(i*X^i,i=0..15);</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L30" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q:=sum(i^i*X^i,i=0..15);</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L31" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R:=expand(P*Q);</Text-field>
+</Input>
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+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L35" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R:=evalf(Multiplication(P,Q)):</Text-field>
+</Input>
+</Group>
+<Group labelreference="L38" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R:=[seq(round(R[j]),j=1..20)];</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L36" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
+</Input>
+</Group>
+</Section>
+</Section>
+</Section>
+</Worksheet>
\ No newline at end of file
diff --git a/TIPE_2007/Maple/TFD.mw b/TIPE_2007/Maple/TFD.mw
new file mode 100644
index 0000000..87d6772
--- /dev/null
+++ b/TIPE_2007/Maple/TFD.mw
@@ -0,0 +1,472 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Worksheet>
+<Version major="7" minor="0"/>
+<Label-Scheme value="2" prefix=""/>
+<View-Properties presentation="false"></View-Properties>
+<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="&gt; " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="extended" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
+<Styles><Font name="Heading 4" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false"/>
+<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
+<Font name="Left Justified Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
+<Font name="Help" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="9" subscript="false" superscript="false" underline="false"/>
+<Font name="Help Variable" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
+<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
+<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[64,128,64]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false"/>
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+<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0"/>
+<Layout name="Ordered List 2" alignment="left" bullet="none" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0"/>
+<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
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+<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
+<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
+<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
+<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
+</Styles>
+<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
+<Task-table>
+    <Task-category name="&lt;default&gt;">
+    </Task-category>
+</Task-table>
+<Group labelreference="L3" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
+</Input>
+</Group>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure &quot;na\303\257ve&quot;</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure calcule les coefficients de Fourier par une m\303\251thode dite &quot;naive&quot;.</Font></Text-field>
+<Group labelreference="L4" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDSimple:=proc(x)
+
+local n,X:
+n:=nops(x):
+
+X:=[seq(sum(x[j]*exp(-2*I*(j-1)*(k-1)*Pi/n),j=1..n),k=1..n)];
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure prend en entr\303\251e une liste repr\303\251sentant les coefficients d'un polyn\303\264me dont on cherche \303\240 calculer les coefficients de Fourier.</Font></Text-field>
+<Group labelreference="L5" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDRecur:=proc(x)
+
+local N,CoefFFT,xp,xi,u,v,omega:
+N:=nops(x):
+
+if N=1 then CoefFFT:=x:
+else
+
+xp:=[seq(x[2*i],i=1..N/2)]:
+xi:=[seq(x[2*i-1],i=1..N/2)]:
+u:=TFDRecur(xp):
+v:=TFDRecur(xi):
+
+omega:=exp(-2*I*Pi/N):
+      
+CoefFFT:=[seq(omega^(k-1)*u[k]+v[k],k=1..N/2),seq(-omega^(k-1)*u[k]+v[k],k=1..N/2)];
+end if:
+CoefFFT;
+
+end proc:</Text-field><Pagebreak></Pagebreak>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par it\303\251ration</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va utiliser l'\303\251criture des divers coefficients en binaire.</Font></Text-field>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L20" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIter:=proc(x)
+local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
+n:=nops(x):
+l:=Array(1..n):
+l:=Array(x):
+p:=n/2:<Font encoding="UTF-8">#p: puissance de 2 dans d\303\251composition.
+</Font>
+while p&gt;=1 do
+<Font encoding="UTF-8">   z:=1: #premi\303\250re valeur de omega.
+</Font>   w:=exp(-I*Pi/p): #c'est omega.
+
+<Font encoding="UTF-8">   for h from 1 to p do #Variable servant \303\240 la d\303\251composition
+</Font>      for m from 1 to n/(2*p) do 
+   #On va calculer le signal xm
+<Font encoding="UTF-8">         a:=h+2*(m-1)*p:  #Premi\303\250re valeur du signal x_(m-1)
+</Font>         b:=a+p:          #Seconde valeur du signal x_(m-1)
+         tmp:=(l[a]-l[b])*z:
+         l[a]:=l[a]+l[b]: #x_m(a) = x_(m-1)(a)+x_(m-1)(b)
+         l[b]:=tmp:       #x_m(b) = (x_(m-1)(a)-x_(m-1)(b))*z
+      end do:
+      #On passe au signal m+1 -&gt; w&lt;-w^(m+1)
+      z:=z*w:
+   end do:
+   p:=p/2:
+end do:
+
+#On a maintenant notre liste contenant les signaux x_r
+<Font encoding="UTF-8">#Il reste \303\240 remettre les signaux dans le bon ordre.</Font>
+j:=1:
+for i from 1 to n do 
+   if j&gt;i then tmp:=l[j]:
+      l[j]:=l[i]:
+      l[i]:=tmp:
+   end if:
+   p:=n/2:
+   while p&gt;=2 and j&gt;p do
+      j:=j-p:
+      p:=p/2:
+   end do:
+   j:=j+p:
+end do:
+l;
+end proc:</Text-field><Pagebreak></Pagebreak>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la Transform\303\251e Inverse.</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">De m\303\252me, il est possible d'effectuer deux m\303\251thodes pour calculer la transform\303\251e inverse de Fourier :</Font></Text-field>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode na\303\257ve</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">En utilisant le m\303\252me algorithme, on obtient : </Font></Text-field>
+<Group labelreference="L6" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDISimple:=proc(X)
+
+local n,F:
+n:=nops(X):
+
+F:=[seq((1/n)*sum(X[i]*exp(2*I*(j-1)*(i-1)*Pi/(n)),i=1..n),j=1..n)];
+
+end proc:</Text-field>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal">Attention : Pour que l'on puisse retrouver les valeurs initiales, </Text-field>
+<Text-field style="Text" layout="Normal">il ne faut pas oublier de diviser par le nombre de valeurs.</Text-field>
+<Group labelreference="L16" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIRecur:=proc(X)
+local Coef,N,Xi,Xp,U,V,Omega,k;
+N:=nops(X);
+
+if N=1 then Coef:=X:
+else
+   Xi:=[seq(X[2*k-1],k=1..N/2)];
+   Xp:=[seq(X[2*k],k=1..N/2)]; 
+   U:=TFDIRecur(Xi);
+   V:=TFDIRecur(Xp);
+   Omega:=exp(2*I*Pi/N);
+   Coef:=[seq(U[k]+Omega^(k-1)*V[k],k=1..N/2),seq(U[k]-Omega^(k-1)*V[k],k=1..N/2)]:
+ end if;
+Coef;
+end proc:</Text-field><Pagebreak></Pagebreak>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode it\303\251rative</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L25" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TFDIIter:=proc(x)
+local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
+n:=nops(x):
+l:=Array(1..n):
+l:=Array(x):
+p:=n/2:
+
+while p&gt;=1 do
+   z:=1:
+<Font encoding="UTF-8">   w:=exp(I*Pi/p); #C'est la diff\303\251rence
+</Font>
+   for h from 1 to p do
+      for m from 1 to n/(2*p) do 
+         a:=h+2*(m-1)*p:
+         b:=a+p:
+         tmp:=(l[a]-l[b])*z:
+         l[a]:=l[a]+l[b]:
+         l[b]:=tmp:
+      end do:
+      z:=z*w:
+   end do:
+   p:=p/2:
+end do:
+
+j:=1:
+for i from 1 to n do 
+   if j&gt;i then tmp:=l[j]:
+      l[j]:=l[i]:
+      l[i]:=tmp:
+   end if:
+   p:=n/2:
+   while p&gt;=2 and j&gt;p do
+      j:=j-p:
+      p:=p/2:
+   end do:
+   j:=j+p:
+end do:
+for i from 1 to n do
+   l[i]:=l[i]/n:
+end do:
+return l;
+end proc:</Text-field><Pagebreak></Pagebreak>
+</Input>
+</Group>
+</Section>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1">Mesure du temps de calcul</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va ici s'int\303\251resser \303\240 la mesure du temps n\303\251cessaire pour calculer les coefficients de Fourier (Transform\303\251e Directe) pour n &quot;grand&quot;, par exemple n=2^5, n=2^10,... .
+Pour cela, on va d\303\251finir la liste de nos coefficients par une m\303\251thode &quot;pseudo-al\303\251atoire&quot; : </Font></Text-field>
+<Text-field style="Text" layout="Normal"></Text-field>
+<Group labelreference="L7" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(RandomTools[MersenneTwister]):
+A:=[seq(GenerateFloat(),i=1..2^8)]:</Text-field>
+</Input>
+</Group>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode na\303\257ve</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On effectue le calcul pour la m\303\251thode na\303\257ve : </Font></Text-field>
+<Group labelreference="L8" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+TFDSimple(A):
+Temps := time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode r\303\251cursive</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Calcul pour la m\303\251thode r\303\251cursive : </Font></Text-field>
+<Group labelreference="L9" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+TFDRecur(A):
+Temps := time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode it\303\251rative</Font></Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Mesure pour la m\303\251thode it\303\251rative :</Font></Text-field>
+<Group labelreference="L24" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t:=time():
+TFDIter(A):
+Temps:= time()-t;</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field><Pagebreak></Pagebreak>
+</Output>
+</Group>
+</Section>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Multiplication de polyn\303\264mes</Font></Text-field></Title>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2">Algorithme</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va prendre en entr\303\251e deux listes contenant les coefficients des deux polyn\303\264mes dont on cherche \303\240 calculer le produit.</Font></Text-field>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Il faut prendre des pr\303\251cautions, car la proc\303\251dure ne v\303\251rifie pas si les deux polyn\303\264mes sont de m\303\252me degr\303\251, qui doit \303\252tre une puissance de 2, si l'on souhaite utiliser la m\303\251thode r\303\251cursive ou it\303\251rative.</Font></Text-field>
+<Group labelreference="L28" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Multiplication:=proc(P,Q)
+
+local n,N,R,A,B,i,j,k:
+
+n:=nops(P):
+N:=2*n:
+
+<Font encoding="UTF-8">#On cr\303\251e la liste des coefficients \303\251tendus \303\240 2n \303\251l\303\251ments.
+</Font>A:=[seq(P[k],k=1..n),seq(0,k=n+1..N)];
+B:=[seq(Q[k],k=1..n),seq(0,k=n+1..N)];
+
+#On calcule la TFD de chacune de ces listes.
+A:=TFDIter(A):
+B:=TFDIter(B):
+
+#On effectue les produits
+R:=[seq(A[k]*B[k],k=1..N)]:
+
+<Font encoding="UTF-8">#On r\303\251cup\303\250re les coefficients.
+</Font>TFDIIter(R);
+
+end proc:</Text-field><Pagebreak></Pagebreak>
+</Input>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 2" layout="Heading 2">Exemple</Text-field></Title>
+<Text-field style="Text" layout="Normal">On va poser <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;P&quot;), Typesetting:-mo(&quot;:=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-munderover(Typesetting:-mo(&quot;\342\210\221&quot;, form = &quot;prefix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;thinmathspace&quot;, stretchy = &quot;true&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;true&quot;, movablelimits = &quot;true&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;i&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mn(&quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mn(&quot;7&quot;), accent = &quot;false&quot;, accentunder = &quot;false&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;iX&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;))">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</Equation> et <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;Q&quot;), Typesetting:-mo(&quot;:=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-munderover(Typesetting:-mo(&quot;\342\210\221&quot;, form = &quot;prefix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;thinmathspace&quot;, stretchy = &quot;true&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;true&quot;, movablelimits = &quot;true&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;i&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mn(&quot;0&quot;)), Typesetting:-mn(&quot;7&quot;), accent = &quot;false&quot;, accentunder = &quot;false&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;i&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mi(&quot;X&quot;), Typesetting:-mi(&quot;i&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;))">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</Equation> donc<Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mo(&quot; &quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mi(&quot;n&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mn(&quot;8&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-msup(Typesetting:-mn(&quot;2&quot;), Typesetting:-mn(&quot;3.&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;))">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</Equation></Text-field>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 3" layout="Heading 3">Algo</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va demander la liste des coefficients du polyn\303\264me R=P*Q. Pour une lecture plus facile, nous en prendrons les valeurs arrondies.</Font></Text-field>
+<Group labelreference="L33" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=[seq(i,i=0..7)]:</Text-field>
+</Input>
+</Group>
+<Group labelreference="L34" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q:=[seq(i^i,i=0..7)]:</Text-field>
+</Input>
+</Group>
+<Group labelreference="L35" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R:=evalf(Multiplication(P,Q)):</Text-field>
+</Input>
+</Group>
+<Group labelreference="L38" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">[seq(R[j],j=1..2*nops(P))];</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L63" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R:=[seq(round(R[j]),j=1..2*nops(P))];</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+</Section>
+<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
+<Text-field style="Heading 3" layout="Heading 3">Maple</Text-field></Title>
+<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va evaluer le polyn\303\264me P*Q :</Font></Text-field>
+<Group labelreference="L39" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=sum(i*X^i,i=0..7):</Text-field>
+</Input>
+</Group>
+<Group labelreference="L42" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q:=sum(i^i*X^i,i=0..7):</Text-field>
+</Input>
+</Group>
+<Group labelreference="L46" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sort(expand(P*Q),X,ascending);</Text-field>
+</Input>
+<Output>
+<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
+</Output>
+</Group>
+<Group labelreference="L57" drawlabel="true">
+<Input>
+<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
+</Input>
+</Group>
+</Section>
+</Section>
+</Section>
+</Worksheet>
\ No newline at end of file
diff --git a/TIPE_2007/Octave/Multiplication.m b/TIPE_2007/Octave/Multiplication.m
new file mode 100644
index 0000000..eb53abc
--- /dev/null
+++ b/TIPE_2007/Octave/Multiplication.m
@@ -0,0 +1,22 @@
+function[R]=Multiplication(P,Q)
+
+n=length(P);
+N=2*n;
+A=zeros(1,N);
+B=zeros(1,N);
+R=zeros(1,N);
+
+for i=1:n
+	A(i)=P(i);
+	B(i)=Q(i);
+end 
+
+%On calcule les transformées de chaque élément.
+A=TFDB(A);
+B=TFDB(B);
+%On effectue les produits
+for i=1:N
+	R(i)=A(i)*B(i);
+end
+R=TFDIB(R);
+endfunction
diff --git a/TIPE_2007/Octave/TFD - Octave.tar.bz2 b/TIPE_2007/Octave/TFD - Octave.tar.bz2
new file mode 100644
index 0000000..6ac824f
--- /dev/null
+++ b/TIPE_2007/Octave/TFD - Octave.tar.bz2
diff --git a/TIPE_2007/Octave/TFD - Octave.zip b/TIPE_2007/Octave/TFD - Octave.zip
new file mode 100644
index 0000000..e540144
--- /dev/null
+++ b/TIPE_2007/Octave/TFD - Octave.zip
diff --git a/TIPE_2007/Octave/TFDI - Octave.tar.bz2 b/TIPE_2007/Octave/TFDI - Octave.tar.bz2
new file mode 100644
index 0000000..696a8a1
--- /dev/null
+++ b/TIPE_2007/Octave/TFDI - Octave.tar.bz2
diff --git a/TIPE_2007/Octave/TFDI - Octave.zip b/TIPE_2007/Octave/TFDI - Octave.zip
new file mode 100644
index 0000000..537115d
--- /dev/null
+++ b/TIPE_2007/Octave/TFDI - Octave.zip
diff --git a/TIPE_2007/index.html b/TIPE_2007/index.html
new file mode 100644
index 0000000..48eeee2
--- /dev/null
+++ b/TIPE_2007/index.html
@@ -0,0 +1,110 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="fr" lang="fr">
+<head>
+<title>Algorithmes de calculs de TFD : Sources et programmes</title>
+<meta name="author" content="Audric SCHILTKNECHT" />
+<meta name="date" content="2009-09-09T17:25:42-0400" />
+<meta name="copyright" content="GPL, Creative Commons, CC, By, Sa" />
+<meta name="keywords" content="FFT, TFD, Fourier, TIPE" />
+<meta name="description"
+	content="Les sources des algorithmes de calculs de TFD et FFT" />
+<meta name="ROBOTS" content="NOINDEX, NOFOLLOW" />
+<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<meta http-equiv="content-type"
+	content="application/xhtml+xml; charset=UTF-8" />
+<meta http-equiv="content-style-type" content="text/css" />
+<meta http-equiv="expires" content="0" />
+<link type="text/css" href="../styles/simpleelegance03/style.css"
+	rel="stylesheet" />
+</head>
+<body>
+<div id="header">Audric Schiltknecht</div>
+<ul id="navtop">
+	<li><a href="../index.html">Accueil</a></li>
+	<li><a href="../cv.html">CV</a></li>
+	<li><a href="../projets.html">Projets</a></li>
+	<li id="current"><a href="../TIPE_2007/index.html">TIPE 2007</a></li>
+</ul>
+
+<div id="maincontainer">
+	<div id="contentwrapper">
+    <div id="contentcolumn">
+    	<h1>TIPE 2007</h1>
+		<div class="hr"><hr/></div>
+		<p>Voici mes réalisations effectuées pour le TIPE que j'ai réalisé lors de ma
+		seconde année de classes préparatoires. Le thème était <em>Le Temps</em>, j'ai pris
+		comme sujet <em>La Transformée de Fourrier</em>.
+		</p>
+		<h3>Programme Maple&nbsp;:</h3>
+		<p>
+		Télécharger le fichier&nbsp;: <a href="Maple/TFD.mw" title="Fichier Maple">TFD.mw</a> 
+		<br/>
+		(Faire "clique-droit/Enregistrer sous" car sinon, cela l'ouvre dans le
+		navigateur)
+		</p>
+		
+		<h3>Sources Octave&nbsp;:</h3>
+		<ul>
+		<li>Télécharger une archive contenant tous les fichiers concernant 
+				la Transformée Directe&nbsp;:
+			<ul>
+				<li><a href="Octave/TFD - Octave.zip"
+					title="Fichier Octave - Format Zip">Format zip</a></li>
+				<li><a
+					href="Octave/TFD - Octave.tar.bz2"
+					title="Fichier Octave - Format tar.bz2">Format tar.bz2</a></li>
+			</ul>
+			</li>
+		<li>Télécharger une archive contenant tous les fichiers concernant
+				la Transformée Inverse&nbsp;:
+				<ul>
+					<li><a href="Octave/TFDI - Octave.zip"
+					title="Fichier Octave - Format Zip">Format zip</a></li>
+					<li><a href="Octave/TFDI - Octave.tar.bz2"
+					title="Fichier Octave - Format tar.bz2">Format tar.bz2</a></li>
+				</ul>
+		</li>
+		<li>Source de l'algorithme de Multiplication de polynômes
+				(Nécessite la présence des deux archives précédentes, extraites dans le
+				même dossier)&nbsp;: <a href="Octave/Multiplication.m"
+					title="Fichier Octave - Multiplication.m">Multiplication.m</a>
+		</li></ul>
+		
+		<h3>Sources C++&nbsp;:</h3>
+		<p>Le programme ne peut s'éxecuter que sur un système GNU/Linux.
+		<br/>
+		Archive contenant les sources&nbsp;: <a href="C/TFD - C.zip"
+					title="Fichier C - Format Zip">Format zip</a> - <a
+					href="C/TFD - C.tar.bz2" title="Fichier C - Format tar.bz2">Format tar.bz2</a>
+		</p>
+
+		<h3>Le dossier&nbsp;:</h3>
+		<ul class="list">
+			<li>Télécharger le <a href="Dossier/Dossier_TIPE_2007_TF.pdf"
+					title="Dossier TIPE">Dossier TIPE</a> (Format PDF)</li>
+			<li>Télécharger les <a
+					href="Dossier/Transparents_TIPE_2007_TF.pdf" title="Transparents">transparents
+				de présentation</a> (Format PDF)</li>
+		</ul>
+    </div>
+	</div>
+	
+	<div id="footer">
+		<p>
+		<a href="http://validator.w3.org/check?uri=referer">
+		Page valide XHTML 1.0 Strict
+		</a>
+		&nbsp;
+		<a href="http://jigsaw.w3.org/css-validator/check/referer">
+		CSS Valide
+    	</a>
+    	&nbsp;
+    	Contenu disponible sous <a rel="license" href="http://creativecommons.org/licenses/GPL/2.0/">CC-GPL</a>
+		<br />
+		Design by <a href="http://www.wfiedler-online.de/index.php">wfiedler</a>
+		</p>
+	</div>
+</div>
+</body>
+</html>
diff --git a/TIPE_2007/index.html.plain b/TIPE_2007/index.html.plain
new file mode 100644
index 0000000..56da487
--- /dev/null
+++ b/TIPE_2007/index.html.plain
@@ -0,0 +1,73 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="fr" lang="fr">
+<head>
+<title>Algorithmes de calculs de TFD : Sources et programmes</title>
+	<meta name="generator" content="VIm"/>
+	<meta name="author" content="Audric SCHILTKNECHT"/>
+	<meta name="date" content="2007-08-10T17:39:30+0200"/>
+	<meta name="copyright" content="GPL, Creative Commons, CC, By, Sa"/>
+	<meta name="keywords" content="FFT, TFD, Fourier, TIPE"/>
+	<meta name="description" content="Les sources des algorithmes de calculs de TFD et FFT"/>
+	<meta name="ROBOTS" content="NOINDEX, NOFOLLOW"/>
+	<meta http-equiv="content-type" content="text/html; charset=UTF-8"/>
+	<meta http-equiv="content-type" content="application/xhtml+xml; charset=UTF-8"/>
+	<meta http-equiv="content-style-type" content="text/css"/>
+	<meta http-equiv="expires" content="0"/>
+<!--
+<style type="text/css">
+h1,h2
+{
+	text-align: center;
+}
+.footer
+{
+	position:absolute;
+	right: 50%;
+}
+</style>
+-->
+</head>
+<body>
+<h1>Algorithmes de calculs de Transformée de Fourier</h1>
+<h3>Programme Maple : </h3>
+<p>
+Télécharger le fichier : <a href="Maple/TFD.mw" title="Fichier Maple">TFD.mw</a>
+<br/>(Faire "clique-droit/Enregistrer sous" car sinon, cela l'ouvre dans le navigateur)
+</p>
+<h3>Sources Octave : </h3>
+<ul>
+<li>Télécharger une archive contenant tous les fichiers concernant la Transformée Directe :
+<a href="Octave/TFD - Octave.zip" title="Fichier Octave - Format Zip">Format zip</a>
+ - <a href="Octave/TFD - Octave.tar.bz2" title="Fichier Octave - Format tar.bz2">Format tar.bz2</a></li>
+ <li>Télécharger une archive contenant tous les fichiers concernant la Transformée Inverse :
+ <a href="Octave/TFDI - Octave.zip" title="Fichier Octave - Format Zip">Format zip</a>
+ - <a href="Octave/TFDI - Octave.tar.bz2" title="Fichier Octave - Format tar.bz2">Format tar.bz2</a></li>
+<li>Source de l'algorithme de Multiplication de polynômes (Nécessite la présence des deux archives précédentes, extraites dans le même dossier) :
+ <a href="Octave/Multiplication.m" title="Fichier Octave - Multiplication.m">Multiplication.m</a></li>
+</ul>
+
+<h3>Sources C++ : (Sous licence GNU/GPL)</h3>
+<p>Le programme ne peut s'éxecuter que sur un système GNU/Linux.</p>
+<ul>
+<li>Archive contenant les sources : <a href="C/TFD - C.zip" title="Fichier C - Format Zip">Format zip</a>
+ - <a href="C/TFD - C.tar.bz2" title="Fichier C - Format tar.bz2">Format tar.bz2</a></li>
+</ul>
+
+<h3>Le dossier : (Sous licence <a rel="license" title="Licence Creative Commons" href="http://creativecommons.org/licenses/by-sa/2.0/fr/">Creative Commons</a>)</h3>
+<ul>
+<li>Télécharger le <a href="Dossier/Dossier_TIPE_2007_TF.pdf" title="Dossier TIPE">Dossier TIPE</a> (Format PDF)</li>
+<li>Télécharger les <a href="Dossier/Transparents_TIPE_2007_TF.pdf" title="Transparents">transparents de présentation</a> (Format PDF)</li>
+</ul>
+
+<p class="footer">
+<a href="http://validator.w3.org/check?uri=referer"><img
+        src="http://www.w3.org/Icons/valid-xhtml10"
+        alt="Valid XHTML 1.0 Strict" height="31" width="88" /></a>
+<a rel="license" href="http://creativecommons.org/licenses/by-sa/2.0/fr/">
+<img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-sa/2.0/fr/80x15.png" />
+</a>
+</p>
+
+</body>
+</html>