From 71024b47aa4a22ccfcf9eace06a32f9136b07e8f Mon Sep 17 00:00:00 2001
From: Orestis Malaspinas <orestis.malaspinas@hesge.ch>
Date: Wed, 20 Mar 2019 00:53:36 +0100
Subject: [PATCH] added minor stuff

---
 tpFourier/fourier2019/Makefile      |   2 +-
 tpFourier/fourier2019/css/prism.css | 142 ++++++++++++++++++++++++++++
 tpFourier/fourier2019/css/prism.js  |   8 ++
 tpFourier/fourier2019/fourier.md    |   8 ++
 4 files changed, 159 insertions(+), 1 deletion(-)
 create mode 100644 tpFourier/fourier2019/css/prism.css
 create mode 100644 tpFourier/fourier2019/css/prism.js

diff --git a/tpFourier/fourier2019/Makefile b/tpFourier/fourier2019/Makefile
index 3021bf5..70c7910 100644
--- a/tpFourier/fourier2019/Makefile
+++ b/tpFourier/fourier2019/Makefile
@@ -20,7 +20,7 @@ PDF=$(MD:%.md=%.pdf)
 all: $(HTML) $(PDF)
 
 %.pdf: %.md Makefile
-	sed -e 's/language-c/C/g' -e 's/language-bash/bash/g' $< > $*_tex.md
+	sed -e 's/language-python/python/g' -e 's/language-bash/bash/g' $< > $*_tex.md
 	pandoc -s $(OPTIONS) $(PDFOPTIONS) -o $@ $<
 	rm $*_tex.md
 
diff --git a/tpFourier/fourier2019/css/prism.css b/tpFourier/fourier2019/css/prism.css
new file mode 100644
index 0000000..f5031f2
--- /dev/null
+++ b/tpFourier/fourier2019/css/prism.css
@@ -0,0 +1,142 @@
+/* PrismJS 1.15.0
+https://prismjs.com/download.html#themes=prism&languages=markup+css+clike+javascript+python */
+/**
+ * prism.js default theme for JavaScript, CSS and HTML
+ * Based on dabblet (http://dabblet.com)
+ * @author Lea Verou
+ */
+
+code[class*="language-"],
+pre[class*="language-"] {
+	color: black;
+	background: none;
+	text-shadow: 0 1px white;
+	font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
+	font-size: 1em;
+	text-align: left;
+	white-space: pre;
+	word-spacing: normal;
+	word-break: normal;
+	word-wrap: normal;
+	line-height: 1.5;
+
+	-moz-tab-size: 4;
+	-o-tab-size: 4;
+	tab-size: 4;
+
+	-webkit-hyphens: none;
+	-moz-hyphens: none;
+	-ms-hyphens: none;
+	hyphens: none;
+}
+
+pre[class*="language-"]::-moz-selection, pre[class*="language-"] ::-moz-selection,
+code[class*="language-"]::-moz-selection, code[class*="language-"] ::-moz-selection {
+	text-shadow: none;
+	background: #b3d4fc;
+}
+
+pre[class*="language-"]::selection, pre[class*="language-"] ::selection,
+code[class*="language-"]::selection, code[class*="language-"] ::selection {
+	text-shadow: none;
+	background: #b3d4fc;
+}
+
+@media print {
+	code[class*="language-"],
+	pre[class*="language-"] {
+		text-shadow: none;
+	}
+}
+
+/* Code blocks */
+pre[class*="language-"] {
+	padding: 1em;
+	margin: .5em 0;
+	overflow: auto;
+}
+
+:not(pre) > code[class*="language-"],
+pre[class*="language-"] {
+	background: #f5f2f0;
+}
+
+/* Inline code */
+:not(pre) > code[class*="language-"] {
+	padding: .1em;
+	border-radius: .3em;
+	white-space: normal;
+}
+
+.token.comment,
+.token.prolog,
+.token.doctype,
+.token.cdata {
+	color: slategray;
+}
+
+.token.punctuation {
+	color: #999;
+}
+
+.namespace {
+	opacity: .7;
+}
+
+.token.property,
+.token.tag,
+.token.boolean,
+.token.number,
+.token.constant,
+.token.symbol,
+.token.deleted {
+	color: #905;
+}
+
+.token.selector,
+.token.attr-name,
+.token.string,
+.token.char,
+.token.builtin,
+.token.inserted {
+	color: #690;
+}
+
+.token.operator,
+.token.entity,
+.token.url,
+.language-css .token.string,
+.style .token.string {
+	color: #9a6e3a;
+	background: hsla(0, 0%, 100%, .5);
+}
+
+.token.atrule,
+.token.attr-value,
+.token.keyword {
+	color: #07a;
+}
+
+.token.function,
+.token.class-name {
+	color: #DD4A68;
+}
+
+.token.regex,
+.token.important,
+.token.variable {
+	color: #e90;
+}
+
+.token.important,
+.token.bold {
+	font-weight: bold;
+}
+.token.italic {
+	font-style: italic;
+}
+
+.token.entity {
+	cursor: help;
+}
+
diff --git a/tpFourier/fourier2019/css/prism.js b/tpFourier/fourier2019/css/prism.js
new file mode 100644
index 0000000..d4f5b09
--- /dev/null
+++ b/tpFourier/fourier2019/css/prism.js
@@ -0,0 +1,8 @@
+/* PrismJS 1.15.0
+https://prismjs.com/download.html#themes=prism&languages=markup+css+clike+javascript+python */
+var _self="undefined"!=typeof window?window:"undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?self:{},Prism=function(g){var c=/\blang(?:uage)?-([\w-]+)\b/i,a=0,C={manual:g.Prism&&g.Prism.manual,disableWorkerMessageHandler:g.Prism&&g.Prism.disableWorkerMessageHandler,util:{encode:function(e){return e instanceof M?new M(e.type,C.util.encode(e.content),e.alias):Array.isArray(e)?e.map(C.util.encode):e.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/\u00a0/g," ")},type:function(e){return Object.prototype.toString.call(e).slice(8,-1)},objId:function(e){return e.__id||Object.defineProperty(e,"__id",{value:++a}),e.__id},clone:function t(e,n){var r,a,i=C.util.type(e);switch(n=n||{},i){case"Object":if(a=C.util.objId(e),n[a])return n[a];for(var l in r={},n[a]=r,e)e.hasOwnProperty(l)&&(r[l]=t(e[l],n));return r;case"Array":return a=C.util.objId(e),n[a]?n[a]:(r=[],n[a]=r,e.forEach(function(e,a){r[a]=t(e,n)}),r);default:return e}}},languages:{extend:function(e,a){var t=C.util.clone(C.languages[e]);for(var n in a)t[n]=a[n];return t},insertBefore:function(t,e,a,n){var r=(n=n||C.languages)[t],i={};for(var l in r)if(r.hasOwnProperty(l)){if(l==e)for(var o in a)a.hasOwnProperty(o)&&(i[o]=a[o]);a.hasOwnProperty(l)||(i[l]=r[l])}var s=n[t];return n[t]=i,C.languages.DFS(C.languages,function(e,a){a===s&&e!=t&&(this[e]=i)}),i},DFS:function e(a,t,n,r){r=r||{};var i=C.util.objId;for(var l in a)if(a.hasOwnProperty(l)){t.call(a,l,a[l],n||l);var o=a[l],s=C.util.type(o);"Object"!==s||r[i(o)]?"Array"!==s||r[i(o)]||(r[i(o)]=!0,e(o,t,l,r)):(r[i(o)]=!0,e(o,t,null,r))}}},plugins:{},highlightAll:function(e,a){C.highlightAllUnder(document,e,a)},highlightAllUnder:function(e,a,t){var n={callback:t,selector:'code[class*="language-"], [class*="language-"] code, code[class*="lang-"], [class*="lang-"] code'};C.hooks.run("before-highlightall",n);for(var r,i=n.elements||e.querySelectorAll(n.selector),l=0;r=i[l++];)C.highlightElement(r,!0===a,n.callback)},highlightElement:function(e,a,t){for(var n,r,i=e;i&&!c.test(i.className);)i=i.parentNode;i&&(n=(i.className.match(c)||[,""])[1].toLowerCase(),r=C.languages[n]),e.className=e.className.replace(c,"").replace(/\s+/g," ")+" language-"+n,e.parentNode&&(i=e.parentNode,/pre/i.test(i.nodeName)&&(i.className=i.className.replace(c,"").replace(/\s+/g," ")+" language-"+n));var l={element:e,language:n,grammar:r,code:e.textContent},o=function(e){l.highlightedCode=e,C.hooks.run("before-insert",l),l.element.innerHTML=l.highlightedCode,C.hooks.run("after-highlight",l),C.hooks.run("complete",l),t&&t.call(l.element)};if(C.hooks.run("before-sanity-check",l),l.code)if(C.hooks.run("before-highlight",l),l.grammar)if(a&&g.Worker){var s=new Worker(C.filename);s.onmessage=function(e){o(e.data)},s.postMessage(JSON.stringify({language:l.language,code:l.code,immediateClose:!0}))}else o(C.highlight(l.code,l.grammar,l.language));else o(C.util.encode(l.code));else C.hooks.run("complete",l)},highlight:function(e,a,t){var n={code:e,grammar:a,language:t};return C.hooks.run("before-tokenize",n),n.tokens=C.tokenize(n.code,n.grammar),C.hooks.run("after-tokenize",n),M.stringify(C.util.encode(n.tokens),n.language)},matchGrammar:function(e,a,t,n,r,i,l){for(var o in t)if(t.hasOwnProperty(o)&&t[o]){if(o==l)return;var s=t[o];s="Array"===C.util.type(s)?s:[s];for(var g=0;g<s.length;++g){var c=s[g],u=c.inside,h=!!c.lookbehind,f=!!c.greedy,d=0,m=c.alias;if(f&&!c.pattern.global){var p=c.pattern.toString().match(/[imuy]*$/)[0];c.pattern=RegExp(c.pattern.source,p+"g")}c=c.pattern||c;for(var y=n,v=r;y<a.length;v+=a[y].length,++y){var k=a[y];if(a.length>e.length)return;if(!(k instanceof M)){if(f&&y!=a.length-1){if(c.lastIndex=v,!(x=c.exec(e)))break;for(var b=x.index+(h?x[1].length:0),w=x.index+x[0].length,A=y,P=v,O=a.length;A<O&&(P<w||!a[A].type&&!a[A-1].greedy);++A)(P+=a[A].length)<=b&&(++y,v=P);if(a[y]instanceof M)continue;N=A-y,k=e.slice(v,P),x.index-=v}else{c.lastIndex=0;var x=c.exec(k),N=1}if(x){h&&(d=x[1]?x[1].length:0);w=(b=x.index+d)+(x=x[0].slice(d)).length;var j=k.slice(0,b),S=k.slice(w),E=[y,N];j&&(++y,v+=j.length,E.push(j));var _=new M(o,u?C.tokenize(x,u):x,m,x,f);if(E.push(_),S&&E.push(S),Array.prototype.splice.apply(a,E),1!=N&&C.matchGrammar(e,a,t,y,v,!0,o),i)break}else if(i)break}}}}},tokenize:function(e,a){var t=[e],n=a.rest;if(n){for(var r in n)a[r]=n[r];delete a.rest}return C.matchGrammar(e,t,a,0,0,!1),t},hooks:{all:{},add:function(e,a){var t=C.hooks.all;t[e]=t[e]||[],t[e].push(a)},run:function(e,a){var t=C.hooks.all[e];if(t&&t.length)for(var n,r=0;n=t[r++];)n(a)}},Token:M};function M(e,a,t,n,r){this.type=e,this.content=a,this.alias=t,this.length=0|(n||"").length,this.greedy=!!r}if(g.Prism=C,M.stringify=function(a,t,e){if("string"==typeof a)return a;if(Array.isArray(a))return a.map(function(e){return M.stringify(e,t,a)}).join("");var n={type:a.type,content:M.stringify(a.content,t,e),tag:"span",classes:["token",a.type],attributes:{},language:t,parent:e};if(a.alias){var r=Array.isArray(a.alias)?a.alias:[a.alias];Array.prototype.push.apply(n.classes,r)}C.hooks.run("wrap",n);var i=Object.keys(n.attributes).map(function(e){return e+'="'+(n.attributes[e]||"").replace(/"/g,"&quot;")+'"'}).join(" ");return"<"+n.tag+' class="'+n.classes.join(" ")+'"'+(i?" "+i:"")+">"+n.content+"</"+n.tag+">"},!g.document)return g.addEventListener&&(C.disableWorkerMessageHandler||g.addEventListener("message",function(e){var a=JSON.parse(e.data),t=a.language,n=a.code,r=a.immediateClose;g.postMessage(C.highlight(n,C.languages[t],t)),r&&g.close()},!1)),C;var e=document.currentScript||[].slice.call(document.getElementsByTagName("script")).pop();return e&&(C.filename=e.src,C.manual||e.hasAttribute("data-manual")||("loading"!==document.readyState?window.requestAnimationFrame?window.requestAnimationFrame(C.highlightAll):window.setTimeout(C.highlightAll,16):document.addEventListener("DOMContentLoaded",C.highlightAll))),C}(_self);"undefined"!=typeof module&&module.exports&&(module.exports=Prism),"undefined"!=typeof global&&(global.Prism=Prism);
+Prism.languages.markup={comment:/<!--[\s\S]*?-->/,prolog:/<\?[\s\S]+?\?>/,doctype:/<!DOCTYPE[\s\S]+?>/i,cdata:/<!\[CDATA\[[\s\S]*?]]>/i,tag:{pattern:/<\/?(?!\d)[^\s>\/=$<%]+(?:\s(?:\s*[^\s>\/=]+(?:\s*=\s*(?:"[^"]*"|'[^']*'|[^\s'">=]+(?=[\s>]))|(?=[\s/>])))+)?\s*\/?>/i,greedy:!0,inside:{tag:{pattern:/^<\/?[^\s>\/]+/i,inside:{punctuation:/^<\/?/,namespace:/^[^\s>\/:]+:/}},"attr-value":{pattern:/=\s*(?:"[^"]*"|'[^']*'|[^\s'">=]+)/i,inside:{punctuation:[/^=/,{pattern:/^(\s*)["']|["']$/,lookbehind:!0}]}},punctuation:/\/?>/,"attr-name":{pattern:/[^\s>\/]+/,inside:{namespace:/^[^\s>\/:]+:/}}}},entity:/&#?[\da-z]{1,8};/i},Prism.languages.markup.tag.inside["attr-value"].inside.entity=Prism.languages.markup.entity,Prism.hooks.add("wrap",function(a){"entity"===a.type&&(a.attributes.title=a.content.replace(/&amp;/,"&"))}),Object.defineProperty(Prism.languages.markup.tag,"addInlined",{value:function(a,e){var s={};s["language-"+e]={pattern:/(^<!\[CDATA\[)[\s\S]+?(?=\]\]>$)/i,lookbehind:!0,inside:Prism.languages[e]},s.cdata=/^<!\[CDATA\[|\]\]>$/i;var n={"included-cdata":{pattern:/<!\[CDATA\[[\s\S]*?\]\]>/i,inside:s}};n["language-"+e]={pattern:/[\s\S]+/,inside:Prism.languages[e]};var i={};i[a]={pattern:RegExp("(<__[\\s\\S]*?>)(?:<!\\[CDATA\\[[\\s\\S]*?\\]\\]>\\s*|[\\s\\S])*?(?=<\\/__>)".replace(/__/g,a),"i"),lookbehind:!0,greedy:!0,inside:n},Prism.languages.insertBefore("markup","cdata",i)}}),Prism.languages.xml=Prism.languages.extend("markup",{}),Prism.languages.html=Prism.languages.markup,Prism.languages.mathml=Prism.languages.markup,Prism.languages.svg=Prism.languages.markup;
+!function(s){var e=/("|')(?:\\(?:\r\n|[\s\S])|(?!\1)[^\\\r\n])*\1/;s.languages.css={comment:/\/\*[\s\S]*?\*\//,atrule:{pattern:/@[\w-]+?[\s\S]*?(?:;|(?=\s*\{))/i,inside:{rule:/@[\w-]+/}},url:RegExp("url\\((?:"+e.source+"|.*?)\\)","i"),selector:RegExp("[^{}\\s](?:[^{};\"']|"+e.source+")*?(?=\\s*\\{)"),string:{pattern:e,greedy:!0},property:/[-_a-z\xA0-\uFFFF][-\w\xA0-\uFFFF]*(?=\s*:)/i,important:/!important\b/i,function:/[-a-z0-9]+(?=\()/i,punctuation:/[(){};:,]/},s.languages.css.atrule.inside.rest=s.languages.css;var a=s.languages.markup;a&&(a.tag.addInlined("style","css"),s.languages.insertBefore("inside","attr-value",{"style-attr":{pattern:/\s*style=("|')(?:\\[\s\S]|(?!\1)[^\\])*\1/i,inside:{"attr-name":{pattern:/^\s*style/i,inside:a.tag.inside},punctuation:/^\s*=\s*['"]|['"]\s*$/,"attr-value":{pattern:/.+/i,inside:s.languages.css}},alias:"language-css"}},a.tag))}(Prism);
+Prism.languages.clike={comment:[{pattern:/(^|[^\\])\/\*[\s\S]*?(?:\*\/|$)/,lookbehind:!0},{pattern:/(^|[^\\:])\/\/.*/,lookbehind:!0,greedy:!0}],string:{pattern:/(["'])(?:\\(?:\r\n|[\s\S])|(?!\1)[^\\\r\n])*\1/,greedy:!0},"class-name":{pattern:/((?:\b(?:class|interface|extends|implements|trait|instanceof|new)\s+)|(?:catch\s+\())[\w.\\]+/i,lookbehind:!0,inside:{punctuation:/[.\\]/}},keyword:/\b(?:if|else|while|do|for|return|in|instanceof|function|new|try|throw|catch|finally|null|break|continue)\b/,boolean:/\b(?:true|false)\b/,function:/\w+(?=\()/,number:/\b0x[\da-f]+\b|(?:\b\d+\.?\d*|\B\.\d+)(?:e[+-]?\d+)?/i,operator:/--?|\+\+?|!=?=?|<=?|>=?|==?=?|&&?|\|\|?|\?|\*|\/|~|\^|%/,punctuation:/[{}[\];(),.:]/};
+Prism.languages.javascript=Prism.languages.extend("clike",{"class-name":[Prism.languages.clike["class-name"],{pattern:/(^|[^$\w\xA0-\uFFFF])[_$A-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\.(?:prototype|constructor))/,lookbehind:!0}],keyword:[{pattern:/((?:^|})\s*)(?:catch|finally)\b/,lookbehind:!0},{pattern:/(^|[^.])\b(?:as|async(?=\s*(?:function\b|\(|[$\w\xA0-\uFFFF]|$))|await|break|case|class|const|continue|debugger|default|delete|do|else|enum|export|extends|for|from|function|get|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|set|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)\b/,lookbehind:!0}],number:/\b(?:(?:0[xX][\dA-Fa-f]+|0[bB][01]+|0[oO][0-7]+)n?|\d+n|NaN|Infinity)\b|(?:\b\d+\.?\d*|\B\.\d+)(?:[Ee][+-]?\d+)?/,function:/[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*(?:\.\s*(?:apply|bind|call)\s*)?\()/,operator:/-[-=]?|\+[+=]?|!=?=?|<<?=?|>>?>?=?|=(?:==?|>)?|&[&=]?|\|[|=]?|\*\*?=?|\/=?|~|\^=?|%=?|\?|\.{3}/}),Prism.languages.javascript["class-name"][0].pattern=/(\b(?:class|interface|extends|implements|instanceof|new)\s+)[\w.\\]+/,Prism.languages.insertBefore("javascript","keyword",{regex:{pattern:/((?:^|[^$\w\xA0-\uFFFF."'\])\s])\s*)\/(\[(?:[^\]\\\r\n]|\\.)*]|\\.|[^/\\\[\r\n])+\/[gimyu]{0,5}(?=\s*($|[\r\n,.;})\]]))/,lookbehind:!0,greedy:!0},"function-variable":{pattern:/[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*[=:]\s*(?:async\s*)?(?:\bfunction\b|(?:\((?:[^()]|\([^()]*\))*\)|[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*)\s*=>))/,alias:"function"},parameter:[{pattern:/(function(?:\s+[_$A-Za-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*)?\s*\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\))/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/[_$a-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*=>)/i,inside:Prism.languages.javascript},{pattern:/(\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\)\s*=>)/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/((?:\b|\s|^)(?!(?:as|async|await|break|case|catch|class|const|continue|debugger|default|delete|do|else|enum|export|extends|finally|for|from|function|get|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|set|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)(?![$\w\xA0-\uFFFF]))(?:[_$A-Za-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*\s*)\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\)\s*\{)/,lookbehind:!0,inside:Prism.languages.javascript}],constant:/\b[A-Z](?:[A-Z_]|\dx?)*\b/}),Prism.languages.insertBefore("javascript","string",{"template-string":{pattern:/`(?:\\[\s\S]|\${[^}]+}|[^\\`])*`/,greedy:!0,inside:{interpolation:{pattern:/\${[^}]+}/,inside:{"interpolation-punctuation":{pattern:/^\${|}$/,alias:"punctuation"},rest:Prism.languages.javascript}},string:/[\s\S]+/}}}),Prism.languages.markup&&Prism.languages.markup.tag.addInlined("script","javascript"),Prism.languages.js=Prism.languages.javascript;
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diff --git a/tpFourier/fourier2019/fourier.md b/tpFourier/fourier2019/fourier.md
index 278f2b1..ccb68f9 100644
--- a/tpFourier/fourier2019/fourier.md
+++ b/tpFourier/fourier2019/fourier.md
@@ -66,8 +66,16 @@ $$
 f[n_1,n_2]=\sum_{k_1=0}^{N_1-1} e^{\frac{2\pi i n_1 k_1}{N_1}}\left(\sum_{k_2=0}^{N_2-1} {\hat{f}}[k_1,k_2] e^{\frac{2\pi i n_2 k_2}{N_2}}\right).
 $$
 
+On peut donc faire une analyse de Fourier d'une image presque aussi facilement qu'on le ferait pour un signal unidimensionnel.
+
 # Travail à réaliser
 
 # Conseils
 
+Les librairies `python` que j'ai essayée pour ce TP sont:
+
+1. `numpy` pour les manipulations de matrices et le calcul de TFR (les fonctions `fft.ifft2()`{.language-python} et `fft.fft2()`).
+2. `imageio` pour la manipulation d'images (en particulier `imread()` et `imwrite()`).
+3. `matplotlib` pour la visualisation des images et ds spectres (en particulier `pyplot.imshow()` et `plot_surface()` respectivement).
+
 [^1]: On représente $f[n]$ et $\hat{f}[k]$ comme des listes (ou vecteurs) de longueur $N$.
\ No newline at end of file
-- 
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