From 9d6794a04e71b44e10a5361642604ddb7660068e Mon Sep 17 00:00:00 2001 From: Klagarge Date: Fri, 2 Feb 2024 12:39:20 +0100 Subject: [PATCH] =?UTF-8?q?add=20signaux=20et=20=C3=A9chantiollnage?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- infotro/Eln/DFT.md | 33 +++++++++++++++++++++ infotro/Eln/README.md | 5 +++- infotro/Eln/Reponse_impulsionelle.md | 10 +++++++ infotro/Eln/Ztransform.md | 29 ++++++++++++++++++ infotro/Eln/transforme_fourier.png | Bin 0 -> 74753 bytes infotro/Eln/transfrom_fourrier_discret.png | Bin 0 -> 32316 bytes infotro/Eln/ztabelle01.png | Bin 0 -> 66782 bytes infotro/Eln/ztabelle02.png | Bin 0 -> 53104 bytes infotro/Eln/ztabelle03.png | Bin 0 -> 131161 bytes infotro/README.md | 3 ++ 10 files changed, 79 insertions(+), 1 deletion(-) create mode 100644 infotro/Eln/DFT.md create mode 100644 infotro/Eln/Reponse_impulsionelle.md create mode 100644 infotro/Eln/Ztransform.md create mode 100644 infotro/Eln/transforme_fourier.png create mode 100644 infotro/Eln/transfrom_fourrier_discret.png create mode 100644 infotro/Eln/ztabelle01.png create mode 100644 infotro/Eln/ztabelle02.png create mode 100644 infotro/Eln/ztabelle03.png diff --git a/infotro/Eln/DFT.md b/infotro/Eln/DFT.md new file mode 100644 index 0000000..669609e --- /dev/null +++ b/infotro/Eln/DFT.md @@ -0,0 +1,33 @@ +

+DFT +

+ +----------- + +# Transformée de Fourier +La transformée de Fourier est une technique de traitement du signal utilisée pour analyser et manipuler les signaux continus. +Elle permet d'exprimer un signal dans le temps en domaine fréquentiel. + +La transformée de Fourier est définie par la formule suivante : + +![Transformée de fourier](transforme_fourier.png) + +# Transformée de Fourier discrète + +La transformée de Fourier discrète (DFT - Discret Fourier Transform) est une transformation discrète utilisée pour analyser le spectre fréquentiel +d'un signal discret. +Elle est l'équivalent discret de la transformée de Fourier, qui est utilisée pour analyser les signaux continus. + +![img.png](transfrom_fourrier_discret.png) + + + + +La DFT est utilisée dans de nombreux domaines, notamment en traitement du signal, en télécommunications, en traitement d'images +et en compression de données. + +> [!NOTE|label:FFT] +> La transformée de Fourier rapide (FFT) est un algorithme efficace pour calculer la DFT. Elle est largement utilisée dans +> de nombreuses applications, notamment en traitement du signal et en compression de données. + + diff --git a/infotro/Eln/README.md b/infotro/Eln/README.md index 96a8ee2..e726937 100644 --- a/infotro/Eln/README.md +++ b/infotro/Eln/README.md @@ -4,4 +4,7 @@ # Convertisseurs - [AD/DA](/infotro/Eln/ADDA) -- [Sigma / Delta](/infotro/Eln/Sigma-Delta) \ No newline at end of file +- [Sigma / Delta](/infotro/Eln/Sigma-Delta) +- [Transformée en Z](/infotro/Eln/Ztransform) +- [DFT](/infotro/Eln/DFT) +- [Réponse impulsionnelle](/infotro/Eln/Reponse_impulsionelle) \ No newline at end of file diff --git a/infotro/Eln/Reponse_impulsionelle.md b/infotro/Eln/Reponse_impulsionelle.md new file mode 100644 index 0000000..1bbcff2 --- /dev/null +++ b/infotro/Eln/Reponse_impulsionelle.md @@ -0,0 +1,10 @@ +

+Réponse impulsionnelle +

+ +----------- + +La réponse impulsionnelle $h[k]$ d'un système discret LIT est sa réponse à l'impulsion unitaire à l'origine $δ[k]$. + +$$ h[k] = \mathcal{H} \{ δ[k] \} $$ + diff --git a/infotro/Eln/Ztransform.md b/infotro/Eln/Ztransform.md new file mode 100644 index 0000000..edb4b96 --- /dev/null +++ b/infotro/Eln/Ztransform.md @@ -0,0 +1,29 @@ +

+Transformée en Z +

+ +----------- + +La transformée en Z, également connue sous le nom de transformée en fréquence Z, est une technique de traitement du +signal utilisée pour analyser et manipuler les signaux numériques. +Elle permet de décomposer un signal en fonction de la fréquence et de fournir des informations sur la nature du signal. + +La principale différence entre la transformée en Z et la transformation de Laplace (ou S) est que la transformée en Z +est adaptée aux signaux discrets, c'est-à-dire aux valeurs qui ne varient pas continuellement dans le temps. +En revanche, la transformation de Laplace est utilisée pour les signaux continus et permet d'étudier leur réponse en +fréquence et en phase. + +En résumé, la transformée en Z est conçue pour les signaux discrets et les systèmes numériques, tandis que la +transformation de Laplace s'applique aux signaux continus et aux systèmes analogiques. + +> [!NOTE|label:S] +> Domaine fréquentiel continue avec Laplace. + +> [!NOTE|label:Z] +> Domaine fréquentiel discret. + +![ztabelle01.png](ztabelle01.png) +![ztabelle02.png](ztabelle02.png) +![ztabelle03.png](ztabelle03.png) + +Dans la théorie Eln la partie transformée en Z commence à la slide 23 de "Eln2_LTI_0910_f.pdf". \ No newline at end of file diff --git a/infotro/Eln/transforme_fourier.png b/infotro/Eln/transforme_fourier.png new file mode 100644 index 0000000000000000000000000000000000000000..1a4dd3884bb5b5d37f9ff1dd553d6bc8121bd221 GIT binary patch literal 74753 zcmeFZWmME{_%2E}QqtWhLrJ$Fh?EE_4k0Ni4bm}mHw+*p2#ONY9Yae9f(S^5fP!>0 z#C}F!-+%4>@tnQZS?9~U)(g(?o9DUXy07cHC-T946=DK90yH!OdPlEe;sohJ{UY0%y1oYHGcB6@8^5?yRxk^ z@AcB-i)ac(Jk}7>KmUoKS`paA`S*XpFRUp!ObGtd5A><<)Bp1e;K~?p{&_L#ZSpM= zVK@H18|vkH|Ifetv7qx(muK>SJcTt2xuCS*e85$U&*9f6v%hIG>TvK(xSj}{7{V6u@yB}7d zF3=((m(A1pW90Sh)bkIUT-k0q$7yZng*)4W!o$C=$)7tNucR6GG)3H!Ip67Y*z4my zesS-m?fZB7x-xW9Zq|MK6mOoFHE_)p-k1rvy5O8hQaL+Wj$eNG0(yC}Oj5T|)WG6nzkF&`5U@6tH0cL=)dt6 z(!j4C(dmagdU18qD?bB6$DHxrC|#p6bZSp>fzNp^$DTZ5gqwDTrJi3ZQ|WQ=bNxL~ 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