From 764ed277e3abcb1edb93c59277ad475c6295796a Mon Sep 17 00:00:00 2001 From: poulpe <poulpe@localhost.localdomain> Date: Wed, 27 Apr 2022 22:09:56 +0200 Subject: [PATCH] [Update] Fix somes fr text --- rapport.md | 22 +++++++++++----------- rapport.pdf | Bin 0 -> 3214445 bytes 2 files changed, 11 insertions(+), 11 deletions(-) create mode 100644 rapport.pdf diff --git a/rapport.md b/rapport.md index 502e465..369a848 100644 --- a/rapport.md +++ b/rapport.md @@ -363,22 +363,22 @@ Vu que sinus(PI) équivaut a 0. (calcule en radiant) cela revient a faire: 0 + \frac {sin(2\pi\omega_2x) sin(\pi\frac{\omega_2}{\omega_1})}{\pi\frac{\omega_2}{\omega_1}} \end{equation} -On a belle est bien annulé la premier composant (signal sinusoïdal) composent le signal de base S(x) +On a belle est bien annulé la première composante (signal sinusoïdal) qui compose le signal de base S(x) ### Convolution discrète -Pour exemplifier ces calcules nous allons implémenter une convolution sur un signal 1d afin de récupérer une de ces composantes. Les calcules sont effectuer en code c est l'affichage avec l'aide d'un tableur. +Pour exemplifier ces calcules nous allons implémenter une convolution sur un signal 1d afin de récupérer une de ces composantes. Les calcules sont effectuer en code c'est l'affichage avec l'aide d'un tableur. -Nous apercevons deux signal sinusoïdal donc le premier **Signal1** possède une fréquence de 25hz pour une amplitude de 5. Le seconde **Signal 2** possède une fréquence de 2.5hz pour une amplitude de 10. +Nous apercevons deux signaux sinusoïdal donc le premier **Signal1** possède une fréquence de 25hz pour une amplitude de 5. Le seconde **Signal 2** possède une fréquence de 2.5hz pour une amplitude de 10. { width=70% } -En additionnant (superposant) les deux composantes sinusoïdale, on obtient ce nouveau signal. Qui n'est rien d'autre qu' une composantes a basse fréquences contenant un oscillation d'un signal plus rapides. +En additionnant (superposant) les deux composantes sinusoïdales, on obtient ce nouveau signal. Qui n'est rien d'autre qu'une composante a basses fréquences contenant une oscillation d'un signal plus rapide. { width=70% } -Nous allons alors convoluer ce signal afin d'y retrouver une des deux composantes de base. Pour cela nous allons utiliser l’équation suivantes avec un filtre carrer. +Nous allons alors convoluer ce signal afin d'y retrouver une des deux composantes de base. Pour cela, nous allons utiliser l’équation suivante avec un filtre carré. -Fonction de convolustion: +Fonction de convolution: \begin{equation} (s\ast u)[t] =\sum_{n=-N}^{+N} s[n]\cdot u[t-n] @@ -393,17 +393,17 @@ f(x)=\left\{\begin{array}{ll} \end{array}\right. \end{equation} -En utilisant $\psi$ de la taille d'une période d'une des deux composant sinusoïdal comme vu au chapitre précédant, nous arrivons a tuer l'autre composantes. Par exemple pour tuer la composantes plus rapides **Signal1** nous allons utiliser $\psi$ = 1/25hz = 0,04. +En utilisant $\psi$ de la taille d'une période d'une des deux composantes sinusoïdales comme vu au chapitre précédent, nous arrivons à tuer l'autre composante. Par exemple pour tuer la composantes plus rapides **Signal1** nous allons utiliser $\psi$ = 1/25hz = 0,04. { width=70% } -Exemple de convolution ou le chois de $\psi$ = 0,03 ne permet pas de tuer une composantes: +Exemple de convolution ou le choix de $\psi$ = 0,03 ne permet pas de tuer une composante : { width=70% } On remarque que l'amplitude c'est rapprocher de celle du **signal2** mais y reste une oscillation réduite du **signal1**. -On peux conclure que la convolution avec un filtre carrer reviens a échantillonner le signal sur une certaine base de fréquences. Si cette fréquences est basée sur l'une des composantes, elle s'annule est ressort que les autres fréquences ou composantes du signal. +On peut conclure que la convolution avec un filtre carré revient à échantillonner le signal sur une certaine base de fréquences. Si cette fréquence est basée sur l'une des composantes, elle s'annule et ressort que les autres fréquences ou composantes du signal. ## Convolution en 2 dimensions @@ -479,7 +479,7 @@ Résultat de la convolution obtenu: { width=50% } -On détermine que le filtre F2 fait une moyenne des différentes valeurs au alentour du centre de la matrice, en donnant plus de poids aux valeurs les plus proches du centre. On aperçoit sur l'image traitée un floutage général qui impact moins les details de l'image. +On détermine que le filtre F2 fait une moyenne des différentes valeurs au alentour du centre de la matrice, en donnant plus de poids aux valeurs les plus proches du centre. On aperçoit sur l'image traitée un floutage général qui impacte moins les détails de l'image. #### filtre F3 $$ @@ -522,7 +522,7 @@ $$ \end{pmatrix} $$ -L'image bruitée est la suivantes: +L'image bruitée est la suivante: { width=50% } diff --git a/rapport.pdf b/rapport.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4947d541d3297fe2ef22b5e6afef8aadb0e3a23a GIT binary patch literal 3214445 zcmeFZbzEIdwk;am-Q8XH#@*d5xVyUs65J)Y1b26rV8PuXSa5<v&|r_RPxrZBx^w$* z-|yXX-aWVXA6uaIUbSY`nsd|`V-<y>s5k?Fkqwq&a<*>~mW!B~*xtwrmX{ZnN!HZP z+{J<z$i+_lZx2`|aZ4K)Qzv33aT`MyQ&Cf6dlOSwetuYI7bjCgTUd{;8L@H-z0B~z zr*|0ql&C}adwItg-IN~%wdU|P6=5T#4_gyqp7^Ee<np?LXdCD{->>B(_P`=z!c%F6 zgk}p_=gFRsjFgkci_Fvz1Xe;sR=_9HI6-A0k602YrD{L{yEOwFU^h4Tp6$4A?b><n zzF-e7$rWvsn#(i>4xQttA0yA!vm2*BX>dA-kN2`7(cQ|>l8I&3)`$in45glt@2eL) zoXW?4zuUU(pVEJ8!`=iQIQ-5@u_Kdl5Hp{5N0F}=j7hBf@VJraS{RkIvn+`5_DPQS zZBuubU*oWb!qgifFSKJ+EttbQV%CfI9q(~a1+e-rewI{lV3jB~5*;hG+v5pw*Dst- 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