From 15639751af1fba9ba1a6c76b7ccec032b0f34cea Mon Sep 17 00:00:00 2001 From: Klagarge Date: Sun, 4 Feb 2024 19:09:35 +0100 Subject: [PATCH 1/3] add filter summary --- infotro/Eln/Filtres.md | 2 ++ infotro/Eln/medias/filters-summary.png | Bin 0 -> 106827 bytes 2 files changed, 2 insertions(+) create mode 100644 infotro/Eln/medias/filters-summary.png diff --git a/infotro/Eln/Filtres.md b/infotro/Eln/Filtres.md index 2b0117f..6a4c604 100644 --- a/infotro/Eln/Filtres.md +++ b/infotro/Eln/Filtres.md @@ -34,6 +34,8 @@ $$H_{4}(s)=\frac{\omega_{0}}{\omega_{0}+s} = \frac{1}{1+\frac{s}{\omega_{0}}}$$ # Filtres numériques +![filters-summary.png](medias%2Ffilters-summary.png) + ## Filtres numériques récursifs (IIR) Les filtres numériques récursifs (IIR) sont des filtres numériques qui utilisent des rétroactions. diff --git a/infotro/Eln/medias/filters-summary.png b/infotro/Eln/medias/filters-summary.png new file mode 100644 index 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zJK+FIWhadCu~Pw+*6)*19QOOF6$K=mKOJ}@-#HcWXD=%a9MUp_9WGf@(RI)gc{?=^ z@*$ZMKDn2**w7(06`6`$MFC(Pr;mqt(5?sVUMTXdy7cBOa)--wksRBu0jw9Ha^&iA z1*_s3=FevFfEPe1;0S6D{(*~a6I=g}|Md*K)!Rh>z)0zmkK5f-fx_oh0KV=dDdRs; CLxe5> literal 0 HcmV?d00001 From 938af714d17b858e8e0ac631154417ff6e33eb2e Mon Sep 17 00:00:00 2001 From: Klagarge Date: Sun, 4 Feb 2024 19:09:45 +0100 Subject: [PATCH 2/3] typo --- infotro/Eln/Filtres.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/infotro/Eln/Filtres.md b/infotro/Eln/Filtres.md index 6a4c604..b8bb5ef 100644 --- a/infotro/Eln/Filtres.md +++ b/infotro/Eln/Filtres.md @@ -96,15 +96,15 @@ $$F(s)=\frac{Y(s)}{U(s)}=\frac{d_{0}+d_{1}s+d_{2}s^{2}}{c_{0}+c_{1}s+c_{2}s^{2}} $$\begin{gather} C = c_{0}+\frac{2c_{1}}{T_{s}}+\frac{4c_{2}}{T_{s}^{2}} \\ \\ -a_{1} = \frac{2\left( c_{0}-\frac{4c_{2}}{T_{s^{2}}} \right)}{C} +a_{1} = \frac{2\left( c_{0}-\frac{4c_{2}}{T_{s}^{2}} \right)}{C} \qquad \qquad -a_{2} = \frac{ c_{0}-\frac{2c_{1}}{T_{s}}+\frac{4c_{2}}{T_{s^{2}}} }{C} +a_{2} = \frac{ c_{0}-\frac{2c_{1}}{T_{s}}+\frac{4c_{2}}{T_{s}^{2}} }{C} \qquad \qquad b_{0} = \frac{d_{0}+\frac{2d_{1}}{T_{s}}+\frac{4d_{2}}{T_{s}^{2}}}{C} \\ \\ -b_{1} = \frac{2\left( d_{0}-\frac{4d_{2}}{T_{s^{2}}} \right)}{C} +b_{1} = \frac{2\left( d_{0}-\frac{4d_{2}}{T_{s}^{2}} \right)}{C} \qquad \qquad -b_{2} = \frac{d_{0}-\frac{2d_{1}}{T_{s}}+\frac{4d_{2}}{T_{s^{2}}}}{C} +b_{2} = \frac{d_{0}-\frac{2d_{1}}{T_{s}}+\frac{4d_{2}}{T_{s}^{2}}}{C} \end{gather}$$ ## Filtre numérique non-récursif (FIR) From f08600e8bc14d10eb3eced8f0eb8fb79637f8b73 Mon Sep 17 00:00:00 2001 From: Klagarge Date: Sun, 4 Feb 2024 19:10:14 +0100 Subject: [PATCH 3/3] add bilinear conversion w0 w0' --- infotro/Eln/SignauxEtEchantillonnage.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/infotro/Eln/SignauxEtEchantillonnage.md b/infotro/Eln/SignauxEtEchantillonnage.md index 001e310..aea765e 100644 --- a/infotro/Eln/SignauxEtEchantillonnage.md +++ b/infotro/Eln/SignauxEtEchantillonnage.md @@ -231,8 +231,12 @@ $$ Pour un filtre passe bas, le gain "bilinear" est : $$k_{d} = k_{a}\cdot \frac{1}{\prod_{i}\left( \frac{2}{T}-p_{ai} \right)}$$ -Pour passer de $\omega_o'$ à $\omega_o$, on utilise la relation suivante : -$$\omega_{0} = 2f_{s}\tan\left( \frac{\omega_{0}'}{2f_{s}} \right)$$ +Pour passer de $\omega_o'$ à $\omega_o$ et vice-versa, on utilise la relation suivante : +$$\begin{align} +\omega_{0} &= 2f_{s}\tan\left( \frac{\omega_{0}'}{2f_{s}} \right) \\ +\\ +\omega_{0}'&=2f_{S}\cdot \arctan\left( \frac{\omega_{0}}{2fs} \right) +\end{align}$$ ## Autres méthodes d'approximation d'un système continu LIT par un syst. discret