diff --git a/ASCEE_lasp.lyx b/ASCEE_lasp.lyx index d3cee1a..a98f1b4 100644 --- a/ASCEE_lasp.lyx +++ b/ASCEE_lasp.lyx @@ -2241,7 +2241,7 @@ Sample time is \begin_layout Standard \begin_inset Formula \begin{equation} -y[n]=\sum_{m=1}^{M}b_{m}y[n-m]+\sum_{p=0}^{P}a_{p}x[n-p] +y[n]=\sum_{m=1}^{M}a_{m}y[n-m]+\sum_{p=0}^{P}b_{p}x[n-p] \end{equation} \end_inset @@ -2253,7 +2253,7 @@ In the -domain, this equation can be written as \begin_inset Formula \begin{equation} -Y[z]=\frac{\sum\limits _{p=0}^{P}a_{p}z^{-p}}{1-\sum\limits _{m=1}^{M}b_{m}z^{-m}}X[z]=H[z]\cdot X[z] +Y[z]=\frac{\sum\limits _{p=0}^{P}b_{p}z^{-p}}{1-\sum\limits _{m=1}^{M}a_{m}z^{-m}}X[z]=H[z]\cdot X[z] \end{equation} \end_inset @@ -4513,7 +4513,7 @@ So we assume that we can fit , we find: \begin_inset Formula \begin{equation} -\underbrace{\sum\limits _{n=1}^{N}\frac{c_{n}}{s-a_{n}}+d+sh}_{\left(\sigma f\right)_{\mathrm{fit}}}=\underbrace{\left(\sum_{n=1}^{N}\frac{\tilde{c}_{n}}{s-a_{n}}+1\right)f(s)}_{\sigma_{\mathrm{fit}}(s)f(s)}, +\underbrace{\sum\limits _{n=1}^{N}\frac{c_{n}}{s-a_{n}}+d+sh}_{\left(\sigma f\right)_{\mathrm{fit}}}=\underbrace{\left(\sum_{n=1}^{N}\frac{\tilde{c}_{n}}{s-a_{n}}+1\right)f(s)}_{\sigma_{\mathrm{fit}}(s)f(s)},\label{eq:sigmaf_eq_sigma_f} \end{equation} \end_inset @@ -4523,10 +4523,22 @@ So we assume that we can fit \begin_layout Standard For a certain set of starting poles -\begin_inset Formula $a_{n}$ +\begin_inset Formula $\overline{a}_{n}$ \end_inset , we are able to fit the zeros. + Eq. +\begin_inset space ~ +\end_inset + + +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:sigmaf_eq_sigma_f" + +\end_inset + + is a linear least squares problem, which is used to fit \end_layout \begin_layout Section @@ -4579,7 +4591,7 @@ G[z]=\frac{\alpha}{1+\left(\alpha-1\right)z^{-1}}G_{\mathrm{required}}(z), which is an approximate first order digital low-pass filter: \begin_inset Note Note -status open +status collapsed \begin_layout Plain Layout Filling in for