State as of Jan. 20, 2023

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