From a6db20a6d9cfe457b5deb643932813b921a04d47 Mon Sep 17 00:00:00 2001
From: Christiaan Baaij <christiaan.baaij@gmail.com>
Date: Sun, 13 Dec 2009 19:18:58 +0100
Subject: [PATCH] Add files for FIR

---
 christiaan/dotproduct.lhs | 56 +++++++++++++++++++++++++++++++
 christiaan/fir.lhs        | 69 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 125 insertions(+)
 create mode 100644 christiaan/dotproduct.lhs
 create mode 100644 christiaan/fir.lhs

diff --git a/christiaan/dotproduct.lhs b/christiaan/dotproduct.lhs
new file mode 100644
index 0000000..4a150c9
--- /dev/null
+++ b/christiaan/dotproduct.lhs
@@ -0,0 +1,56 @@
+%include talk.fmt
+\subsection{Dot Product}
+\begin{frame}
+   \frametitle{Dot Product}
+     \[
+     y = \overrightarrow x  \bullet \overrightarrow h 
+     \]
+\end{frame}
+
+\begin{frame}
+   \frametitle{Dot Product}
+     \[
+     y = \overrightarrow x  \bullet \overrightarrow h 
+     \]
+     \[
+     \overrightarrow x  \bullet \overrightarrow h  = \sum\nolimits_{i = 1}^n {a_1  \cdot b_1  + a_2  \cdot b_2  +  \ldots  + a_n  \cdot b_n } 
+     \]
+\end{frame}
+
+\begin{frame}
+  \frametitle{Dot Product}
+   \begin{itemize}
+    \item Two steps to define: \\
+    \[
+    \overrightarrow x  \bullet \overrightarrow h  = \sum\nolimits_{i = 1}^n {a_1  \cdot b_1  + a_2  \cdot b_2  +  \ldots  + a_n  \cdot b_n } 
+    \]
+    \begin{itemize}
+      \item \emph{Pairwise Multiplication}: \\
+      \begin{verbatim}
+      zipwith (*) xs hs =
+        < x0*h0, x1*h1, x(n-1)*h(n-1)>       
+      \end{verbatim}
+      \item \emph{Summation}: \\
+      \begin{verbatim}
+      foldl (+) 0 zs =
+        (..((0+z0)+z1)+..+z(n-1))
+      \end{verbatim}
+    \end{itemize}
+   \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Dot Product}
+   \begin{itemize}
+    \item Two steps to define: \\
+    \[
+    \overrightarrow x  \bullet \overrightarrow h  = \sum\nolimits_{i = 1}^n {a_1  \cdot b_1  + a_2  \cdot b_2  +  \ldots  + a_n  \cdot b_n } 
+    \]
+    \begin{itemize}
+      \item \emph{Combine the two}: \\
+      \begin{verbatim}
+      xs ** hs = foldl (+) 0 (zipWith (*) xs hs)
+      \end{verbatim}
+    \end{itemize}
+   \end{itemize}
+\end{frame}
\ No newline at end of file
diff --git a/christiaan/fir.lhs b/christiaan/fir.lhs
new file mode 100644
index 0000000..c76e753
--- /dev/null
+++ b/christiaan/fir.lhs
@@ -0,0 +1,69 @@
+%include talk.fmt
+\section{FIR Filter}
+
+\begin{frame}
+   \frametitle{Example: FIR Filter}
+   \begin{itemize}
+     \item FIR Filters, and digital filters in general are essential components in radio's, receivers, and cellphones.
+     \item Equation for a FIR Filter: \\
+     \[
+     y_t  = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i}  \cdot h_i } 
+     \]
+   \end{itemize}
+\end{frame}
+
+\begin{frame}
+   \frametitle{FIR Filter}
+     \[
+     y_t  = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i}  \cdot h_i } 
+     \]
+\end{frame}
+
+\input{christiaan/dotproduct}
+
+\begin{frame}
+   \frametitle{FIR Filter}
+     \[
+     y_t  = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i}  \cdot h_i } 
+     \] \\
+     \begin{verbatim}
+       fir (State pxs) x = (pxs**hs, State (pxs<++x))
+         where hs = $(vectorTH [2::Int16,3,-2,4])
+     \end{verbatim}
+     \centerline{\begin{tabular}{rl}
+     |pxs|  & Previous x's (state)\\
+     |x| & New input value\\
+     |pxs <++ x| & Remember new |x|, remove oldest\\
+     |pxs ** hs| & Output
+     \end{tabular}}
+
+\end{frame}
+
+\begin{frame}
+   \frametitle{FIR Filter}
+   \centerline{\Huge{Demo}}
+\end{frame}
+
+\begin{frame}
+   \frametitle{Synthesized Output}
+   \vspace{-0.8em}
+   \begin{figure} 
+      \centerline{\includegraphics[width=\paperwidth,trim=9mm 4cm 14mm 4cm, clip=true]{fir0.png}}
+    \end{figure}
+\end{frame}
+
+\begin{frame}
+   \frametitle{Synthesized Output}
+   \vspace{-0.8em}
+   \begin{figure} 
+      \centerline{\includegraphics[width=\paperwidth,trim=9mm 4cm 16.5cm 4cm, clip=true]{fir1.png}}
+    \end{figure}
+\end{frame}
+
+\begin{frame}
+   \frametitle{Synthesized Output}
+   \vspace{-0.8em}
+   \begin{figure} 
+      \centerline{\includegraphics[width=\paperwidth,trim=3cm 4cm 4cm 4cm, clip=true]{fir2.png}}
+    \end{figure}
+\end{frame}
\ No newline at end of file
-- 
2.30.2