-%% This documentation was generated with Faust version 0.9.58
-%% Thu Jun 13 10:45:16 2013
-%% http://faust.grame.fr
-
-\documentclass{article}
-
-\usepackage[utf8]{inputenc}
-\usepackage{graphicx}
-\usepackage[usenames]{color}
-\usepackage{listings}
-\usepackage{supertabular}
-\usepackage{amsmath}
-\usepackage{latexsym, amssymb}
-\usepackage{breqn}
-
-% No indent
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-
-% Make LaTeX output a dot when typing an asterisk
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-
-% lstlistings setup
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-
-\newcommand{\faustfilename}{/home/wang/Documents/OcamlProjects/interpreter/interpreter11/dsp_files/make_init.dsp}
-\newcommand{\faustdocdir}{make_init-mdoc}
-\newcommand{\faustprogname}{make_init}
-\newcommand{\faustversion}{0.9.58}
-\newcommand{\faustdocdate}{June 13, 2013}
-
-\begin{document}
-\title{make_init}
-\date{\today}
-\maketitle
-
-\bigskip
-This document provides a mathematical description of the Faust program text stored in the \texttt{\faustfilename} file. See the notice in Section\,\ref{notice} (page\,\pageref{notice}) for details.
-
-
-\section{Mathematical definition of \texttt{process}}
-\label{equation}
-
-The \emph{\faustprogname} program evaluates the signal transformer denoted by \texttt{process}, which is mathematically defined as follows:
-
-% Set of Faust formulas (corresponding to an <equation> tag).
-\begin{enumerate}
-
-\item Output signal $y$ such that
- \begin{dgroup*}
- \begin{dmath*}
- y(t) = r_{1}(t)
- \end{dmath*}
- \end{dgroup*}
-
-\item Input signal (none)
-
-\item Intermediate signals $r_i$ for $i \in [1,2]$, $q_1$ and $m_1$ such that
- \begin{dgroup*}
- \begin{dmath*}
- r_{2}(t) = 1
- \end{dmath*}
- \begin{dmath*}
- r_{1}(t) = 2.000001 + q_{1}(t)
- \end{dmath*}
- \end{dgroup*}
-
-\begin{displaymath}
-q_{1}(t) =
-\left\{\begin{array}{ll}
-2 & \mbox{if \,} \mathrm{int}\left(m_{1}(t)\right) = 0\\
-r_{1}(t\!-\!1) & \mbox{if \,} \mathrm{int}\left(m_{1}(t)\right) = 1
-\end{array}\right.
-\end{displaymath}
-
-\begin{displaymath}
-m_{1}(t) =
-\left\{\begin{array}{ll}
-0 & \mbox{, when \,} t = 0\\
-r_{2}(t\!-\!1) & \mbox{, when \,} t > 0
-\end{array}\right.
-\end{displaymath}
-
-\end{enumerate}
-
-
-\section{Block diagram of \texttt{process}}
-\label{diagram}
-
-The block diagram of \texttt{process} is shown on Figure\,\ref{figure1} (page\,\pageref{figure1}).
-\begin{figure}[ht!]
- \centering
- \includegraphics[width=\textwidth]{../svg/svg-01/process}
- \caption{Block diagram of \texttt{process}}
- \label{figure1}
-\end{figure}
-
-
-\section{Notice}
-\label{notice}
-
-
-\begin{itemize}
- \item This document was generated using Faust version \faustversion\ on \faustdocdate.
- \item The value of a Faust program is the result of applying the signal transformer denoted by the expression to which the \texttt{process} identifier is bound to input signals, running at the $f_S$ sampling frequency.
- \item Faust (\emph{Functional Audio Stream}) is a functional programming language designed for synchronous real-time signal processing and synthesis applications. A Faust program is a set of bindings of identifiers to expressions that denote signal transformers. A signal $s$ in $S$ is a function mapping\footnote{Faust assumes that $\forall \, s \in S, \forall \, t \in \mathbb{Z}, s(t) = 0 \mathrm{\ when\ } t < 0$.} times $t \in \mathbb{Z}$ to values $s(t) \in \mathbb{R}$, while a signal transformer is a function from $S^n$ to $S^m$, where $n,m\in \mathbb{N}$. See the Faust manual for additional information (\textsf{http://faust.grame.fr}).
- \item Every mathematical formula derived from a Faust expression is assumed, in this document, to having been normalized (in an implementation-depen\-dent manner) by the Faust compiler.
- \item A block diagram is a graphical representation of the Faust binding of an identifier I to an expression E; each graph is put in a box labeled by I. Subexpressions of E are recursively displayed as long as the whole picture fits in one page.
- \item $\forall \, x \in \mathbb{R}$,
- \begin{displaymath}
- \mathrm{int}(x) =
- \left\{\begin{array}{cl}
- \lfloor x \rfloor & \mbox{if \,} x > 0 \\
- \lceil x \rceil & \mbox{if \,} x < 0 \\
- 0 & \mbox{if \,} x = 0 \\
- \end{array}\right..
- \end{displaymath}
- \item The \texttt{\faustdocdir/} directory may also include the following subdirectories:
-\begin{itemize}
- \item \texttt{cpp/} for Faust compiled code;
- \item \texttt{pdf/} which contains this document;
- \item \texttt{src/} for all Faust sources used (even libraries);
- \item \texttt{svg/} for block diagrams, encoded using the Scalable Vector Graphics format (\textsf{http://www.w3.org/Graphics/SVG/});
- \item \texttt{tex/} for the \LaTeX\ source of this document.
-\end{itemize}
-\end{itemize}
-
-
-\section{Faust code listing}
-\label{listing}
-
-This section provides the listing of the Faust code used to generate this document.
-
-\bigskip\bigskip
-\begin{lstlisting}[caption=\texttt{make_init.dsp}]
-rec(a, b, i) = a ~ (i : b);
-
-vect0 = case {
- ((y, z)) => vect0(y) : vect0(z);
- (y) => _ , y : +;
-};
-
-init_value = case {
- ((x,y)) => init_value(x) : vect0(y);
- (0) => 0;
- (x) => 0 : vect0(x);
-};
-
-make_init(x) = (0, 1 : prefix), init_value(x), _ : select2;
-
-A = +;
-B = _;
-//B = serialize : _, 2 : vectorize;
-I = make_init((2));
-
-//process = _,_ : > ;
-
-//process = (0.000001, 2 : +) : rec(A,B,I);
-
-process = 0.0000010000000000,2:+:+~((0,1:prefix),(0:_,2:+),_:select2:_);
-\end{lstlisting}
-
-
-\end{document}
-
projects / Faustine.git / blobdiff