# scipy/scipy

Updated .pdf and .tex tutorial files.

 @@ -2,7 +2,7 @@ %% Do not edit unless you really know what you are doing. \documentclass[english]{article} %\usepackage[T1]{fontenc} -%\usepackage[latin1]{inputenc} +\usepackage[latin1]{inputenc} \usepackage{geometry} \geometry{verbose,letterpaper,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} \usepackage{verbatim} @@ -1165,18 +1165,18 @@ \subsubsection{Convolution/Correlation} transforms. Let $x\left[n\right]$ define a one-dimensional signal indexed by -the integer $n.$ Full, convolution of two one-dimensional signals +the integer $n.$ Full convolution of two one-dimensional signals can be expressed as $y\left[n\right]=\sum_{k=-\infty}^{\infty}x\left[k\right]h\left[n-k\right].$ - This equation can only be implemented directly, if we limit the sequences + This equation can only be implemented directly if we limit the sequences to finite support sequences that can be stored in a computer, choose $n=0$ to be the starting point of both sequences, let $K+1$ be that value for which $y\left[n\right]=0$ for all $n>K+1$ and $M+1$ be that value for which $x\left[n\right]=0$ for all $n>M+1$, then the discrete convolution expression is $y\left[n\right]=\sum_{k=\max\left(n-M,0\right)}^{\min\left(n,K\right)}x\left[k\right]h\left[n-k\right].$ - For convenience assume $K\geq M.$ Then, the output of this operation -is \begin{eqnarray*} + For convenience assume $K\geq M.$ Then, more explicitly the output +of this operation is \begin{eqnarray*} y\left[0\right] & = & x\left[0\right]h\left[0\right]\\ y\left[1\right] & = & x\left[0\right]h\left[1\right]+x\left[1\right]h\left[0\right]\\ y\left[2\right] & = & x\left[0\right]h\left[2\right]+x\left[1\right]h\left[1\right]+x\left[2\right]h\left[0\right]\\ @@ -1353,9 +1353,32 @@ \subsubsection{Other filters} \paragraph{Wiener filter} +The Wiener filter is a simple deblurring filter for denoising images. +This is not the Wiener filter commonly described in image reconstruction +problems but instead it is a simple, local-mean filter. Let $x$ be +the input signal, then the output is + +$+y=\left\{ \begin{array}{cc} +\frac{\sigma^{2}}{\sigma_{x}^{2}}m_{x}+\left(1-\frac{\sigma^{2}}{\sigma_{x}^{2}}\right)x & \sigma_{x}^{2}\geq\sigma^{2},\\ +m_{x} & \sigma_{x}^{2}<\sigma^{2}.\end{array}\right.$ + Where $m_{x}$ is the local estimate of the mean and $\sigma_{x}^{2}$ +is the local estimate of the variance. The window for these estimates +is an optional input parameter (default is $3\times3$). The parameter +$\sigma^{2}$ is a threshold noise parameter. If $\sigma$ is not +given then it is estimated as the average of the local variances. + \paragraph{Hilbert filter} +The Hilbert transform constructs the complex-valued analytic signal +from a real signal. For example if $x=\cos\omega n$ then $y=\textrm{hilbert}\left(x\right)$ +would return (except near the edges) $y=\exp\left(j\omega n\right).$ +In the frequency domain, the hilbert transform performs$+Y=X\cdot H$ + where $H$ is 2 for positive frequencies, $0$ for negative frequencies +and $1$ for zero-frequencies. + \paragraph{Detrend} @@ -1402,6 +1425,9 @@ \subsubsection{Arbitrary binary input and output (fopen)} \subsubsection{Read and write Matlab .mat files} +\subsubsection{Saving workspace} + + \subsection{Text-file }