From 55d857ce571c64b3fe660ebccca208159891cf51 Mon Sep 17 00:00:00 2001 From: Francis Russell Date: Wed, 20 Feb 2013 19:22:20 +0000 Subject: [PATCH] Add slide on aliasing. --- images-svg/aliasing.svg | 2192 +++++++++++++++++++++++++++++++++++++++ presentation.tex | 15 + 2 files changed, 2207 insertions(+) create mode 100644 images-svg/aliasing.svg diff --git a/images-svg/aliasing.svg b/images-svg/aliasing.svg new file mode 100644 index 0000000..fac86ca --- /dev/null +++ b/images-svg/aliasing.svg @@ -0,0 +1,2192 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + 0 + + 1 + + 2 + + 3 + + 4 + + 5 + + 6 + + 7 + + 8 + + + + + + + + + + + 0.0 + + + + + + + + + + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + + amplitude + frequency + + 0 + + 1 + + 2 + + 3 + + 4 + + 5 + + 6 + + 7 + + 8 + + + + + + + + + + + 0.0 + + + + + + + + + + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + + amplitude + frequency + + 0 + + 1 + + 2 + + 3 + + 4 + + 5 + + 6 + + 7 + + 8 + + + + + + + + + + + 0.0 + + + + + + + + + + 0.1 + 0.2 + 0.3 + 0.4 + + valid + frequency + + amplitude + aliased + + + + + + + + + + 0 + + 1 + + 2 + + 3 + + 4 + + 5 + + 6 + + 7 + + 8 + + + + + + + + + + + 0.0 + + + + + + + + + + 0.1 + 0.2 + 0.3 + 0.4 + + frequency + + amplitude + aliased + + + + + + + + + × + + ? + + + diff --git a/presentation.tex b/presentation.tex index f90349d..3c5cbe1 100644 --- a/presentation.tex +++ b/presentation.tex @@ -539,6 +539,21 @@ We adopt the following strategy: \frame{ +\frametitle{Reasoning about correctness: an example} + +If we want to evaluate $\int a(x)b(x)dx$ can we use $\sum\limits_{x=0}^{N} a[x]b[x]$? + +\centering +\resizebox{0.9\textwidth}{!}{ +\includegraphics{images-svg/aliasing} +} + +It depends whether we do it on an odd or even number of points. + +} + +\frame{ + \frametitle{Reasoning about correctness} \begin{itemize} -- 2.47.3