sampling theorem
SamplingTheorem
2001-12-25 13:51:53
2002-02-19 03:28:13
Theorem
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
{\bf Sampling Theorem}
The greyvalues of digitized one- or two-dimensional signals are typically generated by an analogue-to-digital converter (ADC), by sampling a continuous signal at fixed intervals (e.g. in time), and quantizing (digitizing) the samples. The sampling (or point sampling) theorem states that a band-limited analogue signal $x_a(t)$, i.e. a signal in a finite frequency band (e.g. between 0 and BHz), can be completely reconstructed from its samples $x(n) = x(nT)$, if the sampling frequency is greater than $2B$ (the Nyquist rate); expressed in the \PMlinkescapetext{time domain}, this \PMlinkescapetext{means} that the sampling interval $T$ is at most $\frac{1}{2B}$ seconds. Undersampling can produce serious errors (aliasing) by introducing artifacts of low frequencies, both in one-dimensional signals and in digital \PMlinkescapetext{images}.
\begin{center}
\includegraphics[scale=.5]{img988.eps}
\end{center}
{\bf References}
\begin{itemize}
\item Originally from the Data Analysis Briefbook (\PMlinkexternal{http://rkb.home.cern.ch/rkb/titleA.html}{http://rkb.home.cern.ch/rkb/titleA.html})
\end{itemize}