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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1 (Feb 5, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>5.1 Anti-aliasing</TITLE><META NAME="description" CONTENT="5.1 Anti-aliasing"><META NAME="keywords" CONTENT="sensors"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="sensors.css" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/sensors.css"></HEAD><BODY BGCOLOR="#FFFFFF" TEXT="#000000" LANG="EN"> <A NAME="tex2html299" HREF="node22.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node22.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif" tppabs="http://ccrma.stanford.edu/Images//next_motif.gif"></A> <A NAME="tex2html297" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif" tppabs="http://ccrma.stanford.edu/Images//up_motif.gif"></A> <A NAME="tex2html291" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif" tppabs="http://ccrma.stanford.edu/Images//previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html300" HREF="node22.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node22.html">5.2 Sample and Hold</A><B>Up:</B> <A NAME="tex2html298" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html">5 Data Acquisition</A><B> Previous:</B> <A NAME="tex2html292" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html">5 Data Acquisition</A><BR> <P><H2><A NAME="SECTION00051000000000000000">5.1 Anti-aliasing</A></H2><P>The Nyquist criterion dictates that all signals must be bandlimited to less than half the
sampling rate of the sampling system. Many signals already have a limited spectrum, so
this is not a problem. However, for broad spectrum signals, an analog lowpass filter must
be placed before the data acquisition system. The minimum attenuation of this filter at the
aliasing frequency should be at least:
<IMG WIDTH=127 HEIGHT=20 ALIGN=TOP ALT="tex2html_wrap_inline2056" SRC="img116.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img116.gif" >
where B is the number of bits of the ADC. This formula is derived from the fact that there
is a minimum noise level inherent in the sampling process and there is no need to attenuate
the sensor signal more than to below this noise level.<P><H3><A NAME="SECTION00051100000000000000">5.1.1 Problems with the Anti-aliasing Filter:</A></H3><P><OL><LI> Time Response: In designing an anti-aliasing filter, there is a temptation to have it's
attenuation roll-off extremely quickly. The way to achieve this is to increase the order
of the filter (see the previous discussion of filter order). A so-called brick-wall filter
(one with infinitely high order), however, causes a sinc function time response that
decays proportionally to 1/<I>t</I>. What this means is that an extremely high order filter that
eliminates all signals above the cutoff frequency will cause signals that change rapidly
to ring on for a long time. A very undesirable effect.<LI> Phase Distortion / Time delay: Most analog filters have a non-linear phase response.
This a problem since non-linear phase causes an unequal time (group) delay as a
function of frequency. The higher frequency signals will arrive later than low frequency
signals. This can especially be a problem when multiple sensor outputs are compared
such as when using a microphone array.<LI> Amplitude Distortion: By definition, the filter will modify the frequency structure of
the sensor signal which is usually not desired
</OL><H3><A NAME="SECTION00051200000000000000">5.1.2 Solutions:</A></H3><P><OL><LI> Increase the sampling rate of the ADC. This allows the antialiasing filter to have a
higher cutoff frequency and still eliminate aliasing. This enables the following:
<OL><LI> The filter rolloff can be more shallow - allowing a better time response<LI> The frequency response of the filter does not attenuate the lower sensor
frequencies of interest<LI> Phase distortion is strongest around the cutoff frequency of the filter so if
this is pushed higher, it will not affect the sensor frequencies this cutoff
</OL><LI> Have linear phase filters. This, of course, will reduce the phase distortion
problems.
</OL><HR><A NAME="tex2html299" HREF="node22.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node22.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif" tppabs="http://ccrma.stanford.edu/Images//next_motif.gif"></A> <A NAME="tex2html297" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif" tppabs="http://ccrma.stanford.edu/Images//up_motif.gif"></A> <A NAME="tex2html291" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif" tppabs="http://ccrma.stanford.edu/Images//previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html300" HREF="node22.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node22.html">5.2 Sample and Hold</A><B>Up:</B> <A NAME="tex2html298" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html">5 Data Acquisition</A><B> Previous:</B> <A NAME="tex2html292" HREF="node20.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node20.html">5 Data Acquisition</A><P><ADDRESS><I>Tim Stilson <BR>Thu Oct 17 16:32:33 PDT 1996</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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