2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
|
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
|
|
|
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
|
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
|
|
|
* with significant contributions from:
|
|
|
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
|
|
|
<HTML>
|
|
|
|
|
<HEAD>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<TITLE>Low-pass and high-pass filters</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Low-pass and high-pass filters">
|
|
|
|
|
<META NAME="keywords" CONTENT="book">
|
|
|
|
|
<META NAME="resource-type" CONTENT="document">
|
|
|
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
|
|
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
|
|
|
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
|
|
|
|
|
|
<LINK REL="STYLESHEET" HREF="book.css">
|
|
|
|
|
|
|
|
|
|
<LINK REL="next" HREF="node130.html">
|
|
|
|
|
<LINK REL="previous" HREF="node128.html">
|
|
|
|
|
<LINK REL="up" HREF="node128.html">
|
|
|
|
|
<LINK REL="next" HREF="node130.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2507"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node130.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2501"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2495"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2503"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2505"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html2508"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node130.html">Band-pass and stop-band filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html2502"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">Taxonomy of filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html2496"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">Taxonomy of filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2504"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2506"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<H2><A ID="SECTION001211000000000000000">
|
2022-04-12 21:54:18 -03:00
|
|
|
Low-pass and high-pass filters</A>
|
|
|
|
|
</H2>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
By far the most frequent purpose for using a filter is extracting either
|
|
|
|
|
the low-frequency or the high-frequency portion of an audio signal, attenuating
|
|
|
|
|
the rest. This is accomplished using a
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10062"></A><A ID="10063"></A><I>low-pass</I> or
|
|
|
|
|
<A ID="10065"></A><A ID="10066"></A><I>high-pass</I>
|
2022-04-12 21:54:18 -03:00
|
|
|
filter.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<DIV ALIGN="CENTER"><A ID="fig08.02"></A><A ID="10070"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.2:</STRONG>
|
|
|
|
|
Terminology for describing the frequency response of low-pass and
|
|
|
|
|
high-pass filters. The horizontal axis is frequency and the vertical
|
|
|
|
|
axis is gain. A low-pass filter is shown; a high-pass filter has the same
|
|
|
|
|
features switched from right to left.</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="491" HEIGHT="318" BORDER="0"
|
|
|
|
|
SRC="img855.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig08.02.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Ideally, a low-pass or high-pass filter would have a frequency response of
|
|
|
|
|
one up to (or down to) a specified cutoff frequency and zero past it; but
|
|
|
|
|
such filters cannot be realized in practice. Instead, we try to find
|
|
|
|
|
realizable approximations to this ideal response. The more design effort
|
|
|
|
|
and computation time we put into it, the closer we can get.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Figure <A HREF="#fig08.02">8.2</A> shows the frequency response of a low-pass
|
|
|
|
|
filter. Frequency is divided into three bands, labeled on the
|
|
|
|
|
horizontal axis. The
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10074"></A><I>passband</I>
|
2022-04-12 21:54:18 -03:00
|
|
|
is the region (frequency band) where the filter should pass its input through
|
|
|
|
|
to its output with unit gain.
|
|
|
|
|
For a low-pass filter (as shown), the passband reaches from a frequency of
|
|
|
|
|
zero up to a certain frequency limit. For a high-pass filter, the passband
|
|
|
|
|
would appear on the right-hand side of the graph and would extend from the
|
|
|
|
|
frequency limit up to the highest frequency possible. Any
|
|
|
|
|
realizable filter's passband will be only approximately flat;
|
|
|
|
|
the deviation from flatness is called the
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10076"></A><I>ripple</I>,
|
2022-04-12 21:54:18 -03:00
|
|
|
and is often specified by giving the ratio between the highest and lowest gain
|
|
|
|
|
in the passband, expressed in decibels. The ideal low-pass or high-pass filter
|
|
|
|
|
would have a ripple of 0 dB.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10078"></A><I>stopband</I>
|
2022-04-12 21:54:18 -03:00
|
|
|
of a low-pass or high-pass filter is the frequency
|
|
|
|
|
band over which the filter is intended not to transmit its input.
|
|
|
|
|
The
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10080"></A><I>stopband attenuation</I>
|
2022-04-12 21:54:18 -03:00
|
|
|
is the difference, in decibels, between the lowest gain in the passband
|
|
|
|
|
and the highest gain in the stopband. Ideally this would
|
|
|
|
|
be infinite; the higher the better.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Finally, a realizable filter, whose frequency response is always a
|
|
|
|
|
continuous function of frequency, must have a frequency
|
|
|
|
|
band over which the gain drops from the passband gain to the stopband
|
|
|
|
|
gain; this is called the
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="10082"></A><I>transition band</I>.
|
2022-04-12 21:54:18 -03:00
|
|
|
The thinner this band can be made, the more nearly ideal the filter.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2507"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node130.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2501"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2495"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2503"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html2505"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html2508"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node130.html">Band-pass and stop-band filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html2502"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">Taxonomy of filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html2496"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node128.html">Taxonomy of filters</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2504"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html2506"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
