239 lines
7.8 KiB
HTML
239 lines
7.8 KiB
HTML
<!DOCTYPE html>
|
|
|
|
<!--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>
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
<TITLE>Time shifts and delays</TITLE>
|
|
<META NAME="description" CONTENT="Time shifts and delays">
|
|
<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="node127.html">
|
|
<LINK REL="previous" HREF="node89.html">
|
|
<LINK REL="up" HREF="book.html">
|
|
<LINK REL="next" HREF="node105.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2094"
|
|
HREF="node105.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2088"
|
|
HREF="book.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2082"
|
|
HREF="node103.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2090"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2092"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2095"
|
|
HREF="node105.html">Complex numbers</A>
|
|
<B> Up:</B> <A ID="tex2html2089"
|
|
HREF="book.html">book</A>
|
|
<B> Previous:</B> <A ID="tex2html2083"
|
|
HREF="node103.html">Exercises</A>
|
|
<B> <A ID="tex2html2091"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2093"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H1><A ID="SECTION001100000000000000000"></A>
|
|
<A ID="chapter-delay"></A>
|
|
<BR>
|
|
Time shifts and delays
|
|
</H1>
|
|
|
|
<P>
|
|
At 5:00 some afternoon, put on your favorite recording of the Ramones string
|
|
quarter number 5. The next Saturday, play the same recording at 5:00:01, one
|
|
second later in the day. The two playings ideally should sound the same.
|
|
Shifting the whole thing one second (or, if you like, a few days
|
|
and a second) has no physical effect on the sound.
|
|
|
|
<P>
|
|
But now suppose you played it at 5:00 and 5:00:01 on the same day (on two
|
|
different playback systems, since the music lasts much longer than one second).
|
|
Now the sound is much different. The difference, whatever it is,
|
|
clearly resides in neither of the two individual sounds, but rather in the
|
|
<A ID="7751"></A><I>interference</I>
|
|
between the two. This interference can be perceived in at least four different
|
|
ways:
|
|
<DL>
|
|
<DT></DT>
|
|
<DD>Canons: Combining two copies of a signal with a time shift sufficient
|
|
for the signal to change appreciably, we might hear the two as separate musical
|
|
streams, in effect comparing the signal to its earlier self. If the signal is
|
|
a melody, the time shift might be comparable to the length of one or several
|
|
notes.
|
|
|
|
<P>
|
|
</DD>
|
|
<DT></DT>
|
|
<DD>Echos: At time shifts between about 30 milliseconds and about a second,
|
|
the later copy of the signal can sound like an echo of the earlier one. An echo
|
|
may reduce the intelligibility of the signal (especially if it consists of
|
|
speech), but usually won't change the overall "shape" of melodies or
|
|
phrases.
|
|
|
|
<P>
|
|
</DD>
|
|
<DT></DT>
|
|
<DD>Filtering: At time shifts below about 30 milliseconds, the copies are
|
|
too close together in time to be perceived separately, and the dominant effect
|
|
is that some frequencies are enhanced and others suppressed. This changes the
|
|
spectral envelope of the sound.
|
|
|
|
<P>
|
|
</DD>
|
|
<DT></DT>
|
|
<DD>Altered room quality: If the second copy is played more quietly than the
|
|
first, and especially if we add many more delayed copies at reduced amplitudes,
|
|
the result can mimic the echos that arise in a room or other acoustic space.
|
|
|
|
<P>
|
|
</DD>
|
|
</DL>
|
|
The sound of a given arrangement of delayed copies of a signal may
|
|
combine two or more of these affects.
|
|
|
|
<P>
|
|
Mathematically, the effect of a time shift on a signal can be described as a
|
|
phase change of each of the signal's sinusoidal components. The phase shift of
|
|
each component is different depending on its frequency (as well as on the
|
|
amount of time shift). In the rest of this chapter we will often consider
|
|
superpositions of sinusoids at different phases. Heretofore we have been
|
|
content to use real-valued sinusoids in our analyses, but in this and later
|
|
chapters the formulas will become more complicated and we will need more
|
|
powerful mathematical tools to manage them. In a preliminary
|
|
section of this chapter we will develop the additional background needed.
|
|
|
|
<P>
|
|
<BR><HR>
|
|
<!--Table of Child-Links-->
|
|
<A ID="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
|
|
|
<UL>
|
|
<LI><A ID="tex2html2096"
|
|
HREF="node105.html">Complex numbers</A>
|
|
<UL>
|
|
<LI><A ID="tex2html2097"
|
|
HREF="node106.html">Complex sinusoids</A>
|
|
</UL>
|
|
<BR>
|
|
<LI><A ID="tex2html2098"
|
|
HREF="node107.html">Time shifts and phase changes</A>
|
|
<LI><A ID="tex2html2099"
|
|
HREF="node108.html">Delay networks</A>
|
|
<LI><A ID="tex2html2100"
|
|
HREF="node109.html">Recirculating delay networks</A>
|
|
<LI><A ID="tex2html2101"
|
|
HREF="node110.html">Power conservation and complex delay networks</A>
|
|
<LI><A ID="tex2html2102"
|
|
HREF="node111.html">Artificial reverberation</A>
|
|
<UL>
|
|
<LI><A ID="tex2html2103"
|
|
HREF="node112.html">Controlling reverberators</A>
|
|
</UL>
|
|
<BR>
|
|
<LI><A ID="tex2html2104"
|
|
HREF="node113.html">Variable and fractional shifts</A>
|
|
<LI><A ID="tex2html2105"
|
|
HREF="node114.html">Fidelity of interpolating delay lines</A>
|
|
<LI><A ID="tex2html2106"
|
|
HREF="node115.html">Pitch shifting</A>
|
|
<LI><A ID="tex2html2107"
|
|
HREF="node116.html">Examples</A>
|
|
<UL>
|
|
<LI><A ID="tex2html2108"
|
|
HREF="node117.html">Fixed, noninterpolating delay line</A>
|
|
<LI><A ID="tex2html2109"
|
|
HREF="node118.html">Recirculating comb filter</A>
|
|
<LI><A ID="tex2html2110"
|
|
HREF="node119.html">Variable delay line</A>
|
|
<LI><A ID="tex2html2111"
|
|
HREF="node120.html">Order of execution and lower limits on delay times</A>
|
|
<LI><A ID="tex2html2112"
|
|
HREF="node121.html">Order of execution in non-recirculating delay lines</A>
|
|
<LI><A ID="tex2html2113"
|
|
HREF="node122.html">Non-recirculating comb filter as octave doubler</A>
|
|
<LI><A ID="tex2html2114"
|
|
HREF="node123.html">Time-varying complex comb filter: shakers</A>
|
|
<LI><A ID="tex2html2115"
|
|
HREF="node124.html">Reverberator</A>
|
|
<LI><A ID="tex2html2116"
|
|
HREF="node125.html">Pitch shifter</A>
|
|
</UL>
|
|
<BR>
|
|
<LI><A ID="tex2html2117"
|
|
HREF="node126.html">Exercises</A>
|
|
</UL>
|
|
<!--End of Table of Child-Links-->
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html2094"
|
|
HREF="node105.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html2088"
|
|
HREF="book.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html2082"
|
|
HREF="node103.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html2090"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html2092"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html2095"
|
|
HREF="node105.html">Complex numbers</A>
|
|
<B> Up:</B> <A ID="tex2html2089"
|
|
HREF="book.html">book</A>
|
|
<B> Previous:</B> <A ID="tex2html2083"
|
|
HREF="node103.html">Exercises</A>
|
|
<B> <A ID="tex2html2091"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html2093"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|