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Lucas Cordiviola
2022-04-12 23:32:40 -03:00
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@@ -30,57 +30,57 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
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<H1><A NAME="SECTION00910000000000000000"></A>
<A NAME="sect5-spectra"></A>
<H1><A ID="SECTION00910000000000000000"></A>
<A ID="sect5-spectra"></A>
<BR>
Taxonomy of spectra
</H1>
<P>
Figure <A HREF="#fig05.01">5.1</A> introduces a way of visualizing the
<A NAME="5595"></A><I>spectrum</I> of an audio signal. The spectrum describes, roughly speaking,
<A ID="5595"></A><I>spectrum</I> of an audio signal. The spectrum describes, roughly speaking,
how the signal's power is distributed into frequencies. (Much more precise
definitions can be given than those that we'll develop here, but they would
require more mathematical background.)
<P>
<DIV ALIGN="CENTER"><A NAME="fig05.01"></A><A NAME="5599"></A>
<DIV ALIGN="CENTER"><A ID="fig05.01"></A><A ID="5599"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.1:</STRONG>
A taxonomy of timbres. The spectral envelope describes the shape of
@@ -95,7 +95,7 @@ frequency; if discretely, it may be harmonic or inharmonic.</CAPTION>
<P>
Part (a) of the figure shows the spectrum of a
<A NAME="5602"></A><I>harmonic signal</I>,
<A ID="5602"></A><I>harmonic signal</I>,
which is a periodic signal whose fundamental frequency is in the range of
perceptible pitches, roughly between 50 and 4000 Hertz.
The Fourier series (Page <A HREF="node14.html#eq-fourierseries"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
@@ -131,7 +131,7 @@ concentrated on a discrete subset of the frequency axis (a discrete
set consists of isolated points, only finitely many in any bounded interval).
We call
this a
<A NAME="5607"></A><I>discrete</I> spectrum.
<A ID="5607"></A><I>discrete</I> spectrum.
Furthermore, the frequencies where the signal's power lies are in the
<IMG
WIDTH="75" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
@@ -140,7 +140,7 @@ Furthermore, the frequencies where the signal's power lies are in the
necessary for <I>all</I> of the harmonic frequencies to be present; some
harmonics may have zero amplitude.)
For a harmonic signal, the graph of the spectrum shows the amplitudes of the
<A NAME="5610"></A>partials of the signals.
<A ID="5610"></A>partials of the signals.
Knowing the amplitudes and phases of all the partials fully determines
the original signal.
@@ -149,7 +149,7 @@ Part (b) of the figure shows a spectrum which is also discrete, so that the
signal can again be considered as a sum of a series of
partials. In this case, however, there is no fundamental frequency, i.e., no
audible common submultiple of all the partials. This is called an
<A NAME="5611"></A>
<A ID="5611"></A>
<I>inharmonic</I> signal. (The terms <IMG
WIDTH="72" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img406.png"
@@ -199,7 +199,7 @@ component of zero frequency, for which
SRC="img4.png"
ALT="$a$">--without dividing by two.
(Components of zero frequency are often called
<I>DC</I><A NAME="5614"></A>
<I>DC</I><A ID="5614"></A>
components; "DC" is historically an acronym for "direct current").
These conventions for amplitudes in spectra will simplify the mathematics later
in this chapter; a deeper reason for them will become apparent in
@@ -209,14 +209,14 @@ Chapter <A HREF="node104.html#chapter-delay">7</A>.
Part (c) of the figure shows a third possibility:
the spectrum might not be concentrated into a discrete set of frequencies, but
instead might be spread out among all possible frequencies. This can be called a
<A NAME="5616"></A><I>continuous</I>, or
<A NAME="5618"></A><I>noisy</I> spectrum.
<A ID="5616"></A><I>continuous</I>, or
<A ID="5618"></A><I>noisy</I> spectrum.
Spectra don't necessarily fall into either the discrete or continuous categories;
real sounds, in particular, are usually somewhere in between.
<P>
Each of the three parts of the figure shows a continuous curve called the
<A NAME="5620"></A><I>spectral envelope</I>. In general, sounds don't have a single,
<A ID="5620"></A><I>spectral envelope</I>. In general, sounds don't have a single,
well-defined
spectral envelope; there may be many ways to draw a smooth-looking curve
through a spectrum. On the other hand, a spectral envelope may be specified
@@ -258,36 +258,36 @@ chapter.
<P>
<HR>
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HREF="node77.html">Multiplying audio signals</A>
<B> Up:</B> <A NAME="tex2html1678"
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HREF="node4.html">Contents</A></B>
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<ADDRESS>