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Lucas Cordiviola
2022-04-12 23:32:40 -03:00
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@@ -30,50 +30,50 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html1711"
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HREF="node79.html">
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<BR>
<B> Next:</B> <A NAME="tex2html1712"
<B> Next:</B> <A ID="tex2html1712"
HREF="node79.html">Frequency and phase modulation</A>
<B> Up:</B> <A NAME="tex2html1706"
<B> Up:</B> <A ID="tex2html1706"
HREF="node75.html">Modulation</A>
<B> Previous:</B> <A NAME="tex2html1700"
<B> Previous:</B> <A ID="tex2html1700"
HREF="node77.html">Multiplying audio signals</A>
&nbsp; <B> <A NAME="tex2html1708"
&nbsp; <B> <A ID="tex2html1708"
HREF="node4.html">Contents</A></B>
&nbsp; <B> <A NAME="tex2html1710"
&nbsp; <B> <A ID="tex2html1710"
HREF="node201.html">Index</A></B>
<BR>
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<!--End of Navigation Panel-->
<H1><A NAME="SECTION00930000000000000000"></A>
<A NAME="sect5.waveshaping"></A>
<H1><A ID="SECTION00930000000000000000"></A>
<A ID="sect5.waveshaping"></A>
<BR>
Waveshaping
</H1>
<P>
Another approach to modulating a signal, called
<A NAME="5674"></A><I>waveshaping</I>,
<A ID="5674"></A><I>waveshaping</I>,
is simply to pass it through a
suitably chosen nonlinear function. A block diagram for doing this is shown in Figure
<A HREF="#fig05.05">5.5</A>.
@@ -81,7 +81,7 @@ The function <IMG
WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img14.png"
ALT="$f()$"> (called the
<A NAME="5677"></A><I>transfer function</I>)
<A ID="5677"></A><I>transfer function</I>)
distorts the incoming waveform into a different shape. The new shape depends
on the shape of the incoming wave, on the transfer function, and
also--crucially--on
@@ -94,7 +94,7 @@ operation, as shown in the block diagram.
<P>
<DIV ALIGN="CENTER"><A NAME="fig05.05"></A><A NAME="5681"></A>
<DIV ALIGN="CENTER"><A ID="fig05.05"></A><A ID="5681"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.5:</STRONG>
Block diagram for waveshaping an input signal using a nonlinear
@@ -113,7 +113,7 @@ the different effect of the wavetable lookup at different amplitudes.</CAPTION>
<P>
The amplitude of the incoming waveform is called the waveshaping
<A NAME="5684"></A><I>index</I>. In many situations a small index leads to relatively little
<A ID="5684"></A><I>index</I>. In many situations a small index leads to relatively little
distortion (so that the output closely resembles the input) and a larger one
gives a more distorted, richer timbre.
@@ -123,7 +123,7 @@ Figure <A HREF="#fig05.06">5.6</A> shows a familiar example of waveshaping, in w
WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img14.png"
ALT="$f()$"> amounts to a
<A NAME="5687"></A>
<A ID="5687"></A>
<I>clipping function</I>. This example shows clearly how the input
amplitude--the index--can
affect the output waveform. The clipping function passes its input
@@ -138,12 +138,12 @@ at the end. This effect will be well known to anyone who has played an
instrument through an overdriven amplifier. The louder the input, the
more distorted will be the output. For this reason, waveshaping is also sometimes
called
<A NAME="5689"></A>
<A ID="5689"></A>
<I>distortion</I>.
<P>
<DIV ALIGN="CENTER"><A NAME="fig05.06"></A><A NAME="5693"></A>
<DIV ALIGN="CENTER"><A ID="fig05.06"></A><A ID="5693"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.6:</STRONG>
Clipping as an example of waveshaping: (a) the input, a decaying
@@ -225,7 +225,7 @@ of the input.
<P>
<DIV ALIGN="CENTER"><A NAME="fig05.07"></A><A NAME="5942"></A>
<DIV ALIGN="CENTER"><A ID="fig05.07"></A><A ID="5942"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.7:</STRONG>
Waveshaping using a quadratic transfer function <IMG
@@ -356,7 +356,7 @@ f(x+y) = {x^2} + 2 x y + {y^2}
<BR CLEAR="ALL">
<P></P>
This effect, called
<A NAME="5708"></A><I>intermodulation</I>,
<A ID="5708"></A><I>intermodulation</I>,
becomes more and more dominant as the number of terms in the input
increases; if there are <IMG
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
@@ -531,7 +531,7 @@ an incoming signal, it is sometimes useful to write the function <IMG
SRC="img112.png"
ALT="$f$"> as
a finite or infinite
<A NAME="5712"></A><I>power series</I>:
<A ID="5712"></A><I>power series</I>:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
@@ -705,8 +705,8 @@ x[n] = \cos (\omega n)
<BR CLEAR="ALL">
<P></P>
and so on.
<A NAME="eq-waveshaping"></A>The numerators of the fractions will be recognized as Pascal's triangle. The
<A NAME="5747"></A>Central Limit Theorem
<A ID="eq-waveshaping"></A>The numerators of the fractions will be recognized as Pascal's triangle. The
<A ID="5747"></A>Central Limit Theorem
of probability implies that each <IMG
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img58.png"
@@ -835,36 +835,36 @@ are developed in detail in Chapter <A HREF="node89.html#chapter-paf">6</A>.
<P>
<HR>
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SRC="contents.png"></A>
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SRC="index.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html1712"
<B> Next:</B> <A ID="tex2html1712"
HREF="node79.html">Frequency and phase modulation</A>
<B> Up:</B> <A NAME="tex2html1706"
<B> Up:</B> <A ID="tex2html1706"
HREF="node75.html">Modulation</A>
<B> Previous:</B> <A NAME="tex2html1700"
<B> Previous:</B> <A ID="tex2html1700"
HREF="node77.html">Multiplying audio signals</A>
&nbsp; <B> <A NAME="tex2html1708"
&nbsp; <B> <A ID="tex2html1708"
HREF="node4.html">Contents</A></B>
&nbsp; <B> <A NAME="tex2html1710"
&nbsp; <B> <A ID="tex2html1710"
HREF="node201.html">Index</A></B>
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<ADDRESS>