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174 lines
4.9 KiB
174 lines
4.9 KiB
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original version by: Nikos Drakos, CBLU, University of Leeds
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<TITLE>Exercises</TITLE>
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HREF="node89.html">Designer spectra</A>
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HREF="node75.html">Modulation</A>
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<B> Previous:</B> <A ID="tex2html1845"
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HREF="node87.html">Phase modulation and FM</A>
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<B> <A ID="tex2html1851"
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html1853"
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HREF="node201.html">Index</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H1><A ID="SECTION00960000000000000000">
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Exercises</A>
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</H1>
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<P>
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<OL>
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<LI>A sound has fundamental 440. How could it be ring modulated to
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give a tone at 110 Hertz with only odd partials? How could you then fill in the
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even ones if you wanted to?
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<P>
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</LI>
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<LI>A sinusoid with frequency 400 and unit peak amplitude is squared. What
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are the amplitudes and frequencies of the new signal's components?
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<P>
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</LI>
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<LI>What carrier and modulation frequencies would you give a two-operator FM
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instrument to give frequencies of 618, 1000, and 2618 Hertz? (This is
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a prominent feature of Chowning's <I>Stria</I> [<A
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HREF="node202.html#r-dodge85">DJ85</A>].)
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<P>
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</LI>
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<LI>Two sinusoids with frequency 300 and 400 Hertz and peak amplitude
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one (so RMS amplitude <IMG
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WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img549.png"
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ALT="$\approx$">0.707) are multiplied. What is the RMS
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amplitude of the product?
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<P>
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</LI>
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<LI>Suppose you wanted to make FM yet more complicated by modulating the
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<I>modulating</I> oscillator, as in:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
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\end{displaymath}
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-->
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<IMG
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WIDTH="243" HEIGHT="29" BORDER="0"
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SRC="img550.png"
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ALT="\begin{displaymath}
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\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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How, qualitatively speaking, would the spectrum differ from that of the simple
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two-modulator example (Section <A HREF="node87.html#sect5.example.fm">5.5</A>)?
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<P>
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</LI>
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<LI>A sinusoid at a frequency <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img27.png"
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ALT="$\omega $"> is ring modulated by another
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sinusoid at exactly the same frequency. At what phase differences will the
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DC component of the result disappear?
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<P>
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</LI>
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</OL>
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<BR>
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<B> Next:</B> <A ID="tex2html1855"
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HREF="node89.html">Designer spectra</A>
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<B> Up:</B> <A ID="tex2html1849"
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HREF="node75.html">Modulation</A>
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<B> Previous:</B> <A ID="tex2html1845"
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HREF="node87.html">Phase modulation and FM</A>
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<B> <A ID="tex2html1851"
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html1853"
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HREF="node201.html">Index</A></B>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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