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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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<B> Next:</B> <A ID="tex2html906"
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HREF="node26.html">Wavetables and samplers</A>
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<B> Up:</B> <A ID="tex2html900"
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HREF="node7.html">Sinusoids, amplitude and frequency</A>
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<B> Previous:</B> <A ID="tex2html896"
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HREF="node24.html">More additive synthesis</A>
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<B> <A ID="tex2html902"
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html904"
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HREF="node201.html">Index</A></B>
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2022-04-12 23:32:40 -03:00
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<H1><A ID="SECTION005100000000000000000">
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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 sinusoid (Page <A HREF="node7.html#eq-realsinusoid"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="crossref.png"></A>) has initial phase <IMG
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WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img162.png"
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ALT="$\phi=0$"> and
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angular frequency <!-- MATH
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$\omega = \pi/10$
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-->
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<IMG
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WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img163.png"
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ALT="$\omega = \pi/10$">. What is its period in samples? What is
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the phase at sample number <IMG
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WIDTH="50" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img164.png"
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ALT="$n=10$">?
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<P>
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</LI>
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<LI>Two sinusoids have periods of 20 and 30 samples, respectively. What is
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the period of the sum of the two?
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<P>
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</LI>
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<LI>If 0 dB corresponds to an amplitude of 1,
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how many dB corresponds to amplitudes of 1.5, 2, 3, and 5?
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<P>
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</LI>
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<LI>Two uncorrelated signals of RMS amplitude 3 and 4 are added; what's the
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RMS amplitude of the sum?
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<P>
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</LI>
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<LI>How many uncorrelated signals, all of equal amplitude, would you have
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to add to get a signal that is 9 dB greater in amplitude?
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<P>
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</LI>
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<LI>What is the angular frequency of middle C at 44100 samples per second?
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<P>
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</LI>
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<LI>Two sinusoids play at middle C (MIDI 60) and the neighboring C sharp
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(MIDI 61). What is the difference, in Hertz, between their frequencies?
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<P>
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</LI>
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<LI>How many cents is the interval between the seventh and the eighth harmonic of
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a periodic signal?
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<P>
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</LI>
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<LI>If an audio signal <!-- MATH
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$x[n], n = 0, ..., N-1$
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-->
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<IMG
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WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img165.png"
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ALT="$x[n], n = 0, ..., N-1$"> has peak amplitude 1, what
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is the minimum possible RMS amplitude? What is the maximum possible?
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<P>
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</LI>
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<B> Next:</B> <A ID="tex2html906"
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2022-04-12 21:54:18 -03:00
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HREF="node26.html">Wavetables and samplers</A>
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2022-04-12 23:32:40 -03:00
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<B> Up:</B> <A ID="tex2html900"
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2022-04-12 21:54:18 -03:00
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HREF="node7.html">Sinusoids, amplitude and frequency</A>
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2022-04-12 23:32:40 -03:00
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<B> Previous:</B> <A ID="tex2html896"
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2022-04-12 21:54:18 -03:00
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HREF="node24.html">More additive synthesis</A>
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2022-04-12 23:32:40 -03:00
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<B> <A ID="tex2html902"
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2022-04-12 21:54:18 -03:00
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html904"
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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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