<!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>Exercises</TITLE> <META NAME="description" CONTENT="Exercises"> <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="previous" HREF="node18.html"> <LINK REL="up" HREF="node7.html"> <LINK REL="next" HREF="node26.html"> </HEAD> <BODY > <!--Navigation Panel--> <A ID="tex2html905" HREF="node26.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A ID="tex2html899" HREF="node7.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A ID="tex2html895" HREF="node24.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A ID="tex2html901" HREF="node4.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A ID="tex2html903" HREF="node201.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> <BR> <B> Next:</B> <A ID="tex2html906" HREF="node26.html">Wavetables and samplers</A> <B> Up:</B> <A ID="tex2html900" HREF="node7.html">Sinusoids, amplitude and frequency</A> <B> Previous:</B> <A ID="tex2html896" HREF="node24.html">More additive synthesis</A> <B> <A ID="tex2html902" HREF="node4.html">Contents</A></B> <B> <A ID="tex2html904" HREF="node201.html">Index</A></B> <BR> <BR> <!--End of Navigation Panel--> <H1><A ID="SECTION005100000000000000000"> Exercises</A> </H1> <P> <OL> <LI>A sinusoid (Page <A HREF="node7.html#eq-realsinusoid"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="crossref.png"></A>) has initial phase <IMG WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" SRC="img162.png" ALT="$\phi=0$"> and angular frequency <!-- MATH $\omega = \pi/10$ --> <IMG WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" SRC="img163.png" ALT="$\omega = \pi/10$">. What is its period in samples? What is the phase at sample number <IMG WIDTH="50" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" SRC="img164.png" ALT="$n=10$">? <P> </LI> <LI>Two sinusoids have periods of 20 and 30 samples, respectively. What is the period of the sum of the two? <P> </LI> <LI>If 0 dB corresponds to an amplitude of 1, how many dB corresponds to amplitudes of 1.5, 2, 3, and 5? <P> </LI> <LI>Two uncorrelated signals of RMS amplitude 3 and 4 are added; what's the RMS amplitude of the sum? <P> </LI> <LI>How many uncorrelated signals, all of equal amplitude, would you have to add to get a signal that is 9 dB greater in amplitude? <P> </LI> <LI>What is the angular frequency of middle C at 44100 samples per second? <P> </LI> <LI>Two sinusoids play at middle C (MIDI 60) and the neighboring C sharp (MIDI 61). What is the difference, in Hertz, between their frequencies? <P> </LI> <LI>How many cents is the interval between the seventh and the eighth harmonic of a periodic signal? <P> </LI> <LI>If an audio signal <!-- MATH $x[n], n = 0, ..., N-1$ --> <IMG WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" SRC="img165.png" ALT="$x[n], n = 0, ..., N-1$"> has peak amplitude 1, what is the minimum possible RMS amplitude? What is the maximum possible? <P> </LI> </OL> <HR> <!--Navigation Panel--> <A ID="tex2html905" HREF="node26.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A ID="tex2html899" HREF="node7.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A ID="tex2html895" HREF="node24.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A ID="tex2html901" HREF="node4.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A ID="tex2html903" HREF="node201.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> <BR> <B> Next:</B> <A ID="tex2html906" HREF="node26.html">Wavetables and samplers</A> <B> Up:</B> <A ID="tex2html900" HREF="node7.html">Sinusoids, amplitude and frequency</A> <B> Previous:</B> <A ID="tex2html896" HREF="node24.html">More additive synthesis</A> <B> <A ID="tex2html902" HREF="node4.html">Contents</A></B> <B> <A ID="tex2html904" HREF="node201.html">Index</A></B> <!--End of Navigation Panel--> <ADDRESS> Miller Puckette 2006-12-30 </ADDRESS> </BODY> </HTML>