121 lines
3.1 KiB
HTML
121 lines
3.1 KiB
HTML
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original version by: Nikos Drakos, CBLU, University of Leeds
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HREF="node184.html">Classical waveforms</A>
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HREF="node199.html">Strategies for band-limiting sawtooth</A>
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<H1><A NAME="SECTION001460000000000000000">
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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 <TT>phasor~</TT> object has a frequency of 441 Hertz (at a sample rate
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of 44100). What is the amplitude of the DC component? The fundamental? The
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partial at 22050 Hertz (above which the partials fold over)?
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<P>
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</LI>
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<LI>A square wave oscillates between 1 and -1. What is its RMS amplitude?
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<P>
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</LI>
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<LI>In Section <A HREF="node188.html#sect10.spectra">10.3</A> a square wave was presented as an odd
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waveform whose Fourier series consisted of sine (and not cosine) functions.
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If the square wave is advanced 1/8 cycle in phase, so that it appears as an
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even function, what does its Fourier series become?
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<P>
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</LI>
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<LI>A rectangle wave is 1 for 1/4 cycle, zero for 3/4 cycles. What are the
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strengths of its harmonics at 0, 1, 2, 3, and 4 times the fundamental?
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<P>
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</LI>
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<LI>How much is <!-- MATH
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$1 + 1/9 + 1/25 + 1/49 + 1/81 + \cdots$
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-->
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ALT="$1 + 1/9 + 1/25 + 1/49 + 1/81 + \cdots$">?
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<P>
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</LI>
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</OL>
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<P>
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<P>
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<BR><HR>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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