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152 lines
5.2 KiB
152 lines
5.2 KiB
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HREF="node194.html">Over-sampling</A>
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HREF="node184.html">Classical waveforms</A>
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HREF="node192.html">General (non-symmetric) triangle wave</A>
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<H1><A ID="SECTION001440000000000000000">
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Predicting and controlling foldover</A>
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</H1>
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<P>
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Now we descend to the real situation, in which the period of the waveform
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cannot be assumed to be arbitrarily long and integer-valued. Suppose (for
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definiteness) we want to synthesize tones at 440 Hertz (A above middle C), and
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that we are using a sample rate of 44100 Hertz, so that the period is about 100.25
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samples. Theoretically, given a very high sample rate, we would expect the
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fiftieth partial to have magnitude <IMG
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WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img1365.png"
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ALT="$1/50$"> compared to the fundamental and
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a frequency about 20 kHz. If we sample this waveform at the (lower) sample
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rate of 44100, then partials in excess of this frequency will be aliased, as
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described in Section <A HREF="node41.html#sect3.sampling">3.1</A>. The relative strength of the
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folded-over partials will be on the order of -32 decibels--quite audible.
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If the fundamental frequency is raised further, more and louder partials reach
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the Nyquist frequency (half the sample rate) and begin to fold over.
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<P>
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Foldover problems are much less pronounced for waveforms with only corners
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(instead of jumps) because of the faster dropoff of higher partial frequencies;
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for instance, a symmetric triangle wave at 440 Hertz would get twice the dropoff, or -64
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decibels. In general, though, waveforms with discontinuities are a better
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starting point for
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<A ID="14464"></A>subtractive synthesis (the most popular classical technique).
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In case you were hoping, subtractive filtering can't remove foldover once it is
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present in an audio signal.
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<A ID="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<LI><A ID="tex2html3456"
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HREF="node194.html">Over-sampling</A>
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<LI><A ID="tex2html3457"
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HREF="node195.html">Sneaky triangle waves</A>
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<LI><A ID="tex2html3458"
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HREF="node196.html">Transition splicing</A>
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HREF="node194.html">Over-sampling</A>
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<B> Up:</B> <A ID="tex2html3449"
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HREF="node184.html">Classical waveforms</A>
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<B> Previous:</B> <A ID="tex2html3443"
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HREF="node192.html">General (non-symmetric) triangle wave</A>
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<B> <A ID="tex2html3451"
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HREF="node4.html">Contents</A></B>
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<B> <A ID="tex2html3453"
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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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