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#X text 75 15 BAND-LIMITED SAWTOOTH GENERATOR USING A TRANSITION TABLE
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#X text 39 657 Now any time we wish to make a discontinuity in the
output signal \, we make it look exactly like the bandlimited square
wave looks. We do this by reading through the table we recorded \,
carefully adding a "digital" \, non-band-limited \, sawtooth to "array1"
so that the discontinuities in the two cancel out and what you have
left is the transition in the table.;
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#X text 242 138 back the phase up one sample;
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#X text 292 216 twice the table length;
#X text 280 193 period is 2000 samples \,;
#X text 80 369 This one is used - first and third harmonics only.;
#X text 28 644 This alternate one puts in harmonics 1 \, 3 \, and 5
;
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#X text 537 179 ----- 1002 samples ----;
#X text 24 27 This network puts a half cycle of a band-limited square
wave into the table "array1.";
#X text 22 64 Logically the half-cycle is in samples 1 through 1000
\; samples 0 and 1001 are provided so that the 4-point interpolation
will work everywhere.;
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#X restore 182 465 pd transition-table;
#X text 351 853 updated for Pd version 0.39;
#X text 37 515 A more sophisticated way to control foldover in sawtooth
waves is to replace the once-a-cycle jump with a bandlimited transition.
To get a band-limited transition we synthesize a band-limited square
wave and harvest the transition from the middle of the top half to
the middle of the bottom half. Here we use a square wave at SR/10 \,
so that only partials 1 and 3 fit below the Nyquist. The transition
should take 1/2 period \, or 5 samples. The table is calculated and
stored in the "transition-table" subpatch.;
#X text 40 767 The "band limit" controls how fast the transition table
is read. If it is set to the Nyquist frequency the table is read at
0.4 times the Nyquist \, or five samples a cycle. Lowering the band
limit cuts off the partials of the generated sawtooth wave at frequencies
below the Nyquist.;
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