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#X text 215 28 bandwidth;
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#X text 111 141 X^2;
#X text 84 171 1+X^2;
#X text 71 196 1/(1+X^2);
#X text 28 4 ANOTHER PULSE WIDTH MOD ALGORITHM;
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#X text 646 461 ---- 0.02 seconds ----;
#X text 614 237 2;
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#X text 622 252 -- partial number --;
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#X text 93 93 Fourier series;
#X text 98 146 magnitude;
#X text 96 131 calculate;
#X text 21 3 This subpatch computes the spectrum of the incoming signal
with a (rectangular windowed) FFT. FFTs aren't properly introduced
until much later.;
#X text 83 61 signal to analyze;
#X text 193 164 delay two samples;
#X text 191 182 for better graphing;
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#X text 301 232 toggle to graph repeatedly;
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#X obj 19 295 tabwrite~ F04-signal;
#X obj 250 291 tabwrite~ F04-spectrum;
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#X msg 224 321 \; pd dsp 1;
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#X text 632 540 updated for Pd version 0.37;
#X text 23 515 NOTE: The PAF algorithm is protected by patents belonging
to IRCAM. Noncommercial use seems to be fine with them but contact
them first if you want to sell something using this.;
#X text 24 473 This is the form of pulse train used in the original
Phase Aligned Formant (PAF) algorithm.;
#X text 23 342 Here we use waveshaping to make another form of pulse
train. This one has a neat spectrum: the partials drop off exponentially
(with the "bandwidth" controlling the rate of dropoff.) In later patches
we'll use a wavetable to do the waveshaping but for simplicity \, it's
done algebraically here. The oscillator runs at half the fundamental
frequency. The symmetry of the waveshaping doubles the frequency of
the output.;
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