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#N canvas 0 0 450 300 graph1 0;
#X array E01-signal 882 float 0;
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#X restore 531 41 graph;
#X obj 40 304 hip~ 5;
#N canvas 0 0 450 300 graph1 0;
#X array E01-spectrum 128 float 0;
#X coords 0 4300 127 -40 257 130 1;
#X restore 485 226 graph;
#X text 134 243 <-- click to graph;
#N canvas 45 83 558 569 fft 0;
#X obj 19 62 inlet~;
#X obj 85 214 inlet;
#X obj 19 92 rfft~;
#X obj 19 125 *~;
#X obj 50 125 *~;
#X obj 19 155 sqrt~;
#X obj 85 248 tabwrite~ E01-spectrum;
#X obj 332 109 block~ 4096 1;
#X obj 19 181 biquad~ 0 0 0 0 1;
#X text 83 93 Fourier series;
#X text 88 146 magnitude;
#X text 86 131 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 62 signal to analyze;
#X text 182 166 delay two samples;
#X text 181 182 for better graphing;
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#X obj 98 494 s fundamental;
#X obj 90 517 ftom;
#X text 146 540 <-just out of curiosity \, here's the pitch;
#X text 14 319 At load time \, calculate a good choice of fundamental
frequency for showing spectra: the 16th bin in a 4096-point spectrum
\, so SR*16/4096 or SR/256.;
#X text 135 216 "bang" into this inlet to graph it;
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#X restore 51 279 pd fft;
#X text 531 173 ---- 0.02 seconds ----;
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#X obj 40 332 output~;
#X obj 111 279 tabwrite~ E01-signal;
#X text 523 800 updated for Pd version 0.37;
#X text 516 359 1;
#X text 550 359 2;
#X text 582 359 3;
#X text 614 359 4;
#X text 647 359 5;
#X text 677 359 6;
#X text 708 359 7;
#X text 484 359 0;
#X text 520 378 -- partial number --;
#X text 733 97 0;
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#X text 303 136 <-- On/Off;
#X text 337 152 for each;
#X text 339 168 partial;
#X text 595 11 WAVEFORM;
#X text 578 204 SPECTRUM;
#X text 25 415 The next series of patches demonstrates various kinds
of modulation: AM \, waveshaping \, and FM. We will need a tool for
graphing spectra which is introduced here. In this patch the signal
to be analyzed is a simple sum of up to six partials of a fundamental
frequency (which is 172 Hz \, close to F below middle C \, if your
sample rate happens to be 44100 Hz. The fundamental is chosen to agree
with the analysis patch ("pd FFT") and is computed within it).;
#X text 25 546 The partials are numbered 0 through 5 \, where 0 means
DC \, or zero frequency \, 1 is the fundamental \, and so on. The toggle
switches allow you to turn them on and off separately. You have to
press the "click to graph" button to update the two graphs.;
#X text 745 344 0;
#X text 743 223 1;
#X text 744 282 0.5;
#X text 26 631 The upper graph is just the (time domain) waveform \,
about four periods long. The lower graph is the magnitude spectrum.
Its peaks are the magnitudes of the partials. Note that a DC signal
of amplitude one is considered a partial of magnitude 1 \, but the
other partials \, which have peak amplitudes of 1 (and RMS 0.707) \,
have peak magnitudes of only 0.5 in the spectrum.;
#X obj 41 222 *~ 1;
#X text 733 37 5;
#X text 734 157 -5;
#X text 81 221 sum;
#X text 96 5 GRAPHING SPECTRA OF AUDIO SIGNALS;
#X text 24 742 Here we're introducing a new feature: multiple signals
connected to a signal inlet (as in the "*~ 1") are added. This is the
most convenient way to sum the six partials.;
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