#N canvas 73 310 580 406 12;
#N canvas 265 48 643 640 fft-analysis 0;
#X obj 15 164 *~;
#X obj 14 99 inlet~;
#X obj 15 218 rfft~;
#X obj 36 140 tabreceive~ \$0-hann;
#X obj 14 353 *~;
#X obj 56 353 *~;
#X obj 15 8 block~ 512 4;
#X text 85 88 The inlet~ now re-uses 3/4 of the previous block \, along
with the 128 new samples.;
#X text 221 141 window function as before.;
#X obj 76 196 tabreceive~ \$0-gain;
#X obj 77 225 *~;
#X obj 16 506 *~;
#X obj 37 481 tabreceive~ \$0-hann;
#X obj 77 283 /~ 768;
#X text 98 301 divide by 3N/2 (factor of N because rfft and rifft aren't
normalized \, and 3/2 is the gain of overlap-4 reconstruction when
Hann window function is applied twice.);
#X text 120 216 Just to show we're doing something \, we multiply each
channel by a gain controlled by an array in the main window. The control
is quartic-scaled for easy editing.;
#X obj 78 251 *~;
#X text 92 357 Multiply the (complex-valued) spectrum amplitudes by
the (real-valued) gain-and-normalization-factor;
#X obj 15 399 rifft~;
#X text 89 396 Real-valued inverse Fourier transform. This uses only
the first N/@ points of its inputs \, supplying the rest by symmerty
(so it's OK that rfft~ obly puts out those N/2 points.) There's only
one outlet because the output is real-valued.;
#X obj 16 566 outlet~;
#X text 88 499 Multiply by the Hann window function again \, necessary
because the operation we performed might result in a signal that doesn't
go smoothly to zero at both ends.;
#X text 89 566 This repackages the output into 64-sample chunks for
the parent window. Since we're operating with an overlap \, the outlet~
object performs an overlapped sum of the blocks computed in this window.
;
#X text 129 8 block~ object specifies vector size of 512 and overlap
four. This window now computes blocks of 512 samples at intervals of
128 samples computed on the parent patch.;
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#X connect 2 0 4 0;
#X connect 2 1 5 0;
#X connect 3 0 0 1;
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#X connect 9 0 10 1;
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#X connect 10 0 16 1;
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#X connect 12 0 11 1;
#X connect 13 0 4 1;
#X connect 13 0 5 1;
#X connect 16 0 13 0;
#X connect 18 0 11 0;
#X restore 26 289 pd fft-analysis;
#X text 290 362 updated for Pd version 0.39;
#N canvas 35 66 592 433 Hann-window 0;
#N canvas 0 0 450 300 graph1 0;
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#X coords 0 1 511 0 200 120 1;
#X restore 293 249 graph;
#X msg 171 263 0;
#X obj 65 312 osc~;
#X obj 65 264 samplerate~;
#X obj 65 335 *~ -0.5;
#X obj 65 358 +~ 0.5;
#X obj 57 383 tabwrite~ \$0-hann;
#X text 279 241 1;
#X text 272 359 0;
#X text 288 372 0;
#X obj 65 288 / 512;
#X obj 57 241 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
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#X text 336 221 Hann window;
#X text 113 310 period 512;
#X text 90 215 recalculate Hann;
#X text 125 230 window table;
#X obj 57 146 loadbang;
#X msg 79 179 \; pd dsp 1;
#X text 40 27 The Hann window is now recomputed on 'loadbang' to make
the file smaller (it doesn't have to be saved with the array.);
#X text 474 375 511;
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#X connect 3 0 10 0;
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#X connect 11 0 1 0;
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#X restore 192 318 pd Hann-window;
#X obj 27 323 output~;
#X obj 25 264 noise~;
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#X restore 22 168 graph;
#X msg 192 264 const 0;
#X obj 192 293 s \$0-gain;
#X text 138 0 FOURIER RESYNTHESIS;
#X text 6 218 0;
#X text 6 159 1;
#X text 19 228 0;
#X text 516 231 22K;
#X text 270 261 <- reset gain;
#X text 224 148 GAIN;
#X text 21 24 Using Fourier resynthesis you can take an incoming sound
\, operate on its spectrum \, and hear the result. Here we start with
white noise and apply a frequency-dependent gain \, which works as
a graphic equalizer. There are N/2 = 256 points \, each spaced SR/512
Hz. apart (although their frequency ranges overlap). Open the "fft-analysis"
patch to see the workings.;
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#X connect 0 0 3 1;
#X connect 4 0 0 0;
#X connect 6 0 7 0;
