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#N canvas 353 76 558 670 fft-analysis 0;
#X obj 32 186 *~;
#X obj 32 105 inlet~;
#X obj 32 248 rfft~;
#X obj 50 160 tabreceive~ \$0-hann;
#X obj 32 365 *~;
#X obj 71 365 *~;
#X obj 30 33 block~ 512 4;
#X text 92 101 The inlet~ now re-uses 3/4 of the previous block \,
along with the 128 new samples., f 49;
#X text 197 159 window function as before.;
#X obj 89 205 tabreceive~ \$0-gain;
#X obj 89 235 *~;
#X obj 32 518 *~;
#X obj 50 492 tabreceive~ \$0-hann;
#X obj 89 310 /~ 768;
#X text 152 292 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.), f 52;
#X text 132 235 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., f 55;
#X obj 89 263 *~;
#X text 107 357 Multiply the (complex-valued) spectrum amplitudes by
the (real-valued) gain-and-normalization-factor, f 50;
#X obj 32 411 rifft~;
#X text 98 403 Real-valued inverse Fourier transform. This uses only
the first N/@ points of its inputs \, supplying the rest by symmetry
(so it's OK that rfft~ only puts out those N/2 points.) There's only
one outlet because the output is real-valued.;
#X obj 31 599 outlet~;
#X text 76 518 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 107 583 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 19 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., f 55;
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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 5 0 18 1;
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#X connect 9 0 10 1;
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#X connect 12 0 11 1;
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#X connect 13 0 5 1;
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#X connect 18 0 11 0;
#X restore 97 372 pd fft-analysis;
#X text 378 471 updated for Pd version 0.39;
#N canvas 687 159 571 372 Hann-window 0;
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#X array \$0-hann 512 float 0;
#X coords 0 1 511 0 200 120 1;
#X restore 293 151 graph;
#X msg 181 165 0;
#X obj 75 214 osc~;
#X obj 75 166 samplerate~;
#X obj 75 237 *~ -0.5;
#X obj 75 260 +~ 0.5;
#X obj 57 285 tabwrite~ \$0-hann;
#X text 279 143 1;
#X text 272 261 0;
#X text 288 274 0;
#X obj 75 190 / 512;
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#000000;
#X text 399 126 Hann window;
#X text 123 212 period 512;
#X text 100 117 recalculate Hann;
#X text 135 132 window table;
#X obj 57 82 loadbang;
#X text 91 26 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 474 277 511;
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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 268 418 pd Hann-window;
#X obj 97 410 output~;
#X obj 97 345 noise~;
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#X restore 54 205 graph;
#X msg 268 364 const 0;
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#X text 70 32 FOURIER RESYNTHESIS;
#X text 38 294 0;
#X text 38 195 1;
#X text 51 304 0;
#X text 548 307 22K;
#X text 267 180 GAIN;
#X text 53 68 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., f 68;
#X text 326 363 <= reset gain;
#X obj 441 20 declare -stdpath ./;
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#X connect 0 0 3 1;
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#X connect 6 0 7 0;
