#N canvas 377 49 580 400 10; #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~ only 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.; #X connect 0 0 2 0; #X connect 1 0 0 0; #X connect 2 0 4 0; #X connect 2 1 5 0; #X connect 3 0 0 1; #X connect 4 0 18 0; #X connect 5 0 18 1; #X connect 9 0 10 0; #X connect 9 0 10 1; #X connect 10 0 16 0; #X connect 10 0 16 1; #X connect 11 0 20 0; #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 23 279 pd fft-analysis; #N canvas 35 66 592 433 Hann-window 0; #N canvas 0 0 450 300 (subpatch) 0; #X array \\$0-hann 512 float 0 black black; #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 -1; #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; #X connect 1 0 2 1; #X connect 2 0 4 0; #X connect 3 0 10 0; #X connect 4 0 5 0; #X connect 5 0 6 0; #X connect 10 0 2 0; #X connect 11 0 3 0; #X connect 11 0 1 0; #X connect 11 0 6 0; #X connect 16 0 11 0; #X connect 16 0 17 0; #X restore 152 340 pd Hann-window; #X obj 24 313 output~; #X obj 22 254 noise~; #N canvas 0 0 450 300 (subpatch) 0; #X array \\$0-gain 256 float 3 black black; #A 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; #X coords 0 1 256 -0.01 512 60 1; #X restore 35 157 graph; #X msg 152 293 const 0; #X obj 152 315 s \\$0-gain; #X text 19 207 0; #X text 19 148 1; #X text 32 217 0; #X text 529 220 22K; #X text 210 293 <- reset gain; #X text 237 137 GAIN; #X text 19 37 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.; #X obj 1 1 cnv 15 445 20 empty \\$0-pddp.cnv.header Fourier_resynthesis 20 10 1 18 -261139 -33289 0; #X obj 407 2 pddp/pddplink http://puredata.info/dev/pddp -text pddp ; #X obj 1 378 cnv 15 445 20 empty \\$0-pddp.cnv.footer empty 20 12 0 14 -233017 -33289 0; #N canvas 44 246 494 284 META 0; #X text 12 105 WEBSITE http://crca.ucsd.edu/~msp/; #X text 12 85 AUTHOR Miller Puckette; #X text 12 65 LIBRARY PDDP; #X text 12 25 LICENSE SIBSD; #X text 12 125 HELP_PATCH_AUTHORS Updated for release 0.39. Jonathan Wilkes revised the patch to conform to the PDDP template for Pd version 0.42.; #X text 12 45 DESCRIPTION Fourier resynthesis; #X text 12 5 KEYWORDS signal tutorial; #X restore 392 380 pd META; #N canvas 13 202 428 190 References 0; #X obj 1 1 cnv 15 425 20 empty \\$0-pddp.cnv.subheading empty 3 12 0 14 -261139 -33289 0; #X text 7 2 Fourier resynthesis- Related Help Documents; #X text 19 37 Links:; #X restore 103 380 pd References; #X obj 6 380 pddp/pddplink ../5.reference/pddp/help.pd -text help; #X connect 0 0 2 0; #X connect 0 0 2 1; #X connect 3 0 0 0; #X connect 5 0 6 0;