From efa45f81b5dcb9609b1e2365a51b7a25a1ba2ce0 Mon Sep 17 00:00:00 2001 From: Georg Holzmann Date: Tue, 12 Jul 2005 14:09:53 +0000 Subject: initial commit of adaptive svn path=/trunk/externals/grh/; revision=3317 --- adaptive/examples/01.system_identification.pd | 318 ++++++++++++++++++++++++++ 1 file changed, 318 insertions(+) create mode 100755 adaptive/examples/01.system_identification.pd (limited to 'adaptive/examples/01.system_identification.pd') diff --git a/adaptive/examples/01.system_identification.pd b/adaptive/examples/01.system_identification.pd new file mode 100755 index 0000000..57ae99f --- /dev/null +++ b/adaptive/examples/01.system_identification.pd @@ -0,0 +1,318 @@ +#N canvas 0 68 891 823 10; +#N canvas 10 567 633 314 unknown_system~ 0; +#X obj 26 26 inlet~; +#X obj 26 268 outlet~; +#X obj 115 227 s~ unknown_signal; +#X text 116 249 (for visualization); +#X obj 26 113 fexpr~ $f2*$x1 + $f3*$x1[-1] + $f4*$x1[-2]; +#X obj 122 81 f 0.33; +#X obj 218 81 f 0.33; +#X obj 315 82 f 0.33; +#X obj 122 53 r a0; +#X obj 218 55 r a1; +#X obj 315 56 r a2; +#X connect 0 0 4 0; +#X connect 4 0 1 0; +#X connect 4 0 2 0; +#X connect 5 0 4 1; +#X connect 6 0 4 2; +#X connect 7 0 4 3; +#X connect 8 0 5 0; +#X connect 9 0 6 0; +#X connect 10 0 7 0; +#X restore 245 268 pd unknown_system~; +#X obj 305 434 tgl 20 0 audio_io empty empty 0 -6 0 8 -262144 -1 -1 +0 1; +#X text 330 436 <- Audio IO; +#N canvas 523 194 390 347 adaptive_filter~ 0; +#X obj 37 35 inlet~; +#X text 22 15 input signal; +#X obj 143 35 inlet~; +#X text 122 15 desired signal; +#X obj 36 291 outlet~; +#X msg 249 63 adaptation 1; +#X obj 249 42 loadbang; +#X obj 224 214 s~ adaptive_signal; +#X text 224 234 (for visualization); +#X obj 249 141 r clear; +#X msg 248 162 clear; +#X obj 37 156 lms2~ 3 0.01; +#X obj 116 265 unpack f f f; +#X obj 116 293 outlet; +#X obj 162 293 outlet; +#X obj 208 293 outlet; +#X obj 249 94 r mu; +#X msg 249 116 mu \$1; +#X connect 0 0 11 0; +#X connect 2 0 11 1; +#X connect 5 0 11 0; +#X connect 6 0 5 0; +#X connect 9 0 10 0; +#X connect 10 0 11 0; +#X connect 11 0 4 0; +#X connect 11 0 7 0; +#X connect 11 2 12 0; +#X connect 12 0 13 0; +#X connect 12 1 14 0; +#X connect 12 2 15 0; +#X connect 16 0 17 0; +#X connect 17 0 11 0; +#X restore 117 337 pd adaptive_filter~; +#X obj 524 255 spectrum~; +#N canvas 0 0 450 300 graph6 0; +#X array adapt 512 float 0; +#X coords 0 1 511 -1 200 140 1; +#X restore 656 625 graph; +#X text 700 769 -- 512 samples ---; +#X obj 46 438 tgl 20 0 scopes_on empty empty 0 -6 0 8 -262144 -1 -1 +0 1; +#X obj 524 238 r~ adaptive_signal; +#X text 125 241 x[n]; +#X text 256 300 d[n]; +#X text 107 356 y[n]; +#X obj 775 238 r scopes_on; +#X obj 775 26 r scopes_on; +#X obj 524 26 r~ unknown_signal; +#N canvas 0 0 450 300 graph6 0; +#X array unkn 512 float 0; +#X coords 0 1 511 -1 200 140 1; +#X restore 654 453 graph; +#X text 698 597 -- 512 samples ---; +#X text 76 438 <- Visualization IO; +#X text 481 137 (1); +#X text 481 338 (2); +#N canvas 452 215 456 231 scope_stuff 0; +#X obj 45 38 r~ adaptive_signal; +#X obj 83 63 r scopes_on; +#X obj 279 69 r scopes_on; +#X obj 241 44 r~ unknown_signal; +#X obj 83 96 metro 1000; +#X obj 44 139 tabwrite~ adapt; +#X obj 279 95 metro 1000; +#X obj 240 138 tabwrite~ unkn; +#X connect 0 0 5 0; +#X connect 1 0 4 0; +#X connect 2 0 6 0; +#X connect 3 0 7 0; +#X connect 4 0 5 0; +#X connect 6 0 7 0; +#X restore 755 795 pd scope_stuff; +#X text 582 510 (3); +#X text 581 686 (4); +#X text 86 760 (3) d[n] in time domain; +#X text 86 777 (4) y[n] in time domain; +#X text 86 742 (2) amplitude of the output signal y[n]; +#X text 86 711 (1) amplitude of the desired signal d[n] (= output of +the unknown system); +#X obj 84 599 bng 20 250 50 0 clear empty empty 0 -6 0 8 -262144 -1 +-1; +#X text 113 601 <- clear coefficients \, so adaptation will start again +; +#X floatatom 46 471 5 0 100 0 - init_tlp tlp; +#X obj 685 26 r tlp; +#X obj 685 238 r tlp; +#X text 90 469 <- temporal lowpass for spectrum view (0...100); +#X text 54 689 VISUALIZATIONS:; +#X text 42 522 unknown system:; +#X text 72 546 d[n] =; +#X floatatom 159 378 5 0 0 1 c0 - -; +#X floatatom 223 378 5 0 0 1 c1 - -; +#X floatatom 285 378 5 0 0 1 c2 - -; +#X text 40 578 adaptive filter:; +#X floatatom 84 627 8 0 0 0 - mur mu; +#X text 146 627 <- step size parameter mu (learning rate); +#N canvas 215 124 617 210 init 0; +#X msg 43 99 2; +#X obj 269 45 loadbang; +#X obj 43 122 s init_tlp; +#X msg 138 98 0.33; +#X msg 179 99 0.33; +#X msg 223 100 0.33; +#X obj 138 121 s a0r; +#X obj 178 122 s a1r; +#X obj 223 123 s a2r; +#X obj 295 123 s mur; +#X msg 294 99 0.01; +#X msg 515 103 \; pd dsp \$1; +#X obj 515 78 r audio_io; +#X obj 381 123 s signalr; +#X msg 380 98 0; +#X connect 0 0 2 0; +#X connect 1 0 0 0; +#X connect 1 0 3 0; +#X connect 1 0 4 0; +#X connect 1 0 5 0; +#X connect 1 0 10 0; +#X connect 1 0 14 0; +#X connect 3 0 6 0; +#X connect 4 0 7 0; +#X connect 5 0 8 0; +#X connect 10 0 9 0; +#X connect 12 0 11 0; +#X connect 14 0 13 0; +#X restore 699 795 pd init; +#X floatatom 125 547 4 0 1 0 - a0r a0; +#X text 158 547 x[n] +; +#X text 244 547 x[n-1] +; +#X floatatom 211 547 4 0 1 0 - a1r a1; +#X floatatom 312 548 4 0 1 0 - a2r a2; +#X text 345 549 x[n-2]; +#N canvas 425 56 479 415 PROBLEM_DESCRIPTION 0; +#X text 33 89 In this example the adaptive filter tries to identify +an unknown system.; +#X text 34 124 The unknown system is a FIR filter of order 3 and the +adaptive system is an adaptive transversal filter using the LMS algorithm +(see lms~ help-patch) with 3 coefficients.; +#X text 75 224 d[n] = h0*x[n] + h1*x[n-1] + h2*x[n-2]; +#X text 35 188 unknown system:; +#X text 74 209 FIR Filter \, order = 3; +#X text 35 259 adaptive system:; +#X text 77 278 LMS \, 3 coefficients (c0 \, c1 \, c2); +#X text 35 342 The System Identification problem is sucessfull \, if +c0=h0 \, c1=h1 and c2=h2. Then the unknown and the adaptive system +have the same behavior.; +#X text 60 40 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT; +#X text 77 292 step-size parameter mu; +#X restore 34 94 pd PROBLEM_DESCRIPTION; +#N canvas 298 58 425 643 OBSERVATIONS 0; +#X text 24 20 OBSERVATIONS; +#X obj 27 119 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 mu1 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 0.5; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 27 143 pd mu1; +#X text 26 95 e.g. mu = 0.5:; +#X obj 29 201 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#X text 26 179 e.g. mu = 1e-05:; +#X text 25 59 1) influenc of mu:; +#X text 84 119 -> very fast adaptation \, but c0 \, c1 \, c2; +#X text 104 134 are not so precise; +#X text 83 201 -> slower adaptation \, but very precise; +#X text 27 430 2) influenc of white vs. non-white input signal:; +#X obj 30 490 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 mu2 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 1e-05; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 29 225 pd mu2; +#N canvas 863 469 389 255 in1 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 0.001; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 30 514 pd in1; +#X obj 32 570 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 in2 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 47 1; +#X msg 20 158 0.001; +#X connect 0 0 4 0; +#X connect 0 0 2 0; +#X connect 0 0 5 0; +#X connect 4 0 1 0; +#X connect 5 0 3 0; +#X restore 32 594 pd in2; +#X text 28 469 white signal:; +#X text 30 550 non-white signal:; +#X text 87 569 -> c0 \, c1 \, c2 not precise; +#X text 90 489 -> c0 \, c1 \, c2 precise; +#X text 29 274 how to choose mu ?; +#X text 72 300 0 < mu < 2/(abs(x[n])^2); +#X text 72 321 -> abs(x[n])^2 is the tap-input energy; +#X text 94 336 at time n (lenght of x[n] is PDs; +#X text 46 373 Note: this only ensures "stability on average"; +#X text 94 351 blocksize - so use block~ to change it!); +#X connect 1 0 2 0; +#X connect 4 0 12 0; +#X connect 11 0 13 0; +#X connect 14 0 15 0; +#X restore 34 120 pd OBSERVATIONS; +#X text 33 73 ReadMe:; +#N canvas 0 0 642 300 input_signal~ 0; +#X obj 77 90 noise~; +#X obj 201 84 inlet; +#X obj 77 217 *~; +#X obj 210 273 outlet~; +#X obj 201 115 sel 0 1; +#X msg 91 190 1; +#X msg 121 190 0; +#X obj 325 88 noise~; +#X text 53 64 white signal:; +#X text 292 63 non white signal:; +#X obj 322 224 *~; +#X msg 336 197 1; +#X msg 366 197 0; +#X obj 324 112 hip~ 300; +#X obj 492 148 bp~ 2543 2; +#X obj 406 149 bp~ 1000 3; +#X obj 323 148 bp~ 100 2; +#X connect 0 0 2 0; +#X connect 1 0 4 0; +#X connect 2 0 3 0; +#X connect 4 0 5 0; +#X connect 4 0 12 0; +#X connect 4 1 6 0; +#X connect 4 1 11 0; +#X connect 5 0 2 1; +#X connect 6 0 2 1; +#X connect 7 0 13 0; +#X connect 10 0 3 0; +#X connect 11 0 10 1; +#X connect 12 0 10 1; +#X connect 13 0 14 0; +#X connect 13 0 15 0; +#X connect 13 0 16 0; +#X connect 14 0 10 0; +#X connect 15 0 10 0; +#X connect 16 0 10 0; +#X restore 117 210 pd input_signal~; +#X obj 117 162 vradio 20 1 1 2 empty signalr empty 0 -6 0 8 -262144 +-1 -1 0; +#X text 144 163 white signal (noise); +#X text 145 183 non white signal (filtered noise); +#X obj 524 43 spectrum~; +#X text 33 32 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT; +#X connect 0 0 3 1; +#X connect 3 1 36 0; +#X connect 3 2 37 0; +#X connect 3 3 38 0; +#X connect 8 0 4 0; +#X connect 12 0 4 2; +#X connect 13 0 56 2; +#X connect 14 0 56 0; +#X connect 30 0 56 1; +#X connect 31 0 4 1; +#X connect 52 0 0 0; +#X connect 52 0 3 0; +#X connect 53 0 52 0; -- cgit v1.2.1