path: root/adaptive/examples/01.system_identification.pd

#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;