externals/grh/adaptive/doc help-lms2~.pd, NONE, 1.1 help-lms~.pd, NONE, 1.1 help-nlms2~.pd, NONE, 1.1 help-nlms~.pd, NONE, 1.1 - Pd-cvs

12 Jul 2005


      Update of /cvsroot/pure-data/externals/grh/adaptive/doc
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv30198/doc
Added Files:
    help-lms2~.pd help-lms~.pd help-nlms2~.pd help-nlms~.pd 
Log Message:
initial commit of adaptive
--- NEW FILE: help-nlms2~.pd ---
#N canvas 108 136 700 678 10;
#X floatatom 37 482 8 0 0 0 - - -;
#X obj 45 279 r message;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 37 460 pd unsig~;
#X text 89 219 input signal x[n];
#X text 182 252 reference signal d[n];
#X text 182 267 (desired signal);
#X text 108 461 output signal y[n];
#X text 35 166 init arg1: nr. of coefficients;
#X text 35 179 init arg2: stepsize parameter mu;
#X text 221 646 (c) Georg Holzmann grh@mur.at , 2005;
#X text 39 520 some more info:;
#X obj 219 24 cnv 15 258 58 empty empty empty 10 22 0 14 -1 -66577
0;
#X obj 223 28 cnv 15 250 50 empty empty nlms2~ 10 24 0 14 -228992 -1
0;
#X text 350 38 adaptive systems;
#X text 360 54 for Pure Data;
#X text 35 599 in the example folder !;
#X text 35 586 For much more examples see patches;
#X obj 38 218 sig~ 2;
#X obj 130 251 sig~ 1;
#X text 93 134 outputs for e[n] and c[n];
#X floatatom 82 434 8 0 0 0 - - -;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 82 412 pd unsig~;
#X text 153 413 error signal e[n];
#X obj 130 342 unpack f f;
#X floatatom 130 382 5 0 0 0 - - -;
#X floatatom 195 365 5 0 0 0 - - -;
#X text 169 382 c0[n];
#X text 237 365 c1[n];
#X text 135 322 coefficients:;
#X text 36 122 nlms2~: same as nlms~ , but with additional;
#X obj 37 304 nlms2~ 2 0.001;
#N canvas 812 118 510 736 NLMS2_EXAMPLE 0;
#X obj 31 109 sig~ 2;
#X obj 123 108 sig~ 1;
#X text 36 87 x[n];
#X text 131 89 d[n];
#X text 31 234 y[n];
#X obj 40 159 r $0-lms;
#X text 115 28 x[n] = 2 , d[n] = 1 , N = 1 (= nr. of coefficients)
;
#X text 26 29 EXAMPLE:;
#N canvas 0 0 450 300 graph3 0;
#X array x 1024 float 0;
#X array y 1024 float 0;
#X array d 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 51 302 graph;
#N canvas 422 247 876 321 plot_logic 0;
#X obj 37 162 tabwrite~ x;
#X obj 123 162 tabwrite~ y;
#X obj 209 162 tabwrite~ d;
#X obj 179 77 metro 100;
#X obj 179 26 loadbang;
#X msg 179 52 1;
#X obj 514 58 loadbang;
#X obj 37 136 r~ x_;
#X obj 123 136 r~ y_;
#X obj 209 136 r~ d_;
#X msg 505 153 ; x yticks 0 0.25 2;
#X msg 489 121 ; x xticks 0 32 2;
#X msg 646 150 ; x ylabel 1060 0 0.5 1 1.5 2;
#X msg 622 105 ; x xlabel -0.2 0 256 512 768 1024;
#X obj 296 102 r~ e_;
#X obj 297 161 tabwrite~ e;
#X obj 297 131 *~;
#X msg 498 224 ; e xticks 0 32 2;
#X msg 514 256 ; e yticks 0 0.25 2;
#X msg 631 208 ; e xlabel -0.2 0 256 512 768 1024;
#X msg 655 253 ; e ylabel 1060 0 0.5 1 1.5 2;
#X obj 541 198 loadbang;
#X connect 3 0 0 0;
#X connect 3 0 1 0;
#X connect 3 0 2 0;
#X connect 3 0 15 0;
#X connect 4 0 5 0;
#X connect 5 0 3 0;
#X connect 6 0 11 0;
#X connect 6 0 10 0;
#X connect 6 0 13 0;
#X connect 6 0 12 0;
#X connect 7 0 0 0;
#X connect 8 0 1 0;
#X connect 9 0 2 0;
#X connect 14 0 16 0;
#X connect 14 0 16 1;
#X connect 16 0 15 0;
#X connect 21 0 17 0;
#X connect 21 0 18 0;
#X connect 21 0 19 0;
#X connect 21 0 20 0;
#X restore 198 246 pd plot_logic;
#X obj 341 244 s $0-lms;
#X msg 341 220 adaptation 1;
#X obj 341 199 loadbang;
#X obj 198 207 s $0-lms;
#X msg 198 171 mu $1;
#X floatatom 210 150 8 0 0 0 - - -;
#X text 275 147 <- try different mu;
#X msg 199 109 clear;
#X text 242 110 <- clear to start new adaptation;
#X text 189 461 -- 1024 samples --;
#X obj 37 131 s~ x_;
#X obj 132 130 s~ d_;
#X obj 31 213 s~ y_;
#X obj 76 213 s~ e_;
#N canvas 0 0 450 300 graph3 0;
#X array e 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 48 534 graph;
#X text 195 693 -- 1024 samples --;
#X text 47 510 squared error e^2[n] (learning curve):;
#X obj 30 181 nlms2~ 1 0.001;
#X connect 0 0 20 0;
#X connect 0 0 27 0;
#X connect 1 0 21 0;
#X connect 1 0 27 1;
#X connect 5 0 27 0;
#X connect 11 0 10 0;
#X connect 12 0 11 0;
#X connect 14 0 13 0;
#X connect 15 0 14 0;
#X connect 17 0 13 0;
#X connect 27 0 22 0;
#X connect 27 1 23 0;
#X restore 38 540 pd NLMS2_EXAMPLE;
#N canvas 347 29 502 539 NLMS_EXPLANATION 0;
#X text 35 135 x[n] ... input signal of the system;
#X text 35 120 c[n] ... coefficient vector of the system;
#X text 35 104 y[n] ... output signal of the system;
#X text 35 398 d[n] ... desired signal , reference signal;
#X text 50 74 -> y[n] = c0[n]*x[n] + c1[n]*x[n-1] + c2[n]*x[n-2] +
...;
#X text 35 312 mu ... step-size parameter (learning rate);
#X text 34 282 c[n] ... new coefficient vector;
#X text 34 297 c[n-1] ... old coefficient vector;
#X text 34 354 e[n] ... error sample at time n , LMS tries to minimize
this error;
#X text 35 382 x[n] ... tap-input vector at time n;
#X text 71 241 with e[n] = d[n] - y[n];
#X text 33 33 An adaptive system is simply a FIR filter with the coefficients
c[n] , which can be learned.;
#X text 36 440 How to choose mu ?;
#X text 36 463 Sufficient (deterministic) stability condition:;
#X text 32 195 The normalized LMS Adaptation Algorithm:;
#X text 70 226 c[n] = c[n-1] + mu/(alpha+abs(x[n])^2) *e[n]*x[n];
#X text 34 327 alpha ... a small positive constant , only to avoid
division by zero;
#X text 152 490 0 < mu < 2;
#X restore 38 561 pd NLMS_EXPLANATION;
#X msg 387 352 getmu;
#X msg 387 331 mu $1;
#X floatatom 395 312 8 0 0 0 - - -;
#X msg 387 460 getN;
#X msg 387 549 help;
#X msg 387 209 clear;
#X msg 387 276 print;
#X msg 387 517 read demo.dat;
#X msg 387 173 getadaptation;
#X obj 387 130 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0
1;
#X msg 387 151 adaptation $1;
#X msg 387 496 write demo.dat;
#X obj 387 578 s message;
#X text 490 151 turn adaptation on/off;
#X text 435 203 clear current coefficients;
#X text 435 216 and set them back to 0;
#X text 436 275 print current coefficients;
#X text 438 335 set/get stepsize parameter;
#X text 439 349 mu (learning rate);
#X text 428 460 get Nr. of coefficients;
#X text 498 513 and mu to file;
#X text 498 499 write/read coefficients;
#X floatatom 395 382 8 0 0 0 - - -;
#X msg 387 401 alpha $1;
#X msg 387 422 getalpha;
#X text 456 403 set/get alpha (normally;
#X text 457 417 you don't need that);
#X msg 387 246 init_unity;
#X text 467 233 set first coefficient to 1 ,;
#X text 469 246 all others to 0 (= delay;
#X text 468 259 free transmission);
#X connect 1 0 30 0;
#X connect 2 0 0 0;
#X connect 17 0 30 0;
#X connect 18 0 30 1;
#X connect 21 0 20 0;
#X connect 23 0 24 0;
#X connect 23 1 25 0;
#X connect 30 0 2 0;
#X connect 30 1 21 0;
#X connect 30 2 23 0;
#X connect 33 0 45 0;
#X connect 34 0 45 0;
#X connect 35 0 34 0;
#X connect 36 0 45 0;
#X connect 37 0 45 0;
#X connect 38 0 45 0;
#X connect 39 0 45 0;
#X connect 40 0 45 0;
#X connect 41 0 45 0;
#X connect 42 0 43 0;
#X connect 43 0 45 0;
#X connect 44 0 45 0;
#X connect 55 0 56 0;
#X connect 56 0 45 0;
#X connect 57 0 45 0;
#X connect 60 0 45 0;
--- NEW FILE: help-nlms~.pd ---
#N canvas 0 0 700 667 10;
#X msg 395 342 getmu;
#X msg 395 321 mu $1;
#X floatatom 403 302 8 0 0 0 - - -;
#X msg 395 450 getN;
#X msg 395 539 help;
#X msg 395 199 clear;
#X msg 395 266 print;
#X floatatom 37 406 8 0 0 0 - - -;
#X msg 395 507 read demo.dat;
#X msg 395 163 getadaptation;
#X obj 395 120 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0
1;
#X msg 395 141 adaptation $1;
#X msg 395 486 write demo.dat;
#X obj 45 320 r message;
#X obj 395 568 s message;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 37 384 pd unsig~;
#X text 89 260 input signal x[n];
#X text 177 287 reference signal d[n];
#X text 177 302 (desired signal);
#X text 108 385 output signal y[n];
#X text 35 172 init arg1: nr. of coefficients;
#X text 498 141 turn adaptation on/off;
#X text 443 193 clear current coefficients;
#X text 443 206 and set them back to 0;
#X text 444 265 print current coefficients;
#X text 35 185 init arg2: stepsize parameter mu;
#X text 446 325 set/get stepsize parameter;
#X text 447 339 mu (learning rate);
#X text 436 450 get Nr. of coefficients;
#X text 506 503 and mu to file;
#X text 506 489 write/read coefficients;
#X text 206 622 (c) Georg Holzmann grh@mur.at , 2005;
#X text 36 481 some more info:;
#X obj 219 24 cnv 15 258 58 empty empty empty 10 22 0 14 -1 -66577
0;
#X obj 223 28 cnv 15 250 50 empty empty nlms~ 10 24 0 14 -228992 -1
0;
#X text 350 38 adaptive systems;
#X text 360 54 for Pure Data;
#X text 34 562 in the example folder !;
#X text 35 548 For much more examples see patches;
#X obj 38 259 sig~ 2;
#X obj 125 286 sig~ 1;
#X text 36 134 Normalized LMS: normalized least mean square;
#X text 146 147 adaptation algorithm;
#N canvas 347 29 502 539 NLMS_EXPLANATION 0;
#X text 35 135 x[n] ... input signal of the system;
#X text 35 120 c[n] ... coefficient vector of the system;
#X text 35 104 y[n] ... output signal of the system;
#X text 35 398 d[n] ... desired signal , reference signal;
#X text 50 74 -> y[n] = c0[n]*x[n] + c1[n]*x[n-1] + c2[n]*x[n-2] +
...;
#X text 35 312 mu ... step-size parameter (learning rate);
#X text 34 282 c[n] ... new coefficient vector;
#X text 34 297 c[n-1] ... old coefficient vector;
#X text 34 354 e[n] ... error sample at time n , LMS tries to minimize
this error;
#X text 35 382 x[n] ... tap-input vector at time n;
#X text 71 241 with e[n] = d[n] - y[n];
#X text 33 33 An adaptive system is simply a FIR filter with the coefficients
c[n] , which can be learned.;
#X text 36 440 How to choose mu ?;
#X text 36 463 Sufficient (deterministic) stability condition:;
#X text 32 195 The normalized LMS Adaptation Algorithm:;
#X text 70 226 c[n] = c[n-1] + mu/(alpha+abs(x[n])^2) *e[n]*x[n];
#X text 34 327 alpha ... a small positive constant , only to avoid
division by zero;
#X text 152 490 0 < mu < 2;
#X restore 38 503 pd NLMS_EXPLANATION;
#N canvas 536 326 510 502 NLMS_EXAMPLE 0;
#X obj 31 109 sig~ 2;
#X obj 116 111 sig~ 1;
#X text 36 87 x[n];
#X text 124 92 d[n];
#X text 31 234 y[n];
#X text 115 28 x[n] = 2 , d[n] = 1 , N = 1 (= nr. of coefficients)
;
#X text 26 29 EXAMPLE:;
#N canvas 0 0 450 300 graph3 0;
#X array x 1024 float 0;
#X array y 1024 float 0;
#X array d 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 51 302 graph;
#N canvas 422 247 725 220 plot_logic 0;
#X obj 72 168 tabwrite~ x;
#X obj 158 168 tabwrite~ y;
#X obj 244 168 tabwrite~ d;
#X obj 191 105 metro 100;
#X obj 191 54 loadbang;
#X msg 191 80 1;
#X obj 386 57 loadbang;
#X obj 72 142 r~ x_;
#X obj 158 142 r~ y_;
#X obj 244 142 r~ d_;
#X msg 362 153 ; x yticks 0 0.25 2;
#X msg 346 121 ; x xticks 0 32 2;
#X msg 503 150 ; x ylabel 1060 0 0.5 1 1.5 2;
#X msg 479 105 ; x xlabel -0.2 0 256 512 768 1024;
#X connect 3 0 0 0;
#X connect 3 0 1 0;
#X connect 3 0 2 0;
#X connect 4 0 5 0;
#X connect 5 0 3 0;
#X connect 6 0 11 0;
#X connect 6 0 10 0;
#X connect 6 0 13 0;
#X connect 6 0 12 0;
#X connect 7 0 0 0;
#X connect 8 0 1 0;
#X connect 9 0 2 0;
#X restore 198 246 pd plot_logic;
#X msg 341 220 adaptation 1;
#X obj 341 199 loadbang;
#X msg 198 171 mu $1;
#X floatatom 210 150 8 0 0 0 - - -;
#X text 275 147 <- try different mu;
#X msg 199 109 clear;
#X text 242 110 <- clear to start new adaptation;
#X text 189 461 -- 1024 samples --;
#X obj 37 131 s~ x_;
#X obj 125 133 s~ d_;
#X obj 31 213 s~ y_;
#X obj 40 159 r $0-nlms;
#X obj 198 207 s $0-nlms;
#X obj 341 244 s $0-nlms;
#X obj 30 181 nlms~ 1 0.001;
#X connect 0 0 17 0;
#X connect 0 0 23 0;
#X connect 1 0 18 0;
#X connect 1 0 23 1;
#X connect 9 0 22 0;
#X connect 10 0 9 0;
#X connect 11 0 21 0;
#X connect 12 0 11 0;
#X connect 14 0 21 0;
#X connect 20 0 23 0;
#X connect 23 0 19 0;
#X restore 38 525 pd NLMS_EXAMPLE;
#X floatatom 403 372 8 0 0 0 - - -;
#X msg 395 391 alpha $1;
#X msg 395 412 getalpha;
#X text 464 393 set/get alpha (normally;
#X text 465 407 you don't need that);
#X obj 38 345 nlms~ 2 0.001;
#X msg 395 236 init_unity;
#X text 475 223 set first coefficient to 1 ,;
#X text 477 236 all others to 0 (= delay;
#X text 476 249 free transmission);
#X connect 0 0 14 0;
#X connect 1 0 14 0;
#X connect 2 0 1 0;
#X connect 3 0 14 0;
#X connect 4 0 14 0;
#X connect 5 0 14 0;
#X connect 6 0 14 0;
#X connect 8 0 14 0;
#X connect 9 0 14 0;
#X connect 10 0 11 0;
#X connect 11 0 14 0;
#X connect 12 0 14 0;
#X connect 13 0 50 0;
#X connect 15 0 7 0;
#X connect 39 0 50 0;
#X connect 40 0 50 1;
#X connect 45 0 46 0;
#X connect 46 0 14 0;
#X connect 47 0 14 0;
#X connect 50 0 15 0;
#X connect 51 0 14 0;
--- NEW FILE: help-lms~.pd ---
#N canvas 148 190 700 570 10;
#X msg 395 341 getmu;
#X msg 395 320 mu $1;
#X floatatom 403 301 8 0 0 0 - - -;
#X msg 395 376 getN;
#X msg 395 465 help;
#X msg 395 196 clear;
#X msg 395 263 print;
#X floatatom 37 365 8 0 0 0 - - -;
#X msg 395 433 read demo.dat;
#X msg 395 163 getadaptation;
#X obj 395 120 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0
1;
#X msg 395 141 adaptation $1;
#X msg 395 412 write demo.dat;
#X text 36 122 LMS: least mean square adaptation algorithm;
#X obj 45 279 r message;
#X obj 395 494 s message;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 37 343 pd unsig~;
#X text 89 219 input signal x[n];
#X text 169 248 reference signal d[n];
#X text 169 263 (desired signal);
#X text 108 344 output signal y[n];
#X obj 37 304 lms~ 2 1e-04;
#X text 35 160 init arg1: nr. of coefficients;
#X text 498 141 turn adaptation on/off;
#X text 443 190 clear current coefficients;
#X text 443 203 and set them back to 0;
#X text 444 262 print current coefficients;
#X text 35 173 init arg2: stepsize parameter mu;
#X text 446 324 set/get stepsize parameter;
#X text 447 338 mu (learning rate);
#X text 436 376 get Nr. of coefficients;
#X text 506 429 and mu to file;
#X text 506 415 write/read coefficients;
#X text 223 536 (c) Georg Holzmann grh@mur.at , 2005;
#N canvas 347 29 502 634 LMS_EXPLANATION 0;
#X text 35 135 x[n] ... input signal of the system;
#X text 35 120 c[n] ... coefficient vector of the system;
#X text 35 104 y[n] ... output signal of the system;
#X text 43 369 d[n] ... desired signal , reference signal;
#X text 50 74 -> y[n] = c0[n]*x[n] + c1[n]*x[n-1] + c2[n]*x[n-2] +
...;
#X text 32 195 The LMS Adaptation Algorithm:;
#X text 70 226 c[n] = c[n-1] + mu*e[n]*x[n];
#X text 43 309 mu ... step-size parameter (learning rate);
#X text 42 279 c[n] ... new coefficient vector;
#X text 42 294 c[n-1] ... old coefficient vector;
#X text 42 325 e[n] ... error sample at time n , LMS tries to minimize
this error;
#X text 43 353 x[n] ... tap-input vector at time n;
#X text 71 241 with e[n] = d[n] - y[n];
#X text 33 33 An adaptive system is simply a FIR filter with the coefficients
c[n] , which can be learned.;
#X text 104 485 0 < mu < 2/(abs(x[n])^2);
#X text 38 517 -> abs(x[n])^2 is the tap-input energy;
#X text 60 532 at time n (lenght of x[n] is PDs;
#X text 35 579 Note: this only ensures "stability on average";
#X text 60 547 blocksize - so use block~ to change it!);
#X text 34 432 How to choose mu ?;
#X text 34 455 Sufficient (deterministic) stability condition:;
#X restore 38 429 pd LMS_EXPLANATION;
#X text 36 407 some more info:;
#N canvas 536 326 510 502 LMS_EXAMPLE 0;
#X obj 31 109 sig~ 2;
#X obj 108 109 sig~ 1;
#X text 36 87 x[n];
#X text 116 90 d[n];
#X text 31 234 y[n];
#X obj 40 159 r $0-lms;
#X text 115 28 x[n] = 2 , d[n] = 1 , N = 1 (= nr. of coefficients)
;
#X text 26 29 EXAMPLE:;
#N canvas 0 0 450 300 graph3 0;
#X array x 1024 float 0;
#X array y 1024 float 0;
#X array d 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 51 302 graph;
#N canvas 422 247 725 220 plot_logic 0;
#X obj 72 168 tabwrite~ x;
#X obj 158 168 tabwrite~ y;
#X obj 244 168 tabwrite~ d;
#X obj 191 105 metro 100;
#X obj 191 54 loadbang;
#X msg 191 80 1;
#X obj 386 57 loadbang;
#X obj 72 142 r~ x_;
#X obj 158 142 r~ y_;
#X obj 244 142 r~ d_;
#X msg 362 153 ; x yticks 0 0.25 2;
#X msg 346 121 ; x xticks 0 32 2;
#X msg 503 150 ; x ylabel 1060 0 0.5 1 1.5 2;
#X msg 479 105 ; x xlabel -0.2 0 256 512 768 1024;
#X connect 3 0 0 0;
#X connect 3 0 1 0;
#X connect 3 0 2 0;
#X connect 4 0 5 0;
#X connect 5 0 3 0;
#X connect 6 0 11 0;
#X connect 6 0 10 0;
#X connect 6 0 13 0;
#X connect 6 0 12 0;
#X connect 7 0 0 0;
#X connect 8 0 1 0;
#X connect 9 0 2 0;
#X restore 198 246 pd plot_logic;
#X obj 341 244 s $0-lms;
#X msg 341 220 adaptation 1;
#X obj 341 199 loadbang;
#X obj 198 207 s $0-lms;
#X msg 198 171 mu $1;
#X floatatom 210 150 8 0 0 0 - - -;
#X text 275 147 <- try different mu;
#X msg 199 109 clear;
#X text 242 110 <- clear to start new adaptation;
#X obj 30 181 lms~ 1 1e-05;
#X text 189 461 -- 1024 samples --;
#X obj 37 131 s~ x_;
#X obj 117 131 s~ d_;
#X obj 31 213 s~ y_;
#X connect 0 0 19 0;
#X connect 0 0 21 0;
#X connect 1 0 19 1;
#X connect 1 0 22 0;
#X connect 5 0 19 0;
#X connect 11 0 10 0;
#X connect 12 0 11 0;
#X connect 14 0 13 0;
#X connect 15 0 14 0;
#X connect 17 0 13 0;
#X connect 19 0 23 0;
#X restore 38 451 pd LMS_EXAMPLE;
#X obj 219 24 cnv 15 258 58 empty empty empty 10 22 0 14 -1 -66577
0;
#X obj 223 28 cnv 15 250 50 empty empty lms~ 10 24 0 14 -228992 -1
0;
#X text 350 38 adaptive systems;
#X text 360 54 for Pure Data;
#X text 34 488 in the example folder !;
#X text 35 474 For much more examples see patches;
#X obj 38 218 sig~ 2;
#X obj 117 247 sig~ 1;
#X msg 395 232 init_unity;
#X text 475 219 set first coefficient to 1 ,;
#X text 477 232 all others to 0 (= delay;
#X text 476 245 free transmission);
#X connect 0 0 15 0;
#X connect 1 0 15 0;
#X connect 2 0 1 0;
#X connect 3 0 15 0;
#X connect 4 0 15 0;
#X connect 5 0 15 0;
#X connect 6 0 15 0;
#X connect 8 0 15 0;
#X connect 9 0 15 0;
#X connect 10 0 11 0;
#X connect 11 0 15 0;
#X connect 12 0 15 0;
#X connect 14 0 21 0;
#X connect 16 0 7 0;
#X connect 21 0 16 0;
#X connect 43 0 21 0;
#X connect 44 0 21 1;
#X connect 45 0 15 0;
--- NEW FILE: help-lms2~.pd ---
#N canvas 213 0 700 678 10;
#X floatatom 37 482 8 0 0 0 - - -;
#X obj 45 279 r message;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 37 460 pd unsig~;
#X text 89 219 input signal x[n];
#X text 176 259 reference signal d[n];
#X text 176 274 (desired signal);
#X text 108 461 output signal y[n];
#X text 35 166 init arg1: nr. of coefficients;
#X text 35 179 init arg2: stepsize parameter mu;
#X text 198 641 (c) Georg Holzmann grh@mur.at , 2005;
#X text 39 520 some more info:;
#X obj 219 24 cnv 15 258 58 empty empty empty 10 22 0 14 -1 -66577
0;
#X obj 223 28 cnv 15 250 50 empty empty lms2~ 10 24 0 14 -228992 -1
0;
#X text 350 38 adaptive systems;
#X text 360 54 for Pure Data;
#X text 35 599 in the example folder !;
#X text 35 586 For much more examples see patches;
#X obj 38 218 sig~ 2;
#X obj 124 258 sig~ 1;
#X text 85 134 outputs for e[n] and c[n];
#X floatatom 82 434 8 0 0 0 - - -;
#N canvas 0 0 260 260 unsig~ 0;
#X obj 22 42 inlet~;
#X text 62 42 ~signal_in~;
#X obj 22 168 outlet;
#X text 69 169 float-out;
#X obj 22 142 snapshot~;
#X obj 39 119 metro 300;
#X obj 40 70 loadbang;
#X msg 40 95 1;
#X connect 0 0 4 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 7 0;
#X connect 7 0 5 0;
#X restore 82 412 pd unsig~;
#X text 153 413 error signal e[n];
#X obj 123 343 unpack f f;
#X floatatom 123 383 5 0 0 0 - - -;
#X floatatom 188 366 5 0 0 0 - - -;
#X text 162 383 c0[n];
#X text 230 366 c1[n];
#X text 128 323 coefficients:;
#X text 36 122 lms2~: same as lms~ , but with additional;
#X obj 37 304 lms2~ 2 1e-04;
#N canvas 347 29 502 634 LMS_EXPLANATION 0;
#X text 35 135 x[n] ... input signal of the system;
#X text 35 120 c[n] ... coefficient vector of the system;
#X text 35 104 y[n] ... output signal of the system;
#X text 43 369 d[n] ... desired signal , reference signal;
#X text 50 74 -> y[n] = c0[n]*x[n] + c1[n]*x[n-1] + c2[n]*x[n-2] +
...;
#X text 32 195 The LMS Adaptation Algorithm:;
#X text 70 226 c[n] = c[n-1] + mu*e[n]*x[n];
#X text 43 309 mu ... step-size parameter (learning rate);
#X text 42 279 c[n] ... new coefficient vector;
#X text 42 294 c[n-1] ... old coefficient vector;
#X text 42 325 e[n] ... error sample at time n , LMS tries to minimize
this error;
#X text 43 353 x[n] ... tap-input vector at time n;
#X text 71 241 with e[n] = d[n] - y[n];
#X text 33 33 An adaptive system is simply a FIR filter with the coefficients
c[n] , which can be learned.;
#X text 104 485 0 < mu < 2/(abs(x[n])^2);
#X text 38 517 -> abs(x[n])^2 is the tap-input energy;
#X text 60 532 at time n (lenght of x[n] is PDs;
#X text 35 579 Note: this only ensures "stability on average";
#X text 60 547 blocksize - so use block~ to change it!);
#X text 34 432 How to choose mu ?;
#X text 34 455 Sufficient (deterministic) stability condition:;
#X restore 38 561 pd LMS_EXPLANATION;
#N canvas 812 118 510 736 LMS2_EXAMPLE 0;
#X obj 31 109 sig~ 2;
#X obj 116 110 sig~ 1;
#X text 36 87 x[n];
#X text 124 91 d[n];
#X text 31 234 y[n];
#X obj 40 159 r $0-lms;
#X text 115 28 x[n] = 2 , d[n] = 1 , N = 1 (= nr. of coefficients)
;
#X text 26 29 EXAMPLE:;
#N canvas 0 0 450 300 graph3 0;
#X array x 1024 float 0;
#X array y 1024 float 0;
#X array d 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 51 302 graph;
#N canvas 422 247 876 321 plot_logic 0;
#X obj 37 162 tabwrite~ x;
#X obj 123 162 tabwrite~ y;
#X obj 209 162 tabwrite~ d;
#X obj 179 77 metro 100;
#X obj 179 26 loadbang;
#X msg 179 52 1;
#X obj 514 58 loadbang;
#X obj 37 136 r~ x_;
#X obj 123 136 r~ y_;
#X obj 209 136 r~ d_;
#X msg 505 153 ; x yticks 0 0.25 2;
#X msg 489 121 ; x xticks 0 32 2;
#X msg 646 150 ; x ylabel 1060 0 0.5 1 1.5 2;
#X msg 622 105 ; x xlabel -0.2 0 256 512 768 1024;
#X obj 296 102 r~ e_;
#X obj 297 161 tabwrite~ e;
#X obj 297 131 *~;
#X msg 498 224 ; e xticks 0 32 2;
#X msg 514 256 ; e yticks 0 0.25 2;
#X msg 631 208 ; e xlabel -0.2 0 256 512 768 1024;
#X msg 655 253 ; e ylabel 1060 0 0.5 1 1.5 2;
#X obj 541 198 loadbang;
#X connect 3 0 0 0;
#X connect 3 0 1 0;
#X connect 3 0 2 0;
#X connect 3 0 15 0;
#X connect 4 0 5 0;
#X connect 5 0 3 0;
#X connect 6 0 11 0;
#X connect 6 0 10 0;
#X connect 6 0 13 0;
#X connect 6 0 12 0;
#X connect 7 0 0 0;
#X connect 8 0 1 0;
#X connect 9 0 2 0;
#X connect 14 0 16 0;
#X connect 14 0 16 1;
#X connect 16 0 15 0;
#X connect 21 0 17 0;
#X connect 21 0 18 0;
#X connect 21 0 19 0;
#X connect 21 0 20 0;
#X restore 198 246 pd plot_logic;
#X obj 341 244 s $0-lms;
#X msg 341 220 adaptation 1;
#X obj 341 199 loadbang;
#X obj 198 207 s $0-lms;
#X msg 198 171 mu $1;
#X floatatom 210 150 8 0 0 0 - - -;
#X text 275 147 <- try different mu;
#X msg 199 109 clear;
#X text 242 110 <- clear to start new adaptation;
#X text 189 461 -- 1024 samples --;
#X obj 37 131 s~ x_;
#X obj 125 132 s~ d_;
#X obj 31 213 s~ y_;
#X obj 74 213 s~ e_;
#N canvas 0 0 450 300 graph3 0;
#X array e 1024 float 0;
#X coords 0 2 1023 0 400 140 1;
#X restore 48 534 graph;
#X text 195 693 -- 1024 samples --;
#X text 47 510 squared error e^2[n] (learning curve):;
#X obj 30 181 lms2~ 1 1e-05;
#X connect 0 0 20 0;
#X connect 0 0 27 0;
#X connect 1 0 21 0;
#X connect 1 0 27 1;
#X connect 5 0 27 0;
#X connect 11 0 10 0;
#X connect 12 0 11 0;
#X connect 14 0 13 0;
#X connect 15 0 14 0;
#X connect 17 0 13 0;
#X connect 27 0 22 0;
#X connect 27 1 23 0;
#X restore 38 540 pd LMS2_EXAMPLE;
#X msg 384 373 getmu;
#X msg 384 352 mu $1;
#X floatatom 392 333 8 0 0 0 - - -;
#X msg 384 408 getN;
#X msg 384 497 help;
#X msg 384 228 clear;
#X msg 384 295 print;
#X msg 384 465 read demo.dat;
#X msg 384 195 getadaptation;
#X obj 384 152 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0
1;
#X msg 384 173 adaptation $1;
#X msg 384 444 write demo.dat;
#X obj 384 526 s message;
#X text 487 173 turn adaptation on/off;
#X text 432 222 clear current coefficients;
#X text 432 235 and set them back to 0;
#X text 433 294 print current coefficients;
#X text 435 356 set/get stepsize parameter;
#X text 436 370 mu (learning rate);
#X text 425 408 get Nr. of coefficients;
#X text 495 461 and mu to file;
#X text 495 447 write/read coefficients;
#X msg 384 264 init_unity;
#X text 464 251 set first coefficient to 1 ,;
#X text 466 264 all others to 0 (= delay;
#X text 465 277 free transmission);
#X connect 1 0 30 0;
#X connect 2 0 0 0;
#X connect 17 0 30 0;
#X connect 18 0 30 1;
#X connect 21 0 20 0;
#X connect 23 0 24 0;
#X connect 23 1 25 0;
#X connect 30 0 2 0;
#X connect 30 1 21 0;
#X connect 30 2 23 0;
#X connect 33 0 45 0;
#X connect 34 0 45 0;
#X connect 35 0 34 0;
#X connect 36 0 45 0;
#X connect 37 0 45 0;
#X connect 38 0 45 0;
#X connect 39 0 45 0;
#X connect 40 0 45 0;
#X connect 41 0 45 0;
#X connect 42 0 43 0;
#X connect 43 0 45 0;
#X connect 44 0 45 0;
#X connect 55 0 45 0;