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+#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;
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+#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:;
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+#X restore 51 302 graph;
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+#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;
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+#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;
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+#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);
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