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+#X text 62 42 ~signal_in~;
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+#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:;
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+#X obj 223 28 cnv 15 250 50 empty empty nlms2~ 10 24 0 14 -228992 -1
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+#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;
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+#X text 93 134 outputs for e[n] and c[n];
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+#X text 153 413 error signal e[n];
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+#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;
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+#X text 36 87 x[n];
+#X text 131 89 d[n];
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+#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 msg 341 220 adaptation 1;
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+#X msg 198 171 mu \$1;
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+#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 --;
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+#X text 195 693 -- 1024 samples --;
+#X text 47 510 squared error e^2[n] (learning curve):;
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+#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
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+#X text 152 490 0 < mu < 2;
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+#X msg 387 549 help;
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+#X msg 387 276 print;
+#X msg 387 517 read demo.dat;
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+#X msg 387 151 adaptation \$1;
+#X msg 387 496 write demo.dat;
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+#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;
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+#X text 456 403 set/get alpha (normally;
+#X text 457 417 you don't need that);
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+#X text 467 233 set first coefficient to 1 \,;
+#X text 469 246 all others to 0 (= delay;
+#X text 468 259 free transmission);
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