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#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:;
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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 85 134 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 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;
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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 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:;
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#X text 115 28 x[n] = 2 \, d[n] = 1 \, N = 1 (= nr. of coefficients)
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#X text 26 29 EXAMPLE:;
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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 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);
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