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#X text 116 249 (for visualization);
#X obj 26 113 fexpr~ $f2*$x1 + $f3*$x1[-1] + $f4*$x1[-2];
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#X restore 245 268 pd unknown_system~;
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#X text 330 436 <- Audio IO;
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#X text 22 15 input signal;
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#X text 122 15 desired signal;
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#X text 224 234 (for visualization);
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#X msg 249 116 mu \$1;
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#X text 700 769 -- 512 samples ---;
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#X text 76 438 <- Visualization IO;
#X text 481 137 (1);
#X text 481 338 (2);
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#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);
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#X text 113 601 <- clear coefficients \, so adaptation will start again
;
#X floatatom 46 471 5 0 100 0 - init_tlp tlp;
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#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] =;
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#X text 40 578 adaptive filter:;
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#X text 146 627 <- step size parameter mu (learning rate);
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#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 77 292 step-size parameter mu;
#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 2 coefficients.;
#X text 77 278 LMS \, 2 coefficients (c0 \, c1);
#X text 60 40 SYSTEM IDENTIFICATION: UNDERMODELING;
#X text 33 85 In the case of undermodeling the order of the unknown
system is higher than the order of the adaptive system.;
#X restore 34 94 pd PROBLEM_DESCRIPTION;
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#X text 24 20 OBSERVATIONS;
#X text 20 71 White Noise Case:;
#X text 22 152 Non-White Case:;
#X text 47 193 this case the error of the adaptive system is;
#X text 48 209 much higher !;
#X text 48 176 h0 \, h1 and h2 have influence on the error \, so in
;
#X text 51 96 only h1 and h2 have influence on the error;
#X text 53 111 (min. error);
#X restore 34 120 pd OBSERVATIONS;
#X text 33 73 ReadMe:;
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#X text 53 64 white signal:;
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#X text 144 163 white signal (noise);
#X text 145 183 non white signal (filtered noise);
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#X text 109 32 SYSTEM IDENTIFICATION: UNDERMODELING;
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