diff options
Diffstat (limited to 'adaptive/examples')
-rwxr-xr-x | adaptive/examples/01.system_identification.pd | 318 | ||||
-rwxr-xr-x | adaptive/examples/02.persistent_excitation.pd | 396 | ||||
-rwxr-xr-x | adaptive/examples/03.undermodeling.pd | 238 | ||||
-rwxr-xr-x | adaptive/examples/04.misadjustment.pd | 475 | ||||
-rwxr-xr-x | adaptive/examples/05.tracking.pd | 791 | ||||
-rwxr-xr-x | adaptive/examples/06.interference_cancelation.pd | 323 | ||||
-rwxr-xr-x | adaptive/examples/07.adaptive_equalization.pd | 447 | ||||
-rwxr-xr-x | adaptive/examples/08.decision-directed_equalization.pd | 167 | ||||
-rwxr-xr-x | adaptive/examples/coef.dat | 12 | ||||
-rwxr-xr-x | adaptive/examples/spectrum~.pd | 243 |
10 files changed, 3410 insertions, 0 deletions
diff --git a/adaptive/examples/01.system_identification.pd b/adaptive/examples/01.system_identification.pd new file mode 100755 index 0000000..57ae99f --- /dev/null +++ b/adaptive/examples/01.system_identification.pd @@ -0,0 +1,318 @@ +#N canvas 0 68 891 823 10; +#N canvas 10 567 633 314 unknown_system~ 0; +#X obj 26 26 inlet~; +#X obj 26 268 outlet~; +#X obj 115 227 s~ unknown_signal; +#X text 116 249 (for visualization); +#X obj 26 113 fexpr~ $f2*$x1 + $f3*$x1[-1] + $f4*$x1[-2]; +#X obj 122 81 f 0.33; +#X obj 218 81 f 0.33; +#X obj 315 82 f 0.33; +#X obj 122 53 r a0; +#X obj 218 55 r a1; +#X obj 315 56 r a2; +#X connect 0 0 4 0; +#X connect 4 0 1 0; +#X connect 4 0 2 0; +#X connect 5 0 4 1; +#X connect 6 0 4 2; +#X connect 7 0 4 3; +#X connect 8 0 5 0; +#X connect 9 0 6 0; +#X connect 10 0 7 0; +#X restore 245 268 pd unknown_system~; +#X obj 305 434 tgl 20 0 audio_io empty empty 0 -6 0 8 -262144 -1 -1 +0 1; +#X text 330 436 <- Audio IO; +#N canvas 523 194 390 347 adaptive_filter~ 0; +#X obj 37 35 inlet~; +#X text 22 15 input signal; +#X obj 143 35 inlet~; +#X text 122 15 desired signal; +#X obj 36 291 outlet~; +#X msg 249 63 adaptation 1; +#X obj 249 42 loadbang; +#X obj 224 214 s~ adaptive_signal; +#X text 224 234 (for visualization); +#X obj 249 141 r clear; +#X msg 248 162 clear; +#X obj 37 156 lms2~ 3 0.01; +#X obj 116 265 unpack f f f; +#X obj 116 293 outlet; +#X obj 162 293 outlet; +#X obj 208 293 outlet; +#X obj 249 94 r mu; +#X msg 249 116 mu \$1; +#X connect 0 0 11 0; +#X connect 2 0 11 1; +#X connect 5 0 11 0; +#X connect 6 0 5 0; +#X connect 9 0 10 0; +#X connect 10 0 11 0; +#X connect 11 0 4 0; +#X connect 11 0 7 0; +#X connect 11 2 12 0; +#X connect 12 0 13 0; +#X connect 12 1 14 0; +#X connect 12 2 15 0; +#X connect 16 0 17 0; +#X connect 17 0 11 0; +#X restore 117 337 pd adaptive_filter~; +#X obj 524 255 spectrum~; +#N canvas 0 0 450 300 graph6 0; +#X array adapt 512 float 0; +#X coords 0 1 511 -1 200 140 1; +#X restore 656 625 graph; +#X text 700 769 -- 512 samples ---; +#X obj 46 438 tgl 20 0 scopes_on empty empty 0 -6 0 8 -262144 -1 -1 +0 1; +#X obj 524 238 r~ adaptive_signal; +#X text 125 241 x[n]; +#X text 256 300 d[n]; +#X text 107 356 y[n]; +#X obj 775 238 r scopes_on; +#X obj 775 26 r scopes_on; +#X obj 524 26 r~ unknown_signal; +#N canvas 0 0 450 300 graph6 0; +#X array unkn 512 float 0; +#X coords 0 1 511 -1 200 140 1; +#X restore 654 453 graph; +#X text 698 597 -- 512 samples ---; +#X text 76 438 <- Visualization IO; +#X text 481 137 (1); +#X text 481 338 (2); +#N canvas 452 215 456 231 scope_stuff 0; +#X obj 45 38 r~ adaptive_signal; +#X obj 83 63 r scopes_on; +#X obj 279 69 r scopes_on; +#X obj 241 44 r~ unknown_signal; +#X obj 83 96 metro 1000; +#X obj 44 139 tabwrite~ adapt; +#X obj 279 95 metro 1000; +#X obj 240 138 tabwrite~ unkn; +#X connect 0 0 5 0; +#X connect 1 0 4 0; +#X connect 2 0 6 0; +#X connect 3 0 7 0; +#X connect 4 0 5 0; +#X connect 6 0 7 0; +#X restore 755 795 pd scope_stuff; +#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); +#X obj 84 599 bng 20 250 50 0 clear empty empty 0 -6 0 8 -262144 -1 +-1; +#X text 113 601 <- clear coefficients \, so adaptation will start again +; +#X floatatom 46 471 5 0 100 0 - init_tlp tlp; +#X obj 685 26 r tlp; +#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] =; +#X floatatom 159 378 5 0 0 1 c0 - -; +#X floatatom 223 378 5 0 0 1 c1 - -; +#X floatatom 285 378 5 0 0 1 c2 - -; +#X text 40 578 adaptive filter:; +#X floatatom 84 627 8 0 0 0 - mur mu; +#X text 146 627 <- step size parameter mu (learning rate); +#N canvas 215 124 617 210 init 0; +#X msg 43 99 2; +#X obj 269 45 loadbang; +#X obj 43 122 s init_tlp; +#X msg 138 98 0.33; +#X msg 179 99 0.33; +#X msg 223 100 0.33; +#X obj 138 121 s a0r; +#X obj 178 122 s a1r; +#X obj 223 123 s a2r; +#X obj 295 123 s mur; +#X msg 294 99 0.01; +#X msg 515 103 \; pd dsp \$1; +#X obj 515 78 r audio_io; +#X obj 381 123 s signalr; +#X msg 380 98 0; +#X connect 0 0 2 0; +#X connect 1 0 0 0; +#X connect 1 0 3 0; +#X connect 1 0 4 0; +#X connect 1 0 5 0; +#X connect 1 0 10 0; +#X connect 1 0 14 0; +#X connect 3 0 6 0; +#X connect 4 0 7 0; +#X connect 5 0 8 0; +#X connect 10 0 9 0; +#X connect 12 0 11 0; +#X connect 14 0 13 0; +#X restore 699 795 pd init; +#X floatatom 125 547 4 0 1 0 - a0r a0; +#X text 158 547 x[n] +; +#X text 244 547 x[n-1] +; +#X floatatom 211 547 4 0 1 0 - a1r a1; +#X floatatom 312 548 4 0 1 0 - a2r a2; +#X text 345 549 x[n-2]; +#N canvas 425 56 479 415 PROBLEM_DESCRIPTION 0; +#X text 33 89 In this example the adaptive filter tries to identify +an unknown system.; +#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 3 coefficients.; +#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 77 278 LMS \, 3 coefficients (c0 \, c1 \, c2); +#X text 35 342 The System Identification problem is sucessfull \, if +c0=h0 \, c1=h1 and c2=h2. Then the unknown and the adaptive system +have the same behavior.; +#X text 60 40 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT; +#X text 77 292 step-size parameter mu; +#X restore 34 94 pd PROBLEM_DESCRIPTION; +#N canvas 298 58 425 643 OBSERVATIONS 0; +#X text 24 20 OBSERVATIONS; +#X obj 27 119 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 mu1 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 0.5; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 27 143 pd mu1; +#X text 26 95 e.g. mu = 0.5:; +#X obj 29 201 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#X text 26 179 e.g. mu = 1e-05:; +#X text 25 59 1) influenc of mu:; +#X text 84 119 -> very fast adaptation \, but c0 \, c1 \, c2; +#X text 104 134 are not so precise; +#X text 83 201 -> slower adaptation \, but very precise; +#X text 27 430 2) influenc of white vs. non-white input signal:; +#X obj 30 490 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 mu2 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 1e-05; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 29 225 pd mu2; +#N canvas 863 469 389 255 in1 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X msg 20 47 0; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 158 0.001; +#X connect 0 0 2 0; +#X connect 0 0 3 0; +#X connect 0 0 5 0; +#X connect 2 0 1 0; +#X connect 5 0 4 0; +#X restore 30 514 pd in1; +#X obj 32 570 bng 20 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 +-1; +#N canvas 863 469 389 255 in2 0; +#X obj 20 14 inlet; +#X obj 20 68 s signalr; +#X obj 20 111 s clear; +#X obj 20 179 s mur; +#X msg 20 47 1; +#X msg 20 158 0.001; +#X connect 0 0 4 0; +#X connect 0 0 2 0; +#X connect 0 0 5 0; +#X connect 4 0 1 0; +#X connect 5 0 3 0; +#X restore 32 594 pd in2; +#X text 28 469 white signal:; +#X text 30 550 non-white signal:; +#X text 87 569 -> c0 \, c1 \, c2 not precise; +#X text 90 489 -> c0 \, c1 \, c2 precise; +#X text 29 274 how to choose mu ?; +#X text 72 300 0 < mu < 2/(abs(x[n])^2); +#X text 72 321 -> abs(x[n])^2 is the tap-input energy; +#X text 94 336 at time n (lenght of x[n] is PDs; +#X text 46 373 Note: this only ensures "stability on average"; +#X text 94 351 blocksize - so use block~ to change it!); +#X connect 1 0 2 0; +#X connect 4 0 12 0; +#X connect 11 0 13 0; +#X connect 14 0 15 0; +#X restore 34 120 pd OBSERVATIONS; +#X text 33 73 ReadMe:; +#N canvas 0 0 642 300 input_signal~ 0; +#X obj 77 90 noise~; +#X obj 201 84 inlet; +#X obj 77 217 *~; +#X obj 210 273 outlet~; +#X obj 201 115 sel 0 1; +#X msg 91 190 1; +#X msg 121 190 0; +#X obj 325 88 noise~; +#X text 53 64 white signal:; +#X text 292 63 non white signal:; +#X obj 322 224 *~; +#X msg 336 197 1; +#X msg 366 197 0; +#X obj 324 112 hip~ 300; +#X obj 492 148 bp~ 2543 2; +#X obj 406 149 bp~ 1000 3; +#X obj 323 148 bp~ 100 2; +#X connect 0 0 2 0; +#X connect 1 0 4 0; +#X connect 2 0 3 0; +#X connect 4 0 5 0; +#X connect 4 0 12 0; +#X connect 4 1 6 0; +#X connect 4 1 11 0; +#X connect 5 0 2 1; +#X connect 6 0 2 1; +#X connect 7 0 13 0; +#X connect 10 0 3 0; +#X connect 11 0 10 1; +#X connect 12 0 10 1; +#X connect 13 0 14 0; +#X connect 13 0 15 0; +#X connect 13 0 16 0; +#X connect 14 0 10 0; +#X connect 15 0 10 0; +#X connect 16 0 10 0; +#X restore 117 210 pd input_signal~; +#X obj 117 162 vradio 20 1 1 2 empty signalr empty 0 -6 0 8 -262144 +-1 -1 0; +#X text 144 163 white signal (noise); +#X text 145 183 non white signal (filtered noise); +#X obj 524 43 spectrum~; +#X text 33 32 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT; +#X connect 0 0 3 1; +#X connect 3 1 36 0; +#X connect 3 2 37 0; +#X connect 3 3 38 0; +#X connect 8 0 4 0; +#X connect 12 0 4 2; +#X connect 13 0 56 2; +#X connect 14 0 56 0; +#X connect 30 0 56 1; +#X connect 31 0 4 1; +#X connect 52 0 0 0; +#X connect 52 0 3 0; +#X connect 53 0 52 0; diff --git a/adaptive/examples/02.persistent_excitation.pd b/adaptive/examples/02.persistent_excitation.pd new file mode 100755 index 0000000..9bafbba --- /dev/null +++ b/adaptive/examples/02.persistent_excitation.pd @@ -0,0 +1,396 @@ +#N struct num float x float y float col; +#N canvas 21 113 829 606 10; +#X obj 34 430 tgl 20 0 audio_io empty empty 0 -6 0 8 -262144 -1 -1 +1 1; +#X text 59 432 <- Audio IO; +#X text 122 266 x[n]; +#X text 251 316 d[n]; +#X text 104 379 y[n]; +#X obj 75 495 bng 20 250 50 0 clear empty empty 0 -6 0 8 -262144 -1 +-1; +#X text 104 497 <- clear coefficients \, so adaptation will start again +; +#X text 542 496 unknown system:; +#X text 571 520 d[n] =; +#X floatatom 178 383 5 0 0 1 c0 - C0; +#X floatatom 242 383 8 0 0 1 c1 - C1; +#X text 31 471 adaptive filter:; +#X floatatom 75 523 8 0 0 0 - mur mu; +#X text 137 523 <- step size parameter mu (learning rate); +#N canvas 215 124 617 210 init 0; +#X msg 43 99 2; +#X obj 269 45 loadbang; +#X obj 43 122 s init_tlp; +#X msg 138 98 0.33; +#X msg 179 99 0.33; +#X msg 223 100 0.33; +#X obj 138 121 s a0r; +#X obj 178 122 s a1r; +#X obj 223 123 s a2r; +#X obj 295 123 s mur; +#X msg 515 103 \; pd dsp \$1; +#X obj 515 78 r audio_io; +#X obj 381 123 s signalr; +#X msg 380 98 0; +#X obj 182 180 s A1r; +#X obj 142 179 s A0r; +#X msg 183 157 2; +#X msg 142 156 1; +#X msg 294 99 0.001; +#X connect 0 0 2 0; +#X connect 1 0 0 0; +#X connect 1 0 3 0; +#X connect 1 0 4 0; +#X connect 1 0 5 0; +#X connect 1 0 18 0; +#X connect 1 0 13 0; +#X connect 1 0 17 0; +#X connect 1 0 16 0; +#X connect 3 0 6 0; +#X connect 4 0 7 0; +#X connect 5 0 8 0; +#X connect 11 0 10 0; +#X connect 13 0 12 0; +#X connect 16 0 14 0; +#X connect 17 0 15 0; +#X connect 18 0 9 0; +#X restore 644 578 pd init; +#X floatatom 623 521 4 0 1.5 0 - A0r A0; +#X text 657 521 x[n] +; +#N canvas 425 56 483 381 PROBLEM_DESCRIPTION 0; +#X text 35 188 unknown system:; +#X text 35 259 adaptive system:; +#X text 77 292 step-size parameter mu; +#X text 74 209 FIR Filter: h=(1 \, 2) \, order = 2; +#X text 75 225 d[n] = h0*x[n] + h1*x[n-1] (N=M); +#X text 77 278 nlms2~ \, 2 coefficients (c0 \, c1); +#X text 34 124 The unknown system is a FIR filter of order 2 and the +adaptive system is an adaptive transversal filter using the NLMS algorithm +(see nlms2~ help-patch) with 2 coefficients.; +#X text 35 89 In this exmaple the adaptation path is beeing visualized +in the c[n]-plane.; +#X text 33 340 When can the unknown system be identified successfully +?; +#X text 32 42 PERSISTENT EXCITATION; +#X restore 34 94 pd PROBLEM_DESCRIPTION; +#N canvas 663 87 465 688 OBSERVATIONS 0; +#X text 24 20 OBSERVATIONS; +#X text 24 60 input signals 1 + 4:; +#X text 48 77 The unknown system can be identified successfully.; +#X text 24 103 input signals 2:; +#X text 54 119 Adaptation doesn't work at all.; +#X text 21 149 input signals 3:; +#X text 51 165 Adaptation works \, but with an offset.; +#X text 23 225 EXPLANATION; +#X text 26 256 The unknown system can be identified \, if the Wiener-Hopf +equation can be solved:; +#X text 69 297 c_opt = R_x^-1 * p; +#X text 257 294 (Wiener-Hopf equation); +#X text 27 323 c_opt ... optimal coefficient vector c0 \, c1 \, c2 +\, ...; +#X text 28 338 R_x ... autocorrelation matrix of the input signal x[n] +; +#X text 156 429 det(R_x) != 0; +#X text 27 393 The Wiener-Hopf equation can only be solved \, if the +determinant of R_x is not singular:; +#X text 45 511 x[n] = sin(theta*n + phi); +#X text 45 530 -> for N=2:; +#X text 133 557 R_x =; +#X text 275 547 cos(theta); +#X text 236 566 cos(theta); +#X text 221 567 [; +#X text 220 547 [; +#X text 355 547 ]; +#X text 355 566 ]; +#X text 175 558 0.5 *; +#X text 239 548 1; +#X text 331 567 1; +#X text 40 622 -> det(R_x) = 0 \, if theta = 0 \, pi \, 2*pi \, ... +; +#X text 40 606 -> det(R_x) = 1 - cos^2(theta); +#X text 24 639 (which is the case with input signal 2 = critical sampling) +; +#X text 26 483 In our example (signal 1+2):; +#X text 28 352 p ... crosscorrelation vector between the desired output +d[n] and the input signal x[n]; +#X restore 34 120 pd OBSERVATIONS; +#X text 33 72 ReadMe:; +#X obj 114 166 vradio 15 1 1 4 empty empty empty 0 -6 0 8 -262144 -1 +-1 2; +#X floatatom 709 521 4 0 2 0 - A1r A1; +#X text 743 521 x[n-1]; +#X text 132 197 3) x[n]=cos[pi*n]+2; +#X text 132 212 4) white noise; +#X text 132 164 1) x[n]=cos[0.5*pi*n] -> f=samplerate/4; +#X text 132 181 2) x[n]=cos[pi*n] -> f=samplerate/2; +#N canvas 0 0 450 300 c-plane 0; +#X scalar num 100 200 600 \;; +#X scalar num 132.83 181.096 841 \;; +#X coords -100 300 200 -100 300 300 1; +#X restore 486 131 pd c-plane; +#N canvas 220 179 544 257 c-plane-stuff 0; +#N canvas 118 400 523 253 num 0; +#X text 104 54 float with x \, y values \; col for color \;; +#X text 97 157 visualization of the float \, col is the color \;; +#X obj 101 88 struct num float x float y float col; +#X obj 90 184 filledpolygon col col 0 0 0 0 0 9 9 9 0 0 9; +#X restore 27 36 pd num; 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+#X msg 219 147 traverse pd-c-plane \, next \, next; +#X obj 84 101 metro 50; +#X msg 197 249 841; +#X connect 0 0 2 3; +#X connect 1 0 11 0; +#X connect 3 0 5 1; +#X connect 4 0 6 1; +#X connect 5 0 2 0; +#X connect 6 0 2 1; +#X connect 7 0 13 0; +#X connect 8 0 5 0; +#X connect 8 1 6 0; +#X connect 9 0 3 0; +#X connect 10 0 4 0; +#X connect 11 0 7 0; +#X connect 11 1 14 0; +#X connect 11 2 12 0; +#X connect 12 0 0 0; +#X connect 13 0 8 0; +#X connect 14 0 2 2; +#X restore 27 107 pd coef_c; +#X msg 165 126 \; . xticks 0 0.1 5; +#X msg 165 164 \; . yticks 0 0.1 5; +#X msg 303 128 \; . xlabel -1.15 -1 0 1 2; +#X msg 302 163 \; . ylabel -1.1 -1 0 1 2 3; +#X obj 165 80 loadbang; +#X connect 9 0 5 0; +#X connect 9 0 6 0; +#X connect 9 0 7 0; +#X connect 9 0 8 0; +#X restore 698 578 pd c-plane-stuff; +#N canvas 0 0 450 300 graph2 0; +#X array . 1 float 3; +#A 0 -0.97332; +#X coords -1 3 2 -1 300 300 1; +#X restore 486 131 graph; +#X text 479 112 c1; +#X text 790 423 c0; +#X text 521 87 orange: adaptive system (c0 \, c1); 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+#X connect 11 0 0 0; +#X connect 11 0 17 0; +#X connect 12 0 15 0; +#X connect 13 0 16 0; +#X connect 14 0 15 1; +#X connect 15 0 11 0; +#X connect 16 0 14 0; +#X restore 78 354 pd channel~; +#N canvas 775 0 479 464 PROBLEM_DESCRIPTION 0; +#X text 166 24 INVERSE MODELLING; +#X text 34 66 Now the signal source is split up into an unknown channel +and the desired signal is delayed added into the adaption process. +; +#X text 32 115 The goal is to adapt the channel \, so that the overal +system has a flat frequency response:; +#X text 32 177 So the overal system is a delayed version of the input +signal.; +#X text 47 312 1 select a channel (dummy system or a real room - so +you will need a loudspeaker and a microphone); +#X text 142 154 H_ch(z) * H_eq(z) = z^-M; +#X text 45 381 3 train the system \, to get H_eq(z) (use speech- or +music samples to train the real room); +#X text 46 414 4 use the euqlized system (in case of a real room you +should have a nearly flat frequency response in that room); +#X text 30 290 Usage of the patch:; +#X text 47 347 2 measure the latency of your system (for real room: +don't forget to turn on the volumes for micro and speaker); +#X text 60 239 a) dummy system: a simple bandpass filter with a delay +; +#X text 62 253 b) real room: loudspeaker - a room - micro; +#X text 29 221 You can select between two different channels:; +#X restore 28 83 pd PROBLEM_DESCRIPTION; +#N canvas 844 224 455 275 OBSERVATIONS 0; +#X text 152 22 OBSERVATIONS; +#X text 32 95 The magnitude of the frequency response can be equalized. +; +#X text 14 75 dummy system:; +#X text 16 128 a real room:; +#X text 33 148 The magnitude of the frequency can only be equalized +if you have an input signal with high energy.; +#X text 31 181 The adaptation has problems with noise as input signal +\, because noise is totally uncorrelated \, so you to measure the latency +very precise.; +#X text 30 227 Because of that it is better to use more correlated +signals such as music or speech samples.; 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+#X restore 29 262 pd channel~; +#N canvas 490 469 479 338 PROBLEM_DESCRIPTION 0; +#X text 57 137 possible symbols: -1 \, 1; +#X text 55 160 the decision device is implemented by d=sign(y); +#X text 72 40 DECISION-DIRECTED CHANNEL EQUALIZATION; +#X text 27 189 The adaptive equalizer tries to invert the channel \, +so that the overal system has a flat frequency response and there are +almost no bit errors.; +#X text 28 280 We simulate the transmission with a simple bandpass +filter and a delay (= the channel).; +#X text 28 241 Bit errors are plotted over time for equalized and unequalized +transmission.; +#X text 27 83 This patch simulates the equalization of a baseband transmission +of a binary signal (similar to the adaptation process in e.g. a modem). +; +#X restore 28 106 pd PROBLEM_DESCRIPTION; +#N canvas 493 226 453 208 OBSERVATIONS 0; +#X text 21 30 OBSERVATIONS; +#X text 19 77 You can see that if you train the system long enough +there are almost no bit errors.; +#X text 20 126 A critical parameter is the delay: If you don't find +the exact delay of the channel adaptation works very bad for uncorrelated +training sequences.; 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