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-rwxr-xr-xadaptive/examples/01.system_identification.pd318
-rwxr-xr-xadaptive/examples/02.persistent_excitation.pd396
-rwxr-xr-xadaptive/examples/03.undermodeling.pd238
-rwxr-xr-xadaptive/examples/04.misadjustment.pd475
-rwxr-xr-xadaptive/examples/05.tracking.pd791
-rwxr-xr-xadaptive/examples/06.interference_cancelation.pd323
-rwxr-xr-xadaptive/examples/07.adaptive_equalization.pd447
-rwxr-xr-xadaptive/examples/08.decision-directed_equalization.pd167
-rwxr-xr-xadaptive/examples/coef.dat12
-rwxr-xr-xadaptive/examples/spectrum~.pd243
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
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+++ b/adaptive/examples/01.system_identification.pd
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+#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];
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+#X restore 245 268 pd unknown_system~;
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+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;
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+#X text 125 241 x[n];
+#X text 256 300 d[n];
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+#X text 698 597 -- 512 samples ---;
+#X text 76 438 <- Visualization IO;
+#X text 481 137 (1);
+#X text 481 338 (2);
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+#X obj 45 38 r~ adaptive_signal;
+#X obj 83 63 r scopes_on;
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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);
+#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 - -;
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+#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);
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+#X text 244 547 x[n-1] +;
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+#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;
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+#X text 26 95 e.g. mu = 0.5:;
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+-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:;
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+#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;
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+#X text 33 73 ReadMe:;
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+#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;
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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
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+#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:;
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+#X text 137 523 <- step size parameter mu (learning rate);
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+#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];
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+#X text 33 72 ReadMe:;
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+#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;
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+#X text 263 93 Initialization;
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+#X text 74 90 add another;
+#X obj 329 172 s pd-c-plane;
+#X msg 250 216 traverse pd-c-plane \, bang;
+#X obj 168 264 append num x y;
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+#X text 80 37 <- graphical representation of a number;
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+#X text 484 47 Visualization in the c-plane:;
+#X text 33 32 PERSISTENT EXCITATION;
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diff --git a/adaptive/examples/03.undermodeling.pd b/adaptive/examples/03.undermodeling.pd
new file mode 100755
index 0000000..7a194da
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+#X text 330 436 <- Audio IO;
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+#X text 22 15 input signal;
+#X obj 143 35 inlet~;
+#X text 122 15 desired signal;
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+#X text 125 241 x[n];
+#X text 256 300 d[n];
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+#X text 698 597 -- 512 samples ---;
+#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
+;
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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 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 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);
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+#X text 109 32 SYSTEM IDENTIFICATION: UNDERMODELING;
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diff --git a/adaptive/examples/04.misadjustment.pd b/adaptive/examples/04.misadjustment.pd
new file mode 100755
index 0000000..8a963dd
--- /dev/null
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+#X text 69 435 <- Audio IO;
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+#X text 113 552 <- clear coefficients \, so adaptation will start again
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+(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 77 292 step-size parameter mu;
+#X text 188 40 MISADJUSTMENT;
+#X text 28 84 This patch calculates the misadjustment in a noisy system
+identification problem.;
+#X text 33 325 The input signal and the additional noise are uniformly
+distributed random numbers with zero mean and different variances.
+;
+#X text 29 399 Mean Square Error: MSE[n] = E[abs(e[n])^2];
+#X text 29 416 MSE_min: Minimum Error = variance^2 of the additional
+noise;
+#X text 29 497 limes n to infinity MSE[n] = MSE_excess + MSE_min;
+#X text 26 538 The ratio of the Excess Error and the Minimum Error
+is defined as the Misadjustment:;
+#X text 109 573 MISADJ = MSE_excess / MSE_min;
+#X text 28 619 LMS Adaptive Filter Design Trade Off:;
+#X text 142 644 tao * MISADJ = N/2;
+#X text 108 673 N ... Nr of coefficients;
+#X text 107 687 tao ... convergence time constant;
+#X text 39 448 v[n] = c[n]-h[n] \, so the difference between the adaptive
+and the unknown system;
+#X text 29 433 MSE_excess: Excess Error = E[v[n]^2*x[n]^2] (Misalignment)
+;
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+#X text 408 65 different cases:;
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diff --git a/adaptive/examples/05.tracking.pd b/adaptive/examples/05.tracking.pd
new file mode 100755
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diff --git a/adaptive/examples/06.interference_cancelation.pd b/adaptive/examples/06.interference_cancelation.pd
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+#X text 24 74 In this example the adaptive filter is used as an adaptive
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+;
+#X text 62 204 LMS \, 100 coefficients (c0 \, c1 \, ...c100) ->sharper
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+#X text 24 122 A speech signal is used as the broadband signal and
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+#X text 529 711 (1) input signal (= voice + sine);
+#X text 529 741 (3) y[n] (~ only sine);
+#X text 529 726 (2) error signal (~ only voice);
+#X text 47 259 modify freq ->;
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diff --git a/adaptive/examples/07.adaptive_equalization.pd b/adaptive/examples/07.adaptive_equalization.pd
new file mode 100755
index 0000000..49ae4af
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+#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:;
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+#X text 32 95 The magnitude of the frequency response can be equalized.
+;
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+#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
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+very precise.;
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+#X text 323 579 <- Audio IO;
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+#X text 69 581 <- Visualization IO;
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+#X text 26 26 ADAPTIVE EQUALIZATION: INVERSE MODELING;
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+#X text 68 183 train to get the inverse system;
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+#X text 517 520 training mode:;
+#X text 86 374 H_chan(z);
+#X text 252 376 H_eq(z);
+#X text 532 536 (1) H_chan(z) * H_eq(z);
+#X text 532 551 (2) H_chan(z) (= channel);
+#X text 516 572 using mode:;
+#X text 529 589 (1) H_eq(z) (= 1/H_chan(z) = equalizer);
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+#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
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+;
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+#X text 19 77 You can see that if you train the system long enough
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