[PD-cvs] externals/grh/adaptive/examples 01.system_identification.pd, NONE, 1.1 02.persistent_excitation.pd, NONE, 1.1 03.undermodeling.pd, NONE, 1.1 04.misadjustment.pd, NONE, 1.1 05.tracking.pd, NONE, 1.1 06.interference_cancelation.pd, NONE, 1.1 07.adaptive_equalization.pd, NONE, 1.1 08.decision-directed_equalization.pd, NONE, 1.1 coef.dat, NONE, 1.1 spectrum~.pd, NONE, 1.1
Georg Holzmann
grholzi at users.sourceforge.net
Tue Jul 12 16:08:20 CEST 2005
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Update of /cvsroot/pure-data/externals/grh/adaptive/examples
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv29426/examples
Added Files:
01.system_identification.pd 02.persistent_excitation.pd
03.undermodeling.pd 04.misadjustment.pd 05.tracking.pd
06.interference_cancelation.pd 07.adaptive_equalization.pd
08.decision-directed_equalization.pd coef.dat spectrum~.pd
Log Message:
initial commit of adaptive
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#X text 119 29 PERIODIC INTERFERENCE CANCELATION;
#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);
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#X text 47 259 modify freq ->;
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#X text 76 438 <- Visualization IO;
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#X text 86 760 (3) d[n] in time domain;
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#X text 146 627 <- step size parameter mu (learning rate);
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#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.;
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#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 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!);
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#X text 33 32 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT;
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--- NEW FILE: 08.decision-directed_equalization.pd ---
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#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 \,
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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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#X text 27 83 This patch simulates the equalization of a baseband transmission
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;
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#X text 487 390 ---- 64 samples ----;
#X text 382 228 biterrors over time:;
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#X text 86 760 (3) d[n] in time domain;
#X text 86 777 (4) y[n] in time domain;
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#X text 90 469 <- temporal lowpass for spectrum view (0...100);
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#X text 74 209 FIR Filter \, order = 3;
#X text 35 259 adaptive system:;
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#X text 77 278 LMS \, 2 coefficients (c0 \, c1);
#X text 60 40 SYSTEM IDENTIFICATION: UNDERMODELING;
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#X text 48 209 much higher !;
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#X text 77 278 nlms2~ \, 2 coefficients (c0 \, c1);
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#X text 35 89 In this exmaple the adaptation path is beeing visualized
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#X text 33 340 When can the unknown system be identified successfully
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#X text 32 42 PERSISTENT EXCITATION;
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#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
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#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
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#X text 28 338 R_x ... autocorrelation matrix of the input signal x[n]
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#X text 156 429 det(R_x) != 0;
#X text 27 393 The Wiener-Hopf equation can only be solved \, if the
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#X text 45 511 x[n] = sin(theta*n + phi);
#X text 45 530 -> for N=2:;
#X text 133 557 R_x =;
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#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)
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#X text 26 483 In our example (signal 1+2):;
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#X text 484 47 Visualization in the c-plane:;
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#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:;
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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
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#X text 31 181 The adaptation has problems with noise as input signal
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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 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 68 163 calculate latency of the channel;
#X text 68 183 train to get the inverse system;
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#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);
#X text 529 604 (2) H_chan(z) * H_eq(z);
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--- NEW FILE: coef.dat ---
adaptivePD
size: 9
mu: 0.0001
1
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#X text 113 552 <- clear coefficients \, so adaptation will start again
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#X text 29 126 The unknown system is a FIR filter of order 3 and the
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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 77 278 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
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#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
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#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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#X text 741 252 <- draw MSE;
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#X text 24 137 3) slow learning \, but adaptation works;
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#X text 24 116 2) too much add-noise;
#X text 24 192 5) very low in-signal and add-noise \, adaptation does
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#X text 24 225 6) adaptation works;
#X text 24 244 7) very high add-noise level \, but adaptation works
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#X text 201 29 TRACKING;
#X text 30 118 The number of coefficients N=9 for the unknown and the
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#X text 30 156 For an observation interval of 2000 samples \, the coefficients
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(h[0] \, h[2] \, ...) decrease linearly from the initial 1 to a final
-1 \, all odd-indexed coefficients are constant 1;
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#X text 55 308 h(n)= 1 for n=0..8;
#X text 60 352 N = 9;
#X text 29 333 number of coefficients for filter and unknown system:
;
#X text 32 66 In this example we want to examine the tracking behaviour
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;
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#X obj 248 158 cnv 15 1 1 empty empty | 0 7 0 10 -262144 -1 0;
#X obj 296 158 cnv 15 1 1 empty empty | 0 7 0 10 -262144 -1 0;
#X text 16 220 draws the power of the spectrum (log);
#X connect 2 0 0 1;
#X connect 3 0 0 0;
#X connect 4 0 0 2;
#X coords 0 0 1 1 330 190 1;
- Previous message: [PD-cvs] externals/grh/adaptive/src adaptive.c, NONE, 1.1 adaptive.h, NONE, 1.1 lms2~.c, NONE, 1.1 lms~.c, NONE, 1.1 makefile, NONE, 1.1 makefile_mingw, NONE, 1.1 makefile_msvc, NONE, 1.1 nlms2~.c, NONE, 1.1 nlms3~.c, NONE, 1.1 nlms~.c, NONE, 1.1
- Next message: [PD-cvs] externals/grh/adaptive/doc help-lms2~.pd, NONE, 1.1 help-lms~.pd, NONE, 1.1 help-nlms2~.pd, NONE, 1.1 help-nlms~.pd, NONE, 1.1
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