[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

12 Jul 2005


      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
--- NEW FILE: 06.interference_cancelation.pd ---
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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 76 438 <- Visualization IO;
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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.;
#X text 60 40 SYSTEM IDENTIFICATION IN A NOISE FREE ENVIRONMENT;
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#X text 83 201 -> slower adaptation , but very precise;
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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 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).
;
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#X text 19 77 You can see that if you train the system long enough
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#X text 487 390 ---- 64 samples ----;
#X text 382 228 biterrors over time:;
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--- NEW FILE: 03.undermodeling.pd ---
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#X text 76 438 <- Visualization IO;
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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;
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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 34 124 The unknown system is a FIR filter of order 3 and the
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#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
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#X text 20 71 White Noise Case:;
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#X text 48 209 much higher !;
#X text 48 176 h0 , h1 and h2 have influence on the error , so in
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#X text 53 111 (min. error);
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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
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
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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):;
#X text 28 352 p ... crosscorrelation vector between the desired output
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#X text 484 47 Visualization in the c-plane:;
#X text 33 32 PERSISTENT EXCITATION;
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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
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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
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
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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 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;
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#X text 24 263 8) adaptation works , high step-size (so in some cases
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#X text 201 29 TRACKING;
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#X text 30 156 For an observation interval of 2000 samples , the coefficients
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#X text 60 352 N = 9;
#X text 29 333 number of coefficients for filter and unknown system:
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#X text 32 66 In this example we want to examine the tracking behaviour
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