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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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#X text 29 126 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 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 33 73 ReadMe:;
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#X text 33 30 MISADJUSTMENT - NOISY SYSTEM IDENTIFICATION;
#X text 408 65 different cases:;
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#X text 387 183 (step-size);
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#X text 790 292 MSE [dB];
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#X text 830 463 [samples];
#X text 741 252 <- draw MSE;
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#X text 22 22 OBSERVATIONS;
#X text 24 61 different cases:;
#X text 24 137 3) slow learning \, but adaptation works;
#X text 24 96 1) little bit add-noise \, adaptation works well;
#X text 24 116 2) too much add-noise;
#X text 24 192 5) very low in-signal and add-noise \, adaptation does
not work;
#X text 24 225 6) adaptation works;
#X text 24 244 7) very high add-noise level \, but adaptation works
;
#X text 24 263 8) adaptation works \, high step-size (so in some cases
this will be unstable);
#X text 23 158 4) more add-noise than in-signal and very high step-size
-> so sometimes this is unstable !;
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