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Extra info for Adaptive Filtering Applications
21) In order to further improve the robustness of the Sun’s algorithm; instead of ignoring the large amplitude sample; we may clip the sample by a threshold value, and thus the reference signal is modiﬁed as ⎧ ⎨ c1 , x ( n ) ≤ c1 x (n ) = c , x ( n ) ≥ c2 (22) ⎩ 2 x (n ), otherwise As stated earlier, ignoring (or even clipping) the peaky samples in the update of FxLMS algorithm does not mean that peaky samples will not appear in the residual error e(n ). The residual error may still be so peaky, that in the worst case might cause ANC to become unstable.
In the case of narrowband noise sources with signal energy being concentrated at a few representative harmonics, the reference microphone in Fig. , a tachometer in the case rotating machines. 5 5 x Fig. 3. The PDFs of standard symmetric α-stable (SαS) process for various values of α. noise, or sinusoids that have the same frequencies as the corresponding harmonic components (Kuo & Morgan, 1996). Essentially, a narrowband ANC system would assume the reference signal x (n ) has the same frequency as the primary noise d(n ) at the error microphone.
It is assumed that the secondary path modeling ﬁlter Sˆ (z) is exactly identiﬁed as S (z). 1 ANC for impulsive noise sources The simulation setup is same as shown in Fig. 1, where noise source is assumed to be impulsive and the ANC ﬁlter W (z) is selected as an FIR ﬁlter of tap-weight length L w = 192. 5 5 4 x 10 (h) Fig. 9. 45. (a) FxLMS algorithm, (b) FxLMP algorithm, (c) Sun’s algorithm, (d) Modiﬁed-Sun’s algorithm, (e) MFxLMS algorithm, (f) MFxLMP algorithm, (g) MNFxLMS algorithm, and (h) MNFxLMP algorithm.