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Additional info for Adaptive Filtering Applications
Since H (z) is excited by x (n ), minimizing the error signal eh (n ) means that the output of H (z), yh (n ), would converge to that part in Eq. (44) which is correlated with x (n ), thus yh (n ) → [ d(n ) − ys (n )], (46) and hence eh (n ) would converge to the remaining uncorrelated part eh (n ) → [ v(n ) − gs (n )]. (47) Comparing Eq. (46) with Eq. (4), we see that that yh (n ) can be used as an error signal for adaptation of W (z), and hence FxLMS algorithm for W (z) is given as w (n + 1) = w (n ) + μ w yh (n )xˆ s (n ) (48) and similarly, comparing Eq.
6. Block diagram of conventional hybrid ANC system with combination of feedforward ANC W (z) and feedback ANC B (z). Thus the reference signal u (n ) comprises two parts; estimates of disturbances d(n ) and v(n ). Since objective of the feedback ANC B (z) is to cancel only uncorrelated primary noise v(n ), the presence of dˆ(n ) (which may be broadband and unpredictable in general) gives a corrupted reference signal for B (z). Thus, both W (z) and B (z) are adapted using inappropriate error signals and may converge slowly.
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