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The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). GANFs are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique. Even though restricted to a single-frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. In addition, it allows one to formulate some useful rules of thumb for choosing design parameters. [ABSTRACT FROM AUTHOR]

The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (sn)n∊Z having a strictly negative Kurtosis γ2 = E[∣sn∣4] - 2(E[∣sn∣²])² - ∣E[sn²∣²] is addressed. This correspondence focuses on the global minimizers of the Godard function. A well-known result states that these minimizers achieve deconvolution at least if the input signal shows the symmetry E[s²] = 0. When this constraint is relaxed, (sn)n∊Z is said to be noncircular symmetric: It is shown that the minimizers achieve deconvolution if and only if 2∣E[sn²]∣² < -γ2 (s). If this condition is not met, the global minimizers are found to be finite-impulse-response filters with two taps. [ABSTRACT FROM AUTHOR]