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Characterization of the undesirable global minima of the Godard cost function: case of noncircular symmetric signals

Abstract : The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (s/sub n/)/sub n/spl isin/z/ having a strictly negative Kurtosis /spl gamma//sub 2/= E[|s/sub n/|/sup 4/]-2(E[|s/sub n/|/sup 2/])/sup 2/-|E[s/sub n//sup 2/|/sup 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[s/sup 2/]=0. When this constraint is relaxed, (s/sub n/)/sub n/spl isin/z/ is said to be noncircular symmetric: It is shown that the minimizers achieve deconvolution if and only if 2|E[s/sub n//sup 2/]|/sup 2/<-/spl gamma//sub 2/(s). If this condition is not met, the global minimizers are found to be finite-impulse-response filters with two taps
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https://hal.archives-ouvertes.fr/hal-02291178
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Submitted on : Wednesday, July 13, 2022 - 4:11:32 PM
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Sébastien Houcke, Antoine Chevreuil. Characterization of the undesirable global minima of the Godard cost function: case of noncircular symmetric signals. IEEE Transactions on Signal Processing, 2006, 54 (5), pp.1917-1922. ⟨10.1109/TSP.2006.872584⟩. ⟨hal-02291178⟩

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