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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications by Antonio Napolitano

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4.7 Measurement of Spectral Correlation –Known Support Curves

In this section, for jointly SC processes the properly normalized frequency-smoothed cross-periodogram along a given support curve is considered as an estimator of the spectral cross-correlation density function on this support curve. Bias and covariance are determined. Moreover asymptotic unbiasedness, consistency, and asymptotic complex Normality are proved.

4.7.1 Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram

Assumption 4.7.1 Lack of Support-Curve Clusters (II). Let

(4.156) equation

be the set of indices of the curves img, mn, that intercept img in f.

There is no cluster of support curves. That is, for every img and img, the set img is finite (or empty) and no curve img with , can be arbitrarily close to the curve in f. That is, ...

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