The BT product as a signal dependent sample size estimate in hypothesis testing: an application to linear/nonlinear discrimination in bandwidth limited systems

This paper investigates the ability of the effective bandwidth-duration (BT) product to improve the accuracy of statistical hypothesis testing on bandwidth limiting systems by estimating the sample size of the signal. To this end, the proposition that the traditional method of assuming the sampled signal length as statistical sample size may be misguided. Simulations between a BT product sample size estimate (BT-estimate) and a discrete signal length sample size estimate (N-estimate) are compared. The BT-estimator outperforms the N-estimator for the two hypothesis tests trialled; the Lilliefors and Bera-Jarque Gaussianity tests. In simulated results the BT-estimator provides an average 19% increase in available signal bandwidth compared to the N-estimator. Physical results show that the BT-estimator improves the detection rate by 31% compared to the N-estimator. The effective BT product of a signal provides a more accurate estimate of the statistical sample size than the discrete signal length for low bandwidth to Nyquist frequency ratio signals. This result improves the accuracy (54% ) of statistical detection of linearity in bandwidth limited systems.