Higher order detection test for deterministic signals

In the contex of electromagnetic signals, we want to detect a transient in a non stationnary gaussian noise by a higher order statistic test. In this paper, we use a new formalism (an extension of Gardner´s work) that enables us to evaluate theoretically the response of higher order statistic test for detection. We develop the theoretical ground and we prove that higher order statistic detection test provides a very short delay detection. We apply our methods to simulation of a simple and typical example : the kurtosis.