We analyze operation of the energy detector in the case of a non-Gaussian noise background. Analytical expressions for the probabilities of correct detection and false alarm of the energy detector receiving unknown signals against the background of Likhter noise are obtained.

A closed form analytic representation of multidimensional periodic functions with a finite Fou rier spectrum is obtained as a modified interpolation series with a finite number of terms. The corresponding theorem is formulated, and the multidimensional periodic kernel of the expansion is analyzed. It is shown that such a representation makes it possible to calculate values of the derivatives of an arbitrary order of a peri odic function with a finite spectrum from the samples of this function.

We find a distribution of the decision statistic of an adaptive energy detector with training. Expressions for the probabilities of false alarm and correct detection are obtained.

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A closed form analytic representation of periodic functions with a finite Fourier spectrum by a modified Kotel'nikov series with a finite number of terms is obtained. It is shown that this representation allows one to exactly calculate arbitrary order derivatives of this function from its sampled values.