Abstract
In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function which is defined on bounded domain. A sample input-output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-mean stationary Gaussian processes that can be represented as the truncated series of Fourier expansion. A criterion on the shape of the impulse response function is given. For this purpose, a theory of square-Gaussian stochastic processes is used.
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Kozachenko, Y., Rozora, I. (2022). On Statistical Properties of the Estimator of Impulse Response Function. In: Malyarenko, A., Ni, Y., Rančić, M., Silvestrov, S. (eds) Stochastic Processes, Statistical Methods, and Engineering Mathematics . SPAS 2019. Springer Proceedings in Mathematics & Statistics, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-031-17820-7_25
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