Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

Details Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

2007-08-02

arxiv.org/abs/0708.0347v5

Journal of Physics A: Mathematical and Theoretical (2008) 41, No 38, 382002 (7pp).

Mathematics

Optimization and Control

10 pages

Scientific paper

10.1088/1751-8113/41/38/382002

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of convolution integrals over future time by integrals over past time. We found that all band-limited processes are predictable in this sense, as well as high-frequency processes with zero energy at low frequencies. It follows that a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.

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