Abstract
In this chapter, square integrable time functions of Lebesgue measure are approximated via hybrid functions and such approximations are compared with similar approximations using BPF and Legendre polynomials. For handling discontinuous functions, a modified method of approximation is suggested in hybrid function domain. This modified approach, named HFm approach, seems to be more accurate than the conventional HF domain technique, termed as HFc approach. The mean integral square errors (MISE) for both the approximations are computed and compared. Finally, error estimates for the SHF domain approximation and TF domain approximation are derived. The chapter contains many tables and graphs along with six illustrative examples.
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Deb, A., Roychoudhury, S., Sarkar, G. (2016). Function Approximation via Hybrid Functions. In: Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions. Studies in Systems, Decision and Control, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-26684-8_3
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DOI: https://doi.org/10.1007/978-3-319-26684-8_3
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