Asymptotic properties of least squares estimators and sequential least squares estimators of a chirp-like signal model parameters. (English) Zbl 1509.94016
Circuits Syst. Signal Process. 40, No. 11, 5421-5465 (2021); correction ibid. 40, No. 11, 5466-5467 (2021).
Summary: Sinusoidal model and chirp model are the two fundamental models in digital signal processing. Recently, a chirp-like model was introduced by R. Grover et al. [GUCON 2018, 1095–1100 (2018; doi:10.1109/GUCON.2018.8674970)]. A chirp-like model is a generalization of a sinusoidal model and provides an alternative to a chirp model. We derive, in this paper, the asymptotic properties of least squares estimators and sequential least squares estimators of the parameters of a chirp-like signal model. It is observed theoretically as well as through extensive numerical computations that the sequential least squares estimators perform at par with the usual least squares estimators. The computational complexity involved in the sequential algorithm is significantly lower than that involved in calculating the least squares estimators. This is achieved by exploiting the orthogonality structure of the different components of the underlying model. The performances of both the estimators for finite sample sizes are illustrated by simulation results. In the specific real-life data analyses of signals, we show that a chirp-like signal model is capable of modeling phenomena that can be otherwise modeled by a chirp signal model, in a computationally more efficient manner.
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
sinusoidal model; chirp model; chirp-like model; least squares; sequential least squares; asymptotic propertiesSoftware:
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