Sinusoidal model and chirp model are the two fundamental models in digital signal processing. Recently, a chirp-like model was introduced by Grover et al. (International conference on computing, power and communication technologies, IEEE, pp. 1095–1100, 2018). 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.

正弦模型和线性调频模型是数字信号处理中的两个基本模型。最近，Grover等人引入了线性调频模型。（计算，电源和通信技术国际会议，IEEE，第1095–1100页，2018年）。类似线性调频的模型是正弦模型的泛化，并提供了线性调频模型的替代方案。在本文中，我们推导了chi样信号模型的参数的最小二乘估计量和顺序最小二乘估计量的渐近性质。从理论上以及通过广泛的数值计算可以观察到，顺序最小二乘估计器的性能与通常的最小二乘估计器同等。顺序算法所涉及的计算复杂度明显低于计算最小二乘估计量所涉及的计算复杂度。这是通过利用基础模型的不同组件的正交性结构来实现的。仿真结果说明了两种估计器在有限样本量下的性能。在信号的特定实际数据分析中，我们表明类似线性调频的信号模型能够以更有效的计算方式对可以通过线性调频信号模型进行建模的现象进行建模。