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Generalized Lyapunov Demodulator for Amplitude and Phase Estimation by the Internal Model Principle

机译：内模原理的广义Lyapunov解调器的幅相估计

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摘要

Effective demodulation of amplitude and phase is a requirement in a wide array of applications. Recent efforts have increased the demodulation performance, in particular, the Lyapunov demodulator allows bandwidths up to the carrier frequency of the signal. However, being inherently restricted to a single order filtering of the input signal, signal components outside its passband are not sufficiently attenuated for all applications, such as in multifrequency atomic force microscopy. In this article, the structure of the Lyapunov demodulator is transformed to an equivalent form, taking advantage of the internal model representation of the sinusoid to be tracked. A generalization of this formulation allows the application of standard filtering techniques in order to shape the characteristics of the demodulator, while retaining the perfect tracking condition provided by the internal model. Guidelines for the filter design are provided in order to achieve the desired characteristics, such as filtering order, tracking bandwidth, and transient performance. The resulting generalized Lyapunov demodulator structure is highly flexible, allows for direct employment of any standard filter type, is computationally simple, and easy to implement requiring only a bandpass filter, a single integrator, and two nonlinear transformations. Numerical results demonstrate the effectiveness of the approach, and provide a comparison of the various filters considered.
机译：在广泛的应用中，要求有效地幅度和相位解调。最近的努力提高了解调性能，特别是Lyapunov解调器允许带宽达到信号的载波频率。但是，由于固有地仅限于输入信号的单次滤波，其通带之外的信号分量并未在所有应用中得到充分衰减，例如在多频原子力显微镜中。在本文中，利用要跟踪的正弦波的内部模型表示，将Lyapunov解调器的结构转换为等效形式。该公式的一般化允许应用标准过滤技术以塑造解调器的特性，同时保留内部模型提供的理想跟踪条件。提供了滤波器设计指南，以实现所需的特性，例如滤波顺序，跟踪带宽和瞬态性能。所得的广义Lyapunov解调器结构具有高度的灵活性，可以直接使用任何标准滤波器类型，计算简单，并且易于实现，仅需要一个带通滤波器，一个积分器和两个非线性变换。数值结果证明了该方法的有效性，并提供了所考虑的各种滤波器的比较。

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