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

Abstract

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.