Spectral Observer with Reduced Information Demand

Spectral observer is appropriate for investigating the frequency domain properties of signals. Since the spectral analysis is a very common method, this observer can be used widely in many applications. The paper introduces a novel resonator based spectral observer and control algorithm that require reduced amount of data for the operation, so they are appropriate for the utilization in signal processing systems with limited resources (e.g. wireless sensor networks). The data reduction is achieved by the deployment of the sign error principle. For the improvement of the transient properties of the sign error structures a new method is proposed that tunes the speed of the adaptation according to the norm of the error. This algorithm makes possible to find a trade-off between the settling time and the amount of data required for the operation. The algorithm can be used for recursive Fourier analysis of signals and control of linear systems. As a practical application a wireless active noise control system is presented.