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.
