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Recently, an observer-based algorithm was reviewed that is able to perform recursive sliding discrete Fourier transform (SDFT) [1]. DFT is the basic algorithm used for Fourier analysis [2], but it provides unbiased estimates only if the sampling is coherent, i.e., the ratio of the sampling frequency fs and the input signal frequency fin is a rational number. Coherent sampling of real-life periodic signals (e.g., mains voltage) can only be achieved if fin and fs are synchronized.

The Adaptive Fourier Analyzer has been developed for measuring the harmonic components of periodic signals with changing or unknown fundamental frequency. Vibration analysis of rotating machines, active noise control or harmonic component measurements of the lines are typical applications. Nowadays, radio or Internet-based communication is gaining popularity in various fields, e.g., in signal processing. Due to the not reliable real-time communication, some of the data are lost during the transmission. In this paper, an extension of the Adaptive Fourier Analyzer is presented which is able to handle data loss. The paper briefly presents the mathematical description of the data loss and the modification of the Resonator-Based Observer for data loss. The novelty of this paper is the modification of the Adaptive Fourier Analyzer for signals with missing samples. The performance of the algorithm is demonstrated with simulation and measurement examples.

Nowadays, radio- or Internet-based communication is gaining popularity in various fields, e.g., in signal processing. As these are not reliable real-time communications, some of the data are lost during the transmission. There are several stochastic models allowing the analysis of this phenomenon. The spectral properties of these models result in specific distortion in the signals’ spectra. As the spectrum of the signal can easily be calculated via the fast Fourier transform (FFT), FFT-based identification methods of the data loss can be developed. In this article, a new identification method is proposed for the simpler cases of the Gilbert–Elliott model class. The article summarizes the mathematical description of data loss and introduces the Gilbert–Elliott model family. The novelty of the article is the identification method that is based on the autocorrelation function of the Gilbert–Elliott model. The proposed method is compared with classical procedures based on the Baum–Welch algorithm and the novel ones based on global optimization. The theoretical results are supported by extensive simulations.

Nowadays, the usage radio channel or Internet connection grows for real-time transmission of measurement data or signals. For these applications, not reliable communication needs to be analyzed from a signal processing point of view. Our paper contributes to this topic with the analysis of data loss as a signal distorting phenomenon. The paper contains a possible mathematical description of the data loss via the indicator function. Moreover, the Gilbert-Elliott data loss model class is presented, which gives a framework to analyse numerous data loss phenomena in general. In order to analyse the data loss in the frequency domain, the spectrum of the indicator function is required. This paper presents the derivation of the power spectral density of the Gilbert-Elliott model. The paper reviews a possible identification method for the simpler models derived from the Gilbert-Elliott model. Theoretical analysis and simulations are supported by measurements. The measurement results are used to show how the data loss models function in practice.

The efficiency of active noise control (ANC) is largely dependent on the arrangement of the microphones and loudspeakers, and the acoustic environment as well. The paper presents a simulation tool, which allows the performance evaluation of ANC systems without the difficulty of physical experiments. The proposed simulation integrates sound field calculation and noise control. Field calculation is based on robust FDTD techniques, while the discrete time controller is realized in a usual way. The simulation is performed in three stages. First the program determines the discrete transfer function models of the acoustic paths between specific points of interest. In the next stage the controller’s operation is evaluated without field simulation. Having the steady state parameters of the adaptive controller, the field simulation is re-run for the reverberation time providing the sound pressure map. Sound field calculation is implemented on modern GPGPU devices. A series of ANC experiments were compared to the results of the simulations, and they prove the applicability of our simulation method in a convincing manner.

This paper introduces a new, adaptive-filter-based controller that shows advantageous properties from the viewpoint of its communication requirement. The algorithm is called signed-error filtered-x LMS (SE-FxLMS). Its novelty is characterized by the fact that it makes possible data compression in the feedback path of adaptive-filter-based control loops in a very simple way. This feature is especially useful in such closed-loop systems where the feedback signals are transmitted over a low-bandwidth communication channel. This is a typical case in so-called networked control systems (NCS), where the communication is carried out over a shared communication channel, e.g., using a wireless sensor network. The paper introduces an analysis of the algorithm as well.

A nonparametric identification method for linear systems is proposed. The identification is done via synchronized multisine measurements where the synchronization is ensured by a resonator-based generator-observer pair. The advantage of the proposed structure is that it works as a filter bank and, hence, provides the measurement results online. Exponential averaging is an option of the method and it requires no extra calculations. A further advantage is that the identification can be done over any frequency set without any loss of performance. Explicit formulas are given for noise suppression and settling time. The method is illustrated by practical examples.

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.

This paper deals with the synchronization in wireless adaptive signal processing systems. Wireless communication offers high flexibility, however, the distributed structure of wireless systems requires the synchronization of the subsystems. The synchronization becomes particularly important if the signal bandwidth is in the kHz range, and it is inevitable in distributed control systems. The demand on the synchronization is presented through the introduction of a wireless active noise control system. In this system wireless sensors (microphones) receive the signal, and the main signal processing algorithm is implemented on a central unit which produces the signal for the actuators (loudspeakers). In spite of the special application, the system has a general structure, so the results are valid for other adaptive systems. First a PLL like algorithm is described for the synchronization of the sampling in a wireless real-time signal processing system, then a higher-level synchronization is introduced for a distrib uted Fourier-analyzer based noise control system. The effectiveness of the algorithms is demonstrated by measurement results.

The paper presents an on-line digital signal processing method for active cancelation of distortion of sinusoidal sources. Generation of a sinusoidal signal of several volts is a simple task, but many measurements need high voltage, current, or nonelectrical excitation. This signal conversion often leads to distortion. The proposed active distortion controller is a resonator-based observer which determines the harmonic content of the signal, and the distorting components are subtracted from the output signal. The paper introduces the controller design in details, and a practical example illustrates the effectiveness of the proposed method.

Active cancellation of acoustic noise seems to be a real alternative to passive isolation in the low frequency region. There are already many methods to solve this control problem, typically based on adaptive filter techniques. If the noise is periodic, a simple signal model can be integrated into the adaptive controller, the parameters of which are set using the error signal. This control loop behaves like an observer of the signal to be suppressed. The authors have developed this method which is already proved to work efficiently in practice, as well. The paper describes the design of this observer and gives the relations to the conventional structures and adaptation mechanisms.