Vol 4, No 4 (2024)

For the first time, the tasks of extrapolation and filtering of random processes were set in the middle of the 20th century by academician A.N. Kolmogorov. Simultaneously with A.N.Kolmogorov, the American mathematician N. Wiener dealt with this problem, who managed to identify a fairly wide class of processes for which it is possible to obtain explicit extrapolation formulas. These are processes with a rational spectral density. Subsequently, this class was expanded by the followers of A.N.Kolmogorov to the class of quasi-rational spectral densities, the main component of which are quasi-polynomials with roots in the upper half-plane. Therefore, the problem of constructing such quasi-polynomials is extremely relevant. In this paper, based on the Chebotarev method and the generalized Sturm's theorem, necessary and sufficient conditions are obtained for the roots of quasi–polynomials forming the spectral densities of video signals and L-Markov processes to belong to the upper half-plane. This fact plays a very important role in constructing the best linear extrapolators and filtering operators for these processes.

Early diagnosis and monitoring of cancer is critical to successful treatment and improved patient survival. Current methods for detecting malignant tumors include magnetic resonance imaging, computed tomography, and biopsy, but are limited by the high cost, complexity of equipment, and invasiveness of the procedures. In recent years, special attention has been paid to the development of non-invasive optical diagnostic methods, among which fiber Bragg gratings occupy one of the leading positions due to their high sensitivity, compactness and biocompatibility. The paper reviews the application of FBG in various aspects of oncologic diagnostics and patient rehabilitation. Methods of temperature control and thermography based on the measurement of local temperature anomalies characteristic of tumor processes are considered. Developments in the field of tactile sensors using FBG for non-invasive mechanical diagnostics of tumors are analyzed. Research results on the application of 3D printed tactile sensors integrated with FBG for objective tissue palpation are presented. Biochemical detection of oncomarkers realized using FBG is discussed. Optoelectronic sensor circuits designed for selective detection of specific cancer biomarkers (e.g., HER2) without the use of additional tags are presented. Attention is given to rehabilitation systems for cancer patients utilizing FBG sensors to monitor physical activity and motor recovery. Solutions for remote patient monitoring within eHealth platforms using FBG s to measure grip strength and forearm muscle activity are described. The paper emphasizes the prospects of fiber optic technologies in oncology, their potential for clinical implementation and possible directions for further research, including the development of multifunctional sensor systems, integration with machine learning methods and improvement of algorithms for automatic data analysis.

Precise transmission of the signal spectrum is necessary for building 4G mobile digital networks (tens of Gbit/s) consisting of multiple base radio stations and remote radio nodes, which actualizes the task of monitoring the spectral characteristics of wideband Mach-Zehnder amplitude modulators (WB AMZM) and photodetectors (WB PD), on the basis of which fiber-optic transport domains connecting the specified stations and nodes are built. In the transport domains of 5G mobile systems, the required bitrate for the connection will be even higher (hundreds of Gbit/s). In addition, in 5G and higher mobile systems, analog "radio-over-fiber" channels containing WB AMZM and WB PD are also used to build transport domains and inter-node connections in order to maintain their required bitrate or throughput. This technology belongs to microwave photonics. Additionally, we can talk about the widespread use of WB AMZM and WB PD in microwave photonic sensor systems. The objective of this work, consisting of three parts, is to solve the problems of combined application of the fundamentals of wideband and ultra-narrowband discrete frequency packages (WB DFP and UN DFP) to improve the metrological characteristics, minimize the structure and reduce the cost of radio-photonic analyzers of spectral characteristics WB AMZM and WB PD, implemented on the import-substituting element base. The first part considers the issues of constructing a symmetrical dual-band multi-frequency probing radiation with a suppressed carrier and equal component amplitudes, which is the basis of the WB DFP, and evaluates its functional and system characteristics necessary to achieve the goal of the work.

In the systems for spectral characteristics analysis of wideband amplitude Mach-Zehnder modulators (WBAMMZ) and photodetectors (WBPD), the efficiency of conversion of symmetrical dual-band dual-frequency probing radiation (DDPR) generated in the former can be obtained in the latter from the ratio between the optical power of the DDPR and the electric power of the single-frequency beat signal between its components. When the extinction coefficient of the calibrated WBAMMZ is large enough, the spectral profile of the WBPD does not depend on the frequency response of the modulator. Thus, by monitoring or stabilizing the power of the DDPR, we can measure the frequency response of the tested WBPD. WBPD, the frequency response of which is calibrated by the DDPR, can be used in turn to determine the characteristics of optical transmitters based on WBAMMZ at different operating optical wavelengths. And vice versa, calibrated WBAMMZ can be used for a multi-range study of the frequency response of WBPD in the optical range. The resolution of measurements in the radio range is provided by an electronic vector analyzer (EVA), which significantly increases the cost of the spectral characteristic analyzers. The objective of this work, consisting of three parts, is to solve the problems of combined application of the fundamentals of wideband and ultra-narrowband discrete frequency packages (WBDFP and SNDFP) to improve the metrological characteristics, minimize the structure and reduce the cost of microwave photonic spectral characteristic analyzers, implemented on an import-substituting element base. The first part considers the issues of forming a DDPR with a suppressed carrier and equal amplitudes of the components that form the basis of the WBDFP, and evaluates its functional and system characteristics necessary to achieve the goal of the work. The present, second part of the work presents the fundamentals of the DDPR analysis, converted into a WBPD, based on a simple in structure microwave photonic interrogator, which differs significantly in the principle of operation from the EVA and allows to reduce the cost of the analyzer.

This research proposes a brand-new approach based on the modified POLS (Procedure of the Optimal Linear Smoothing). The concept is based on an iterative process that consists of two crucial steps: (a) smoothing an initial trendless sequence successively, and (b) subtracting the smoothed replica at each iterative step. In terms of the traditional noise/signal ratio, this suggested method enables the setting of completely new records. At least this ratio as it is estimated on available data is equaled to –100 dB and even less. Md-POLS formula allows to receive resolution about +3dB and therefore to detect the presence of the super weak signal. The method is rather universal and can be applied to wide class of trendless sequences. One requirement is important. The tested sequence should have sufficient number of stable digits after dividing point. It implies to use ADC with high resolution. It will open new possibilities in chemistry (detection of different "traces" in the given solutes) and detection of different early-stage diseases, in radio-electronics, in optics where detection of small signals plays a central role etc.