The paper compares the characteristics of optimum Chebyshev filters with a finite transmission zero pair of arbitrary multiplicity to those of optimum Chebyshev allpole filters. By introducing a transmission zero pair (single or multiple) at a real frequency into the transcendental form of the Chebyshev polynomial, the filter achieves a specified minimum attenuation extreme value in the stopband, thereby improving the cutoff slope. Additionally, the paper presents a new method for deriving a rational polynomial form of the optimum Chebyshev filtering function from its transcendental form, which is essential for determining the poles of the filter's transfer function. The method is straightforward and does not rely on optimization or recursive formulas. The proposed approach is validated and illustrated using an example. Although this approximation is primarily intended for microwave filter applications, it can also be applied to both analog and digital signal processing.

This paper presents an efficient design procedure for generalized optimum modified Chebyshev filtering functions with symmetrically located transmission zeros, making it particularly suitable for enhanced even-degree filter designs. Two primary challenges are addressed in the approximation of this low-pass filtering function. The first is the analytical determination of the positions of an arbitrary number of symmetrically distributed distinct transmission zeros that ensure an equiripple stopband insertion loss. This is achieved by solving a system of nonlinear equations using Newton’s method, building upon a closed-form expression for calculating the frequencies of the local extrema in the characteristic function. The second challenge involves extracting the rational polynomial representation of the generalized optimum modified Chebyshev filtering function from its transcendental form. Additionally, it is shown that only a prototype network with a single pair of transmission zeros can be transformed into the microwave domain using the Richards–Kuroda procedure. The validity and applicability of the proposed method are demonstrated through a numerical example of a sixth-degree filter featuring one pair of transmission zeros.

In this paper, a simplified design framework for low-order nearly-optimal linear-phase infinite impulse response integrators is proposed. The approach is based on symbolic regression, which is employed to derive closed-form analytical expressions for the coefficients of optimal integrators as functions of the boundary of the frequency range of interest. In this way, the need for solving computationally demanding optimization problems is effectively eliminated. Numerical results demonstrate that the resulting nearly-optimal integrators exhibit negligible degradation in magnitude response compared to the optimal designs.

Carbon footprint is one of the key indicators of the environmental impact of human activities, particularly in the context of global warming and climate change. Accurate calculation of this indicator is essential for making sustainable environmental and economic decisions. This paper analyzes various methods for calculating the carbon footprint, including life cycle analysis, economic–ecological models, as well as emission measurement and empirical approaches. Through comparative analysis, the advantages and limitations of these methods are presented, along with their applicability across different sectors, from industry and transportation to individual consumption. The aim of this study is to provide a systematic review of existing methods and recommendations for selecting the most reliable and practical tools for carbon footprint assessment, contributing to the development of strategies to reduce negative environmental impacts.

A new approach to the design of nearly linear-phase infinite impulse response fullband differentiators is discussed in this paper. Transfer function of these differentiators is expressed as the product of a ( 1-z^-1) term, a minimum-phase function, and an all-pass transfer function, whose coefficients are determined by minimizing the Chebyshev norms of relative magnitude and phase response linearity errors. Design examples demonstrate that proposed second- and third-order minimum-phase differentiators can have relative magnitude response errors below 1

The paper examines the effect of introducing distinct pairs of finite transmission zeros into the characteristic function of an optimum Chebyshev all-pole filter. To ensure the equiripple stopband, the transmission zero locations are determined using the Newton-Raphson method. A novel approach is proposed to transform the characteristic function from its transcendental into a rational polynomial form. Notably, the derivation process is straightforward, eliminating the need for recursion or optimization. These filters preserve the same magnitude response in the passband, while achieving enhanced stopband performance compared to their equiripple all-pole counterparts. To illustrate the effectiveness of this method, an approximation procedure is presented for a 7th-degree optimum Chebyshev low-pass filter with one, two, or three distinct simple transmission zeros, achieving a minimum stopband attenuation of 50 dB. A comparative analysis demonstrates the enhanced performance of the proposed filters.

Valorization of industrial by-products through thermal processes represents an efficient and sustainable solution for waste reduction and the development of new functional materials. This study investigates the potential application of cathode ray tube (CRT) glass, iron slag, fly ash from thermal power plants, and natural zeolite in sintering processes. Characterization was performed using XRF, FTIR, SEM, and TGA methods to examine the chemical, morphological, and thermal properties of the materials. The obtained results indicate complementary chemical and structural characteristics, with SiO2 and CaO as the dominant components in the analyzed materials. TGA analysis of the mixture, conducted under a controlled temperature regime, simulated the sintering process and demonstrated the thermal compatibility of the materials. In addition to spectroscopy/microscopy, composition-based proxies (basicity, silica modulus, network former/modifier ratio, and rule-of-mixtures density), together with a stable sintering region quantified by TGA (similar to 750-990 degrees C), were used to appraise sinterability and application-oriented feasibility. The results show that this multicomponent composition enables the optimization of sintered products while preserving structural stability and ensuring negligible mass loss during thermal treatment. The materials analyzed, both individually and in synergy, represent sustainable components for the development of new sintered systems, thereby contributing to advanced recycling technologies and the principles of the circular economy.

This paper discusses two well-known types of generalized Chebyshev (C) lowpass prototype filters, both characterized by an equiripple passband response. The number of transmission zeros at infinity and the locations of the remaining transmission zero pairs at finite real frequencies are considered as design parameters. It is shown that, when the filters share the same set of transmission-zero pairs, both approximations produce filtering functions with an identical rational polynomial form. As an illustrative example, the LC ladder realization of an 8th-degree generalized optimum C low-pass filter is presented.

Analysis of air quality in the city of Niš indicates a presence of increased concentrations of pollutants in outdoor air. In the period from 2019 to 2023 air quality in the area of the city of Niš was in the category of excessively polluted air, because of increased concentrations of PM10 and PM2.5 particulate matter. Multiple exceedances of the limit and tolerance values of PM10 and PM2.5 particulate matter are the basis for the emergence of a health risk that manifests itself through various types of pathological conditions. The physicochemical properties and chemical composition of PM10 and PM2.5 particulate matter are the criteria for classifying these particles as carcinogenic substances. This paper presents the probability of the occurrence of cancerous diseases during exposure to suspended PM10 and PM2.5 particles. The risk of cancer development (Ri) was determined based on intake dose and unit risk. The calculated probability is in the range of the level of possible and the level of probable carcinogenic risk, depending on the length of exposure. The probability was determined using the methodology provided by US EPA.

This paper proposes two methods for designing linear-phase infinite impulse response integrators. The first method, referred to as the maximally-flat one, imposes flatness conditions on the frequency response error function, leading to a system of linear equations that have to be solved to determine unknown coefficients. Furthermore, a relation is established between the proposed maximally-flat integrators and existing integer-order linear-phase integrators derived using the algebraic polynomial-based quadrature rules, demonstrating that the latter represent special cases of the proposed integrators. The second method, referred to as the optimal one, minimizes the complex frequency response error function in the weighted Chebyshev sense, which is achieved by an efficient exchange algorithm that exhibits rapid convergence. The proposed linear-phase integrators are also compared with several existing linear- and nearly linear-phase integrators.

Linear, or almost linear phase in the design of digital differentiators depends both on the method of calculation of the filter coefficients and the adopted structural design. Acknowledging the importance of this design objective, we developed a method to derive infinite impulse response differentiators which tackles it from both perspectives and yields improved characteristics compared to our previous design. We have replaced the differentiator structure comprising an all-pass filter and a delay line with a configuration of two infinite impulse response all-pass filters. Furthermore, we provide a procedure for determining an improved initial solution to the optimization of filter coefficients, as well as a procedure for improving the differentiator's magnitude response. The final solution exhibits considerably lower error at low frequencies and is thus suitable for the common scenario where the relevant spectral content decreases with frequency. The proposed filters of third and fifth order outperform many existing solutions in literature, especially in terms of the phase characteristic and time-domain performance.

The paper suggests that optimum Chebyshev filters present an excellent choice for microwave filter design, as this approximation offers minimum return loss in the half-power passband, provides a maximum cutoff slope, and maintains low sensitivity in the passband. A comparative analysis is conducted with the chained-function filters to demonstrate the efficacy of this approximation, since chained-function filters also utilize Chebyshev polynomials to shape the filter’s characteristic function. The optimum Chebyshev filter, along with two chained-function filters, each of the sixth-degree, are realized, simulated, and compared as lowpass stepped impedance filters with a half-power passband of 1 GHz. After a detailed comparison, it is concluded that the optimum Chebyshev filter outperforms, or at least matches, the performance of the chained-function filters. This suggests that the optimum Chebyshev filter can effectively replace chained-function filters in all applications, offering a superior solution.

In assessing ecological risk in the paint and coatings industry, stressors are examined from the perspective of exposed hazardous substances, whether as input substances or substances leaving the technological process and entering the environment. The extent of their negative impact on humans, living organisms, non-living nature, and material goods depends on their characteristics and the frequency and degree of their effects. When assessing risks, the frequency and degree of their effects are considered in terms of regular operational regimes and accident scenarios. The spatial distribution of hazardous substances reaching watercourses is also presented based on calculations of maximum emission quantities and volumes of substances, as well as the determination of the area of contaminated watercourses. Risk is assessed concerning the probability of the most likely unwanted events in the paint and coatings industry and their consequences for human life, health, and the environment.

Fire protection in hazardous materials warehouses is based on a complex analysis of calculations and the current state to determine appropriate protection measures. This paper explores the fire hazards associated with storing hazardous materials in a warehouse setting. It provides a detailed assessment of potential risks, focusing on the unique challenges posed by the nature of the materials stored. The study examines various factors that contribute to fire risk, including the flammability of materials, storage conditions, and existing fire prevention measures. The objective is to identify critical vulnerabilities and propose strategies for enhancing safety and reducing the likelihood of fire incidents. The findings aim to inform best practices for managing fire risks in hazardous material storage facilities.

In this paper, design of infinite impulse response lowpass differentiators that can be realized by parallel connection of two allpass filters whose orders differ by two, where one of the allpass branches is pure delay, is considered. As adopted structure of proposed lowpass differentiators allows formulation of their magnitude and phase responses as functions of allpass filter phase response, a set of nonlinear equations in unknown allpass filter coefficients is derived and iteratively solved in a way that magnitude response approximates the ideal one in weighted Chebyshev sense, in both passband and stopband. On the other hand, passband phase response linearity is shown to be related to the maximum of the magnitude response, which can be directly controlled by an additional design parameter. Design examples reveal that proposed infinite impulse response lowpass differentiators of low order can have very low relative passband magnitude errors and nearly linear phases, while results of comparison with existing lowpass differentiators show that proposed differentiators usually require fewer multiplications.

A design method for the allpass-based infinite impulse response multi-notch filters with identical pole radiuses is derived in the paper. According to the standard procedure when design of the allpass-based filters is considered, the multi-notch filters? magnitude response specifications are first formulated as the phase response specifications of the corresponding allpass filter. Then, for the specified identical pole radiuses, it is shown that unknown allpass filter coefficients can be obtained determined from the square system of linear equations. On the other hand, the minimum value of the pole radius, such that specifications of the the magnitude response are satisfied in all passbands, can be determined using the bisection method. Results of comparison with some of the existing design methods lead to the conclusion that proposed filters have higher area under the squared passbands magnitude response compared to filters with the same maximum pole radius. Furthermore, utilization of the proposed method can result in transfer functions that have the lowest possible maximum pole radius.

The maximum power transfer between source and load is extremely important in analog signal processing. The main disadvantage of signal processing using the even-degree Chebyshev filter is the impossibility of LC ladder network realization between two equal resistors. Therefore, either the utilization of the ideal transformer or the Chebyshev filter of odd-degree is required to achieve the maximum power transfer. To overcome this limitation, the class of even-degree polynomials with the equiripple behavior, referred to as scaled modified Chebyshev polynomials, can be used as the filter’s characteristic function. Passband ripples of obtained filters can be controlled through an embedded parameter, while normalized half-power frequency is kept equal to unity. Furthermore, these filters can be optimized for the minimum amount of reflected power at the input terminals. In this paper, the optimum modified Chebyshev filters are first compared to the classic Chebyshev filters to show that both filters exhibit similar performances. Second, proposed filters are compared to the Least Square Monotonic (LSM) filters that are optimized by minimizing the area under the characteristic function in the passband. Results of comparison reveal that the proposed even-degree scaled modified Chebyshev filters outperform the LSM filters, as is already proved for the odd-degree filters.

The paper provides the physicochemical analysis of galvanic sludge to determine the presence and concentration of toxic metals. Two sludges sampled from the same factory, but from different technological processes, alkaline galvanic sludge obtained from galvanizing process and acidic sludge generated from the chromium plating process were analyzed. Inductively Coupled Plasma - Optical Emission Spectrometry (ICP-OES) revealed increased concentrations of toxic heavy metal ions Zn2+, Cr3+, Ni2+ and Pb2+ in the sludge from the galvanizing process and Cr3+, Cu2+, Ni2+, Pb2+, Cd2+ and Zn2+ from the chroming process. Moreover, the sludges were further physicochemically characterized by Reflectance Fourier Transform InfraRed Spectrometry (FTIR), Scanning Electron Microscopy with Energy-dispersive X-ray Spectroscopy Analysis (SEM-EDX) and X-ray diffraction (XRD). The results of ICP-OES were corroborated by FTIR. Analysis of FTIR spectra revealed the specific bands indicating the existence of metal oxides in the analyzed sludges, as well as the presence of organic substances, i.e. solvents and surfactants, used in the electroplating process. The analysis was accomplished following international norms and confirmed the increased concentrations of heavy metal ions from both sludges. In line with the regulations of the Environmental Protection Agency (EPA), the results proved the hypothesis that galvanic sludge is hazardous waste.

Technogenic risk is the result of creation and development of hazards that originate from accidents in the technosphere. It involves emissions of hazardous industrial substances into the work and natural environments, fires, radioactive contamination, and contamination by toxic substances during their transport and storage. The qualitative and quantitative technogenic risk assessment has to be performed during the use, handling, transport, and storage of hazardous substances if it is decided that specific environmental elements at a specific location are likely to become exposed to hazardous substances, leading to environmental degradation. This paper discusses vulnerability zones - specifically, the high lethality zone and the irreversible effects zone - that are formed due to hazardous events or accidents in the paints and varnishes industry. Accidents are discussed in terms of exposure to solvents classified as hazardous to ecosystem components, the biosphere, anthroposphere, and the human population during their atmospheric dispersion. The vulnerability zones are designated using the REHRA (Rapid Environmental and Health Risk Assessment) methodology and their spatial arrangement is used to perform the risk assessment for the purpose of notifying authorized institutions and the public about a potentially increased risk at the hazard location and/or the immediate vicinity.

The paper investigates, for the first time, the design of recursive digital filters that exhibit optimum equiripple passband magnitude characteristics. After a brief description of the optimum equiripple filters in the analog domain, digital optimum C (Chebyshev) tan and sine filters are derived directly in the digital domain through the minimization of the area under the passband characteristic function. The influence of the truncated coefficients is also considered and its effects are demonstrated through an example proving the robustness of the magnitude function. Furthermore, a design procedure is proposed for the optimum C tan half-band filter. To highlight the effectiveness of the proposed approximation, a comparative analysis is conducted with the staircase digital filter, as both filters optimize passband responses by minimizing the area under the characteristic function. The results of comparison demonstrate that the optimum equiripple approximation surpasses the staircase approximation, not only in the analog but also in the digital domain.