First-order Sections Research Articles

First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation

A bistatic high-frequency surface wave radar (HFSWR) with both receiving and transmitting stations placed on different ships (platforms) is a new radar system and referred to as shipborne bistatic HFSWR. In this paper, a first-order ocean surface cross section of shipborne bistatic HFSWR was derived. The first-order cross-section models for three different cases, i.e., ships moving with uniform, periodic, and hybrid motion states, respectively, are presented. The corresponding first-order Doppler spectra were simulated, and the spread width of the first-order spectrum was investigated. The simulation results show that the characteristics of the first-order spectrum are similar to those of a shore-based bistatic HFSWR when the transmitting and receiving platforms move in opposite directions. The first-order spectral spread width in the case of platforms with opposite directions is much smaller than that in the case of platforms with the same direction. This finding is useful for reducing HFSWR first-order spectrum spread due to platform motion, thus improving the target detection performance of the shipborne bistatic HFSWR. In addition, periodic oscillation motion of both platforms will cause complex motion-induced peaks in the first-order spectrum, which may be detrimental to target detection and ocean remote sensing. These results have important implications for the application of shipborne bistatic HFSWR.

The influence of relief morphometric characteristics upon the occurrence of the species Cordulegaster bidentata in the particular conditions of the Western Carpathians

The study concerns a monitoring survey of Cordulegaster bidentata Selys, 1843 (Odonata, Cordulegastridae), which is considered near threatened in the European Red List of Dragonflies, in order to show its habitat preferences and clarify the influence of slope and orientation of slopes on the occurrence of the species. Investigations of water habitats were carried out during the period from 2019 to 2020 in the Kysuce Region in northwest Slovakia. The protocol consists of looking for larvae and characterizing larval micro-habitat of C. bidentata so as to show their habitat preferences and clarify the influence of slope and orientation of slopes on the occurrence of the species. We sampled 32 watercourses (epicrenal, hypocrenal, rheocren, heleocren, epirhithral, metarhithral) at altitudes 420–950 m above sea level. A total of 79 larvae and 10 imagines (7♂ 3♀) of C. bidentata were found at 12 streams. In the present study, C. bidentata clearly preferred first-order stream sections, the slopes were steep and the proportion of small sediment grain sizes was high. The results show that the number of C. bidentata larvae grew with the increasing percentage of forests around streams. We also confirmed the trend for the number of C. bidentata larvae to increase with increasing values of slope and altitude of watercourses. Most of the individuals were recorded at the south and southwest oriented streams; we did not record larvae on the north and northwest oriented slopes. We assume that more suitable conditions for development of population exist in the streams on the south and southwest oriented slopes. The preference for watercourses oriented south and southwest ensures optimal conditions for the development of the population of this dragonfly species. The finding of larvae at the stages of instars shows the permanent occurrence of the species in the Kysuce Region.

On the Design of an Energy Efficient Digital IIR A-Weighting Filter Using Approximate Multiplication.

This paper presents a new A-weighting filter’s design and explores the potential of using approximate multiplication for low-power digital A-weighting filter implementation. It presents a thorough analysis of the effects of approximate multiplication, coefficient quantization, the order of first-order sections in the filter’s cascade, and zero-pole pairings on the frequency response of the digital A-weighting filter. The proposed A-weighting filter was implemented as a sixth-order IIR filter using approximate odd radix-4 multipliers. The proposed filter was synthesized (Verilog to GDS) using the Nangate45 cell library, and MATLAB simulations were performed to verify the designed filter’s magnitude response and performance. Synthesis results indicate that the proposed design achieves nearly 70% reduction in energy (power-delay product) with a negligible deviation of the frequency response from the floating-point implementation. Experiments on acoustic noise suggest that the proposed digital A-weighting filter can be deployed in environmental noise measurement applications without any notable performance degradation.

Исследование температурного режима элементов конструкции вакуумной электропечи сопротивления методом структурного математического моделирования

The article demonstrates the importance of developing a structural mathematical model of a high-temperature vacuum electrical resistance furnace (ERF) for studying the thermal processes in it with determining the temperature of each furnace element, predicting the service life of heating elements, screens, and other furnace structural elements, selecting the temperature sensor installation place, and making relevant adjustment of the temperature control system. The commonly used model, in which the furnace is represented by a first-order inertial section, does not provide such possibility, because the furnace average temperature is calculated in that case. Therefore, it is necessary to construct a model based on the energy balance equations for macro elements (heater, each of the screens, loading, etc.) taking into account radiant heat transfer between the macro elements. A mathematical structural model of a Tamman vacuum high-temperature electric furnace equipped with a heater in the form of a coal or graphite pipe and thermal insulation in the form of graphite cylinders-screens has been developed and implemented in the Simulink software package. The thermal resistance of graphite screens thermal conductivity, which is commonly neglected in design calculations of widely used thin metal screens, was taken into account in simulating the thermal processes. The temperature operating conditions of individual structural elements (heaters, screens, etc.) are analyzed, both at constant power supply voltage of the heaters and in using a closed-loop temperature control system. The effect the temperature sensor installation place has on the automatic temperature control quality is shown. The advisability of using the developed model for adjusting the proportional-integral-differential controller to ensure the required control quality is substantiated.

Dual-Behavior Resonator-Based Fully Reconfigurable Input Reflectionless Bandpass Filters

A class of input reflectionless dual-behavior resonator (DBR)-based bandpass filters (BPFs) with reconfigurable center frequency, bandwidth, out-of-band attenuation, and intrinsic switching-off capabilities is reported. They exploit a complementary-duplexer approach, in which the resistively terminated bandstop-filter (BSF) channel dissipates the RF input signal energy that is not transmitted by the main BPF channel in its out-of-band region. Spectral reconfiguration is realized through the synchronous tuning of the counterpart resonators in the DBR-based BPF and BSF channels—i.e., without variable couplings—which results in a dynamic transmission-zero (TZ) reallocation process. The theoretical analysis of the first-order section and design examples for higher order schemes are presented. Furthermore, for experimental-validation purposes, a microstrip prototype that can be tuned within the frequency range 1.3–2 GHz is manufactured and characterized.

Ocean Surface Wind Direction Inversion Using Shipborne High-Frequency Surface Wave Radar

Shipborne high-frequency surface wave radar (SHFSWR) has exhibited great advantages over onshore HFSWR (OHFSWR) in ocean remote sensing. Unlike OHFSWR, SHFSWR suffers the problem of Doppler spectrum spread owing to platform movement, which is a great challenge preventing the extraction of ocean surface parameters for SHFSWR. To address this challenge, in this letter, the mathematical model of ocean surface wind direction is first investigated based on the first-order SHFSWR cross section. Furthermore, a method for the wind direction inversion without ambiguity from the spread Doppler spectrum is proposed using a single receiving antenna. Meanwhile, the wind directions of the sea area covered by radar can be obtained by sequentially utilizing the proposed method, which is more appropriate for the application of SHFSWR with limited deck space and less cost. Experimental results of the real data collected in Taiwan Strait preliminarily verify the detection accuracy and the distance limit of the wind direction inversion, as the root-mean-square error and the detection range are 9.85° and 120 km, respectively

CMOS Realization of All-Positive Pinched Hysteresis Loops

Two novel nonlinear circuits that exhibit an all-positive pinched hysteresis loop are proposed. These circuits employ two NMOS transistors, one of which operates in its triode region, in addition to two first-order filter sections. We show the equivalency to a charge-controlled resistance (memristance) in a decremental state via detailed analysis. Simulation and experimental results verify the proposed theory.

Bistatic High Frequency Radar Ocean Surface Cross Section for an FMCW Source with an Antenna on a Floating Platform

The first- and second-order bistatic high frequency radar cross sections of the ocean surface with an antenna on a floating platform are derived for a frequency-modulated continuous wave (FMCW) source. Based on previous work, the derivation begins with the general bistatic electric field in the frequency domain for the case of a floating antenna. Demodulation and range transformation are used to obtain the range information, distinguishing the process from that used for a pulsed radar. After Fourier-transforming the autocorrelation and comparing the result with the radar range equation, the radar cross sections are derived. The new first- and second-order antenna-motion-incorporated bistatic radar cross section models for an FMCW source are simulated and compared with those for a pulsed source. Results show that, for the same radar operating parameters, the first-order radar cross section for the FMCW waveform is a little lower than that for a pulsed source. The second-order radar cross section for the FMCW waveform reduces to that for the pulsed waveform when the scattering patch limit approaches infinity. The effect of platform motion on the radar cross sections for an FMCW waveform is investigated for a variety of sea states and operating frequencies and, in general, is found to be similar to that for a pulsed waveform.

General state-to-state transitions in atoms for either Yukawa or Coulomb potentials via Fourier transforms

In a previous paper we used our integro-differential extension of Gaussian transforms to find the closed analytic form for hydrogenic bound-state transitions with arbitrarily high quantum numbers due to projectile impact excitation via Coulomb potentials (in the intermediate representation). Here we extend that result to Yukawa potentials, but do so by utilizing Fourier transforms. The result is used to find the first-order cross section for proton impact excitation of hydrogen to the 2s–7s final states. Because the results hold for any initial and final quantum states, and the amplitude may be easily converted for use with pseudostates, it may be used to automatically calculate sums over intermediate pseudostate propagators whose (bound and free) principal and angular quantum numbers can become very large. This result may be extended to multi-electron transition amplitudes by representing initial and final states by configuration–interaction wave-functions.

Second-Order Ocean Surface Cross Section for Shipborne HFSWR

To investigate the characteristics of sea clutter in monostatic shipborne high-frequency surface-wave radar (HFSWR) with uniform linear motion, the second-order patch scatter cross section is derived. With the previously proposed first-order ocean surface cross section, both cross sections could be reduced to the existing results in land-based HFSWR. Illustrations and discussions are provided on the basis of the simulation results for different situations. Although the spread Bragg lines vary with the ocean surface wind direction, the second-order contributions contaminate the energies of the Bragg lines in the high sea state, which may affect the application of shipborne HFSWR to wind direction extraction from the ratio of the positive and negative Bragg line energies. The derivations and analyses would be of importance to future investigations and applications, not only for target detection but also for ocean remote sensing.

Linearization of a heat-transfer system model with approximation of transport time delay

A method is proposed for linearizing the nonlinear model of a heat-transfer facility the state variables of which at equilibrium points are determined by numerically solving the initial bilinear system of differential equations for a stationary position of the control valve equipped with a constant-speed electric drive. The considerable transport time delay resulting from the distributed design of the heat-transfer system secondary circuit is approximated by a limited number of first-order inertial sections for obtaining a mathematical model in the Cauchy form. The proposed linearization method is tested on an operating hot-water supply heat-transfer system, and the study results are presented in the form of transient curves.

Transformation to implement computationally efficient IIR decimation filters

A new technique is proposed to transform an IIR filter into a computationally efficient decimation filter. In this technique, the recursive transfer function is transformed and noble identity is invoked to get sample rate reduction. The magnitude and phase response of the original filter are unaltered after the transformation. A higher order IIR transfer function is decomposed into parallel first-order sections and each section is transformed for sample rate reduction. The transformation is computationally efficient since current output can be directly computed from single M th old output and M inputs processed using polyphase decomposition. Filtering and down sampling are performed in the same stage. Filters are designed and mapped on FPGA. Hardware and computational complexities are reduced and throughput is enhanced.

Extraction of Ocean Wave Spectra From Simulated Noisy Bistatic High-Frequency Radar Data

An algorithm is developed for the inversion of bistatic high-frequency (HF) radar sea echo to give the nondirectional wave spectrum. The bistatic HF radar second-order cross section of patch scattering, consisting of a combination of four Fredholm-type integral equations, contains a nonlinear product of ocean wave directional spectrum factors. The energy inside the first-order cross section is used to normalize this integrand. The unknown ocean wave spectrum is represented by a truncated Fourier series. The integral equation is then converted to a matrix equation and a singular value decomposition (SVD) method is invoked to pseudoinvert the kernel matrix. The new algorithm is verified with simulated radar Doppler spectrum for varying water depths, wind velocities, and radar operating frequencies. To make the simulation more realistic, zero-mean Gaussian noise from external sources is also taken into account

HARDWARE IMPLEMENTATION OF FRACTIONAL-ORDER SYSTEMS AS INFINITE IMPULSE RESPONSE FILTERS

In this paper we approximate fractional-order systems as IIR filters using field programmable gate arrays (FPGAs). The resulting implementations are low cost and high speed, with guaranteed stability. Our method implements the IIR approximation as a parallel combination of first-order sections, and quantizes each filter coefficient in fixed-point according to its own independent contribution to the frequency response. This makes it possible to explore the tradeoffs between system quality and hardware cost easily, with a short design time.

New voltage and current-mode APS using current controlled conveyor

A first-order all-pass section (APS) is introduced employing a single second-generation current conveyor and three passive components. The translinear conveyor version of the circuit employing only two passive components is also proposed. A fully tunable version of the circuit employing two current controlled conveyors (CCCIIs) and a single capacitor is finally derived. All the three versions of APS can be operated both in voltage as well as current mode without changing the circuit configuration. As an application, a quadrature oscillator providing two quadrature currents and two phase-shifted voltage outputs simultaneously, is realized using the proposed APS. RSPICE simulation results for the translinear-C APS, and the translinear-C quadrature oscillator are included to verify the theory.

Audio Effects Based on Biorthogonal Time-Varying Frequency Warping

We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping. These effects alter the frequency content of a signal via spectral mapping. They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters. In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform. However, most musical signals require a time-varying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing. The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response. Thus, time-varying warping results in a space-varying, inhomogeneous, propagation structure. We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow time-varying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.

A recursive method for solving unconstrained tangential interpolation problems

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recursive procedure admits a physical interpretation in terms of discretized transmission lines. In this framework the generating system is constructed as a cascade of first-order sections. Singular steps occur only when the input data is contradictory, i.e., only when the interpolation problem does not have a solution. Various pivoting schemes can be used to improve numerical accuracy or to impose additional constraints on the interpolants. The algorithm also provides coprime factorizations for all rational interpolants and can be used to solve polynomial interpolation problems such as the general Hermite matrix interpolation problem. A recursive method is proposed to compute a column-reduced generating system that can be used to solve the minimal tangential interpolation problem.

Formation of antihydrogen in the ground state and n=2 level.

The cross sections of antihydrogen formation in the ground state and {ital n}=2 level by the impact of antiprotons on the ground state of positronium have been calculated under the framework of the eikonal approximation for incident energy of 30--1000 keV. The excited-state capture cross sections are quite appreciable and are even larger than the ground-state cross sections for impact energies {le}75 keV. The total eikonal cross sections ({sigma}={sigma}{sub 1{ital s}}+{sigma}{sub 2{ital s}}+{sigma}{sub 2{ital p}}) are always higher than the corresponding first-order Born approximation cross section throughout the present energy span.

Fast algorithms for generalized displacement structures and lossless systems

We derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure that includes, as special cases, a variety of previously studied classes such as Toeplitz-like and Hankel-like matrices. The derivation is based on combining a simple Gaussian elimination procedure with displacement structure, and leads to a transmission-like interpretation in terms of two cascades of first-order sections. We further derive state-space realizations for each section and for the entire cascades, and show that these realizations satisfy a generalized embedding result and a generalized notion of J-losslessness. The cascades turn out to have intrinsic blocking properties, which can be shown to be equivalent to interpolation constrains.

Inelastic atomic scattering by high-energy photons and charged particles.

The first-order cross section for Compton scattering is expressed in terms of the cross section for scattering by fast charged particles in the plane-wave Born approximation as a function of the momentum, [bold Q], transferred by the projectile to the atomic electron(s). As an example of this relationship, the high-energy photon limit for the ratio of double to single ionization by Compton scattering, [ital R][sub [ital C]]([ital Q]), is expressed in terms of the ratio, [ital R][sub [ital Z]]([ital Q]), for scattering by charged particles at large [ital Q]. Results for [ital R][sub [ital C]]([ital Q]) are presented.