125 results about "Bessel function" patented technology

The invention discloses a method for extracting a Rayleigh surface wave frequency dispersion curve. The method comprises the following steps: a, performing Fourier transform on noise cross-correlation signals recorded by a seismometer pair which are spaced by R to obtain a frequency spectrum W(f); b, performing Gauss narrow-band filtering on the obtained frequency spectrum to obtain WG(f); c, extracting a real part curve of the WG(f), finding out null points of the real part curve, and recording fn as the frequency of the nth null point; d, finding out a root of a first-class zero Bessel function as Zn; e, solving a Rayleigh surface wave phase velocity value V(f) being equal to 2pifnR/Zn at a single frequency point according to the relation between a real part curve of a cross-correlation spectrum and the first-class zero Bessel function; f, connecting and drawing the solved phase velocities of single frequency points into a smooth curve as a frequency dispersion curve of Rayleigh surface waves. By using the relation between the Bessel function and the cross-correlation spectrum, the calculation efficiency of the frequency dispersion curve is effectively improved.

In an array speaker system that performs multi-channel reproduction using an array speaker constituted by arraying a plurality of speaker units in a matrix manner, a left channel signal, a right channel signal, and a center channel signal, all of which instruct reproduction of sound at a front side of a listener, are subjected to weighting using weight coefficients based on a Bessel function so as to drive the speaker units, thus realizing spherical sound emission characteristics. In addition, a surround left channel signal and a surround right channel signal, both of which instruct reproduction of sound at a rear side of the listener, are subjected to beam processing, whereby sound is reflected on a sound reflection position such as a wall surface or a ceiling and is then emitted in the form of a sound beam reaching the rear side of the listener.

The invention provides an unmanned aerial vehicle (UAV) trajectory smoothing method based on Bessel curve transition, comprising the following steps: constructing a Bessel transition function according to known linear route segments, and quickly establishing flight trajectory geometrical characteristics satisfying curvature continuity; with the length of the linear route segments and the allowed maximum trajectory smoothing error as constraints, establishing and solving an optimization problem of the smoothing transition length of each Bessel curve; determining maximum speed, acceleration and jerk constraints, and determining the maximum flight speed of transition segments based on the nature of the Bessel function; performing S-shaped motion planning for all linear segments, and determining the acceleration and deceleration time of each linear segment; iteratively searching and planning the flight speed of each segment to ensure the kinematic compatibility; and performing real-time interpolation to complete flight path generation. The flight performance of UAV can be improved greatly under the premise of guaranteeing the calculation efficiency.

A harmonic generation/beam shaping system to generate a shaped beam having a harmonic relationship with a beam generated by a laser, including a first harmonic generation element and a second harmonic generation element arranged sequentially along an axial beam path extending between an input from the laser and an output of the harmonic generation/beam shaping system and at least two beam shaping elements located along the axial beam path. At least one of the least two beam shaping elements is located between the second harmonic generation element and the laser to transform the beam energy profile into a preferred profile to distribute the beam energy across a larger cross sectional area of at least one harmonic generation element or to reduce peaks in the energy distribution profile of the beam, or both, wherein the preferred profile may be a flat-top profile or a Bessel function profile.

The invention discloses an array sparse method for a broadband non-frequency-variable multi-beam imaging sonar. With the Bessel function, fitting of influences on array guiding vectors by different frequency points in the broadband signal bandwidth is performed and a broadband signal multi-beam forming model under the far-field situation is established; on the premise that the formed multiple beams approximate a reference beam, a minimum number of effective array elements are searched and multiple sets of weighting coefficients are calculated; a highly nonlinear sparse array optimization problem is transformed into a sparse signal reconstruction problem in the compressed sensing theory, a reconstruction weighting coefficient is calculated iteratively by an underdetermined system localizedsolution algorithm, and a sparse array structure is determined; a convex optimization theory is introduced so as to form a plurality of low-side-lobe beams and a multi-beam array sparse side-lobe suppression model for array element excitation is established. According to the invention, the main lobes of a plurality of formed beams are not extended with changes of signal operating frequencies; andpeak side-lobe levels of multiple beams formed by the sparse array are reduced effectively.

A radial slot antenna (1; 60) comprising a radial waveguide, which includes an upper plate (5), having a centroid (O) and an edge region (14) and provided with a plurality of radiating apertures (4), formed as slots in the upper plate (5), which develop according to an ideal annular pattern (16) around the centroid (O). The radiating apertures (4) are arranged in such a way as to form at least one first radiating region (31a) and one second radiating region (31b), which are distinct and radially separated by a dwell region (33a) without radiating apertures and wherein, in the first and second radiating regions (31a, 31b), radially adjacent radiating apertures (4) are separated from one another by a respective mutual radial distance, the dwell region (33a) having a radial width (δ) greater than the mutual radial distances of the radiating apertures (4) in the first and second radiating regions (31a, 31b). The slot antenna further comprises a signal feeder (10) operable for supplying am electromagnetic field (Ψ₀, Ψ₁) so as to assume, in the first and second radiating regions, opposite phases, in such a way that the electromagnetic field emitted by the slot antenna can be expressed via Bessel functions.

The invention provides a Bessel function based sparse concentric ring array design method. The method includes: taking a ring radius of a sparse concentric ring array as an optimized parameter, and generating a plurality of weed individuals randomly to form an initial group; as for every weed individual, determining a minimum number of array elements on a ring according to the ring radius so as to determine peak sidelobe level of the sparse concentric ring array as a weed individual adaptation value; generating a seed for every weed individual; combining filial individuals formed by optimized variable ring radiuses with parent individuals together to form new groups, sequencing all the individuals in the group according to an increasing sequence of the adaption values, only keeping a specific number of individuals as an initial group for next evolution and weeding out the rest individuals; repeating the process until stopping criterion for iteration is satisfied, and outputting an optimal individual in the ultimate group.

The present invention includes a device and method to create a light beam having substantially uniform far-field intensity. Light from a laser source is directed to at least one multimode optical fiber configured produce an intensity profile approximated by a Bessel function.

A piezoelectric blower includes a valve, a housing, a vibrating plate, and a piezoelectric element. The vibrating plate forms, together with the housing, a column-shaped blower chamber such that the blower chamber is interposed therebetween in a thickness direction of the vibrating plate. The vibrating plate and the housing are formed such that the blower chamber has a radius (a). The piezoelectric element causes the vibrating plate to undergo concentric bending vibration at a resonance frequency (f). The radius (a) of the blower chamber and the resonance frequency (f) of the vibrating plate satisfy a relationship of 0.8×(k₀c)/(2π)≦af≦1.2×(k₀c)/(2π), where an acoustic velocity of gas that passes through the blower chamber is (c) and a value that satisfies a relationship of a Bessel function of a first kind of J₀(k₀)=0 is k₀.

Embodiments of the present invention provide a method for non-contact detection techniques of mechanical vibrations utilizing a radio frequency system incorporating multiple carrier wavelengths. The new detection method measures multiple harmonic pairs at a carrier frequency and improves the detection accuracy and reliability by first inspecting the Bessel function coefficient of each harmonic and then determining the harmonic amplitude. The original mechanical vibration can then be reconstructed. Embodiments can be used to realize sensing of complex non-sinusoidal vibrations using a wavelength division sensing technique and allow non-contact detection through walls, smoke, fog or other low visibility environments with the advantage of longer range detection and easy integration at a low cost.

To provide a numerical simulation apparatus capable of executing a numerical simulation with high speed and precision by reducing computational complexity. A numerical simulation apparatus (100) that executes a numerical simulation using a wave function which is a solution of a time dependent Schrödinger equation includes: a real time evolution calculation unit (106) that calculates a second wave function while evolving the second wave function from an initial time in increments of a predetermined time period, the second wave function being obtained by applying a central difference approximation in a real-space finite-difference method to a first wave function expressed using a propagator, and being expressed using a Bessel function; and a calculation result storage unit (108) that stores a calculation result of the second wave function obtained at each time by the time evolution calculation unit (106) while evolving the second wave function in increments of the predetermined time period.

The invention discloses a method for designing array antennae distributed in a circular aperture field based on Bessel function. The method comprises the following steps of: distributing antenna arrays on a circular aperture; distributing aperture fields on a concentric circle array which consists of two or more concentric circular rings; arranging at least three antenna units which are uniformly distributed in central symmetry on each concentric circular ring; regulating distribution of the aperture fields by using a parameter weighting method based on the Bessel function, and thus obtaining continuously-distributed aperture fields in which different types of wave beams are formed; and computing the radius and excitation of each concentric circular ring in the concentric circle array which corresponds to different types of wave beams by using a discrete method. The invention has the advantages that complicated and unordered multidimensional optimization process is eliminated, a determined and quick implementation method for array antenna layout and excitation parameters is provided, the method can be widely applied to analysis and design of the antenna arrays for phased array radars and navigation satellites, and quick forming of the wave beams in different occasions is realized.

The disclosure relates to a method and device for determining frequency shift and Doppler spread in a high-speed mobile scenario; the method comprises: acquiring effective paths according to channel impulse response, acquiring effective path related value of each effective path, and acquiring frequency shift estimation of each effective path according to the phase of the corresponding effective path related value; calculating combined weight according the powers of the effective paths, weighting and combining the frequency shift estimations of the effective paths through the combined weight so as to obtain weighted average frequency shift estimation; acquiring root-mean-square frequency shift spread as Doppler spread estimation according to the frequency shift estimations of the effective paths, the weighted average frequency shift estimation and the combined weight. The problem can be solved that a conventional method is unavailable in the high-speed mobile scenario when multi-path line-of-sight components are great and bear different frequency shifts; the frequency shifts can be estimated effectively; the problem can also be solved that a uniform scattering model is inconsistent and Bessel function is unsuitable in conventional Doppler estimation methods; Doppler spread in the high-speed mobile scenario can be acquired.

The invention discloses a method for designing a wind turbine airfoil by using a Bessel function curve. According to the method, the third-order Bessel function is adopted and can represent a section of curve through four control points only, and in addition, the starting point and the end point are fixed, so that only two control points are required to be changed for a section of the curve; each of an upper wing surface and a lower wing surface of the airfoil is represented by a section of curve, the starting points and the end points of the upper wing surface and the lower wing surface respectively coincide, and then the staring points and the end points are in smooth connection. According to the invention, the airfoil profile can be controlled more conveniently and effectively by using several points in space, so that optimization design time of the airfoil is shortened, and airfoil design efficiency is improved; the designed airfoil has an extremely high lift coefficient, so that chord length of a blade is reduced, and the material required by the blade is reduced; a higher lift-drag ratio is realized, so that the wind-power utilization coefficient is increased; the method can be popularized to design of wind turbine airfoils of different thicknesses, plane airfoils, turbine blade profiles and other complex curves and has a high social value and a good economic benefit.

The invention discloses a volume modeling method for coal bed underground combustion space areas. The volume modeling method includes: deducing temperature field control equation under the action of seepage by analyzing affection mechanisms from the seepage to the temperature fields on the basis of high temperature of the coal bed underground space areas and relative constant temperature of normal underground temperature fields according to the thermal conduction basic theory,; introducing Bessel function to deduce peripheral temperature field distribution equation of combustion passages, introducing finite element values to solve, inverting the distribution of the temperature fields under the action of seepage through finite element value software by the aid of field temperature detection data, and determining high-temperature affection boundary of the combustion passages; acquiring the coal bed temperature distribution matched with the field detection best by adjusting section size of the combustion space areas, inverting the shape and the size of the coal bed underground combustion space areas, and computing approximate volume of the combustion space areas. The volume modeling method for the coal bed underground combustion space areas is capable of determining the shape and the size of the coal bed underground combustion passages more accurately, and thermal source models of the combustion space areas of the combustion passages, which are provided by the volume modeling method, have a certain practical value when the volume modeling method is compared with other computing methods.

The invention discloses a pulse ultrasonic sound field detection device and method. The pulse ultrasonic sound field detection method comprises steps of: adjusting the distance between a photoelectric detector and a third convex lens in order that the diffracted light in each order focuses on the photoelectric detector; adjusting a light-shielding plate to shield the zero-order light and negative first-order diffracted light and to enable the positive first-order diffracted light to enter the photoelectric detector, recording the maximum value of the optical pulse amplitude as the positive first-order diffracted light intensity, wherein the ratio of the positive first-order diffracted light intensity to the total light intensity I satisfies the first specie of first-order first Bessel function; turning down the time scale of an oscilloscope, wherein the diffracted optical pulse signal includes an intensity modulation signal with a modulation frequency the same as the ultrasonic frequency; calculating the phase information according to the waveform of the modulation signal; obtaining the sound pressure and phase distribution of a ultrasonic sound field in the moving direction of a displacement platform; rotating a ultrasonic probe by a certain angle by using a stepping motor to obtain the sound pressure and phase distribution of the ultrasonic sound field in different rotation directions; and combining different angle detection data so as to obtain the sound pressure and phase distribution of the ultrasonic sound field in the plane.

The invention provides a Bessel integral adaptive segmentation method and system in rapid calculation of an integrated circuit. The method comprises the following steps: determining the order of a Bessel function used in a Holographic Green function; calculating a zero point of the Bessel function by adopting an iterative method according to the order of the Bessel function; determining the range or the number of the zero points; adaptively segmenting the mth sub-interval, calculating the accumulation of the Bessel integral after the segmentation of the mth sub-interval, and accumulating the accumulation result to the Bessel integral of the whole integral sub-interval; and if the conditions are met, calculating a union vector Green function of a field generated by the source point of the current integrated circuit at the field point. The system comprises an order determination module, a zero point determination module, an integral subinterval setting module, a subinterval segmentation module, a subinterval judgment module and a field calculation module. According to the method, unnecessary redundancy calculation in the Bessel integral adaptive segmentation method is reduced, and the Bessel integral of the whole interval is ensured to be accurate.