scholarly journals Development of a Digital Model of a Beta Function Based on Mellin’s Integral Transforms

2021 ◽  
Vol 2096 (1) ◽  
pp. 012108
Author(s):  
A M Makarov ◽  
A S Ermakov ◽  
E A Pisarenko ◽  
V A Ryndiuk
Keyword(s):  
Signal Processing ◽  
High Speed ◽  
Beta Function ◽  
Integral Transforms ◽  
Digital Model ◽  
Computer Algorithms ◽  
Unknown Phase ◽  
Phase Sequence ◽  
Logarithmic Functions ◽  
Special Case

Abstract The implementation of a digital model of the beta function for use in computer algorithms is a time-consuming task. This is due to the complexity of the high-precision representation of its integrand functions, which require a large number of intermediate operations, which entails a large load on the computational power. Purpose: Development of the basic theoretical provisions of the integral Mellin transform in relation to the theory of signal processing against the background of noise and research of their discrete representation. Results: It is shown in the paper that the beta function can be considered as a special case of Mellin’s integral transforms. Based on this statement, a mathematical model of the beta function was developed. Using the properties of parametrically periodic oscillations belonging to the class of trigonometric-logarithmic functions, it was possible to create a digital model for representing the beta function. Practical relevance: Based on the established digital model can be realized a high-speed algorithm for calculating the beta function with a given accuracy. Such algorithms can serve as a basis for creating signal processing programs in order to detect wideband phase-shift keyed signals against a background of noise with an unknown phase sequence. An example of using such algorithms is the search for Wi-Fi bugs.

scholarly journals Three-Axis Inductive Displacement Sensor Using Phase-Sensitive Digital Signal Processing for Industrial Magnetic Bearing Applications

Actuators ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 115
Author(s):  
Teemu Sillanpää ◽  
Alexander Smirnov ◽  
Pekko Jaatinen ◽  
Jouni Vuojolainen ◽  
Niko Nevaranta ◽  
...  
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
Eddy Current ◽  
High Speed ◽  
Digital Signal ◽  
Magnetic Bearing ◽  
Air Gap ◽  
Sensor Design ◽  
Quadrature Demodulation ◽  
Displacement Sensors

Non-contact rotor position sensors are an essential part of control systems in magnetically suspended high-speed drives. In typical active magnetic bearing (AMB) levitated high-speed machine applications, the displacement of the rotor in the mechanical air gap is measured with commercially available eddy current-based displacement sensors. The aim of this paper is to propose a robust and compact three-dimensional position sensor that can measure the rotor displacement of an AMB system in both the radial and axial directions. The paper presents a sensor design utilizing only a single unified sensor stator and a single shared rotor mounted target piece surface to achieve the measurement of all three measurement axes. The sensor uses an inductive measuring principle to sense the air gap between the sensor stator and rotor piece, which makes it robust to surface variations of the sensing target. Combined with the sensor design, a state of the art fully digital signal processing chain utilizing synchronous in-phase and quadrature demodulation is presented. The feasibility of the proposed sensor design is verified in a closed-loop control application utilizing a 350-kW, 15,000-r/min high-speed industrial induction machine with magnetic bearing suspension. The inductive sensor provides an alternative solution to commercial eddy current displacement sensors. It meets the application requirements and has a robust construction utilizing conventional electrical steel lamination stacks and copper winding.

scholarly journals A general stochastic model for bivariate episodes driven by a gamma sequence

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Charles K. Amponsah ◽  
Tomasz J. Kozubowski ◽  
Anna K. Panorska
Keyword(s):  
Stochastic Model ◽  
Joint Distribution ◽  
Pareto Distribution ◽  
Integral Transforms ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
General Stochastic Model ◽  
Heavy Tailed ◽  
Discrete Pareto Distribution ◽  
Special Case

AbstractWe propose a new stochastic model describing the joint distribution of (X,N), where N is a counting variable while X is the sum of N independent gamma random variables. We present the main properties of this general model, which include marginal and conditional distributions, integral transforms, moments and parameter estimation. We also discuss in more detail a special case where N has a heavy tailed discrete Pareto distribution. An example from finance illustrates the modeling potential of this new mixed bivariate distribution.

Design of Virtex-7 FPGA-Based High-Speed Signal Processor Carrier Board

2015 ◽  
Vol 719-720 ◽  
pp. 534-537
Author(s):  
Wen Hua Ye ◽  
Huan Li
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
High Speed ◽  
Processing System ◽  
Digital Signal ◽  
Signal Processing System ◽  
High Speed Adc ◽  
High Speed Data ◽  
Processor Speed ◽  
Signal Processor

With the development of digital signal processing technology, the demand on the signal processor speed has become increasingly high. This paper describes the hardware design of carrier board in high-speed signal processing module, which using Xilinx's newest Virtex-7 FPGA family XC7VX485T chip, and applying high-speed signal processing interface FMC to transport and communicate high-speed data between carrier board and daughter card with high-speed ADC and DAC. This design provides a hardware implementation and algorithm verification platform for high-speed digital signal processing system.

scholarly journals A New Approach to Assess the Quality of Small High-Speed Centrifugal Fans Using Noise Measurement

1999 ◽  
Vol 5 (2) ◽  
pp. 147-153 ◽  
Author(s):  
Dingjun Cui ◽  
Ian A. Craighead
Keyword(s):  
Signal Processing ◽  
Quality Assessment ◽  
Condition Monitoring ◽  
High Speed ◽  
Noise Levels ◽  
New Approach ◽  
Commercial Market ◽  
Centrifugal Fans ◽  
Special Approach

The requirements for a special approach for the quality assessment of small high-speed centrifugal fans are outlined and a new parameter designating the noise levels from the product in comprehensive form will be discussed and described as a criterion for such quality assessment.By applying techniques of signal processing and condition monitoring, the sources of the vibration and noise in different sections of the product can be identified, then the noise from each source from different components can be determined. Using this criterion, more aspects of the quality of the products can be assessed and suggestions to improve the quality of the products can be made. Finally, the assessment of a number ofvacuum cleaner motor/fan units available in the commercial market will be presented and compared with conventional specifications. It will be shown that the new parameter provides a more useful indication of appliance quality.

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