scholarly journals Digital Algorithms for the Discrete Frequency Selection of Signals that Do Not Use Algorithmic Multiplication Operations

TEM Journal ◽  
2020 ◽  
pp. 501-506
Author(s):  
Adeliya Yu. Burova ◽  
Timur O. Usatenko
Keyword(s):  
Digital Filtering ◽  
Software Implementation ◽  
Integer Coefficients ◽  
Frequency Selection ◽  
Discrete Signals ◽  
Multi Stage ◽  
Digital Algorithms ◽  
Hardware Costs ◽  
Special Processor ◽  
Necessary And Sufficient

The issues related to the problem of minimizing hardware costs in the digital algorithms’ hardware and software implementation for the discrete signals’ frequency selection on programmable logic devices (PLD) and special processor microelectronic devices are considered. Possible ways to solve these problems are described based on the computational algorithms for non-recursive digital filtering (NDF) and difference digital filtering with integer coefficients use. A necessary and sufficient condition is given for using a computational algorithm’s hardware and software implementation of discrete signals’ difference digital filtering for their multi-stage discrete Fourier transform without performing arithmetic multiplication operations.

scholarly journals Reduced hardware costs with software and hardware implementation of digital methods multistage discrete Fourier transform on programmable logic devices

2020 ◽  
Vol 9 (27) ◽  
pp. 227-233
Author(s):  
Adeliya Yu. Burova ◽  
Anatoly V. Ryapukhin ◽  
Alexandra R. Muntyan
Keyword(s):  
Software Implementation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Digital Signals ◽  
Research Results ◽  
Digital Filtration ◽  
Multi Stage ◽  
Programmable Logic Devices ◽  
Hardware Costs ◽  
Necessary And Sufficient

Let us consider questions, which are connected to the research of terms of hardware and software implementation digital signal processing (DSP) methods. Theoretical basis of this research are methods of non-recursive difference of digital filtration with integer difference coefficients different orders of difference and methods of multistage discrete Fourier transform (DFT) based on such digital filtration. The purpose of the study is the research and formalization of necessary and sufficient condition of lowering hardware costs in hardware and software implementation of methods multistage DFT of digital signals on programmable logic devices (PLD). For reaching the research goal there are used methods of direct search and comparative analysis of results of such realization of methods of multi-stage DFT of digital multi-band signals, while filtering these signals, which are based on their non-recursive difference digital filtering with integer difference values coefficients and different orders of magnitude of difference. There are described abilities and specialties of PLD, which are built using architecture of a coarse-grained or fine-grained architecture or using combined architecture, which connects the convenience of implementing digital processing algorithms signals on the basis of tables of code conversion and reconfigurable memory modules. It is clear that a necessary and sufficient condition of lowering hardware costs in terms of hardware and software realization of methods for multi-stage DFT of digital signals on PLD is the triviality of meanings of integer difference coefficients of a non-recursive difference digital high difference orders’ filtration, which ensure this information. There is mentioned a formula, which allows making such condition. The practical significance of the research results consists of defining the necessary and sufficient condition of lowering hardware costs in terms of hardware and software implementation on PLD methods of multi-stage DFT signals based on their non-recursive digital difference filtering with integer values differential coefficients of various orders of magnitude difference. The novelty of research results lies in formalization of this condition. The reliability of the research results confirms their compliance with the results of well-known developments of DSP methods.

AUTOMATED OPERATIONAL SCHEDULING SYSTEM FOR MULTI-STAGE PRODUCTION: MATHEMATICAL MODEL AND SOFTWARE IMPLEMENTATION

2021 ◽  
Vol 3 (102) ◽  
pp. 18-37
Author(s):  
OXANA S. LOGUNOVA ◽  
MIKHAIL B. ARKULIS
Keyword(s):  
Mathematical Model ◽  
Raw Materials ◽  
Software Implementation ◽  
Scheduling System ◽  
Operation Conditions ◽  
Multi Stage ◽  
Complete Set ◽  
Wip Inventory ◽  
Production Areas ◽  
Strip Production

The purpose of the study is to improve the efficiency of production areas of multi-stage production with the possibility of rational use of equipment capacity and stocks of WIP inventory in the operation conditions of the automated operational scheduling system. Features of the considered problem regarding operative calendar planning are: necessity of processing raw materials at several stages according to the flow chart; an array of the equipment which demands division of work into three periods for each party; availability of planned and unscheduled equipment downtime; necessity to complete set of orders from several suborders; availability of incomplete production in a warehouse; restrictions in order and timing of orders. In the work, the authors construct a mathematical model with the use of multidimensional matroids with structured elements in the construction of free time scale for equipment loading. The research was carried out for a metallurgical plant at the cold strip production site...

scholarly journals A Method of Increasing Digital Filter Performance Based on Truncated Multiply-Accumulate Units

2020 ◽  
Vol 10 (24) ◽  
pp. 9052
Author(s):  
Pavel Lyakhov ◽  
Maria Valueva ◽  
Georgii Valuev ◽  
Nikolai Nagornov
Keyword(s):  
Signal Processing ◽  
Theoretical Analysis ◽  
Digital Signal Processing ◽  
Digital Filter ◽  
Digital Filters ◽  
Digital Signal ◽  
Digital Filtering ◽  
Filter Performance ◽  
Filter Architecture ◽  
Hardware Costs

This paper proposes new digital filter architecture based on a modified multiply-accumulate (MAC) unit architecture called truncated MAC (TMAC), with the aim of increasing the performance of digital filtering. This paper provides a theoretical analysis of the proposed TMAC units and their hardware simulation. Theoretical analysis demonstrated that replacing conventional MAC units with modified TMAC units, as the basis for the implementation of digital filters, can theoretically reduce the filtering time by 29.86%. Hardware simulation showed that TMAC units increased the performance of digital filters by up to 10.89% compared to digital filters using conventional MAC units, but were associated with increased hardware costs. The results of this research can be used in the theory of digital signal processing to solve practical problems such as noise reduction, amplification and suppression of the frequency spectrum, interpolation, decimation, equalization and many others.

scholarly journals An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes

2018 ◽  
Vol 12 (1) ◽  
pp. 166-177
Author(s):  
Ivan Pavkov ◽  
Nebojsa Ralevic ◽  
Ljubo Nedovic
Keyword(s):  
Efficient Algorithm ◽  
Sufficient Condition ◽  
Polynomial Factorization ◽  
Necessary And Sufficient Condition ◽  
Bivariate Polynomials ◽  
Bivariate Polynomial ◽  
Integer Coefficients ◽  
Necessary And Sufficient ◽  
The Given

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

High Performance Digital Filtering on Modified Multiply and Accumulate Unit in Residue Number System with Special Type of Moduli

2021 ◽  
Vol 27 (4) ◽  
pp. 171-179
Author(s):  
P. A. Lyakhov ◽  
◽  
A. S. Ionisyan ◽  
M. V. Valueva ◽  
A. S. Larikova ◽  
...  
Keyword(s):  
High Performance ◽  
Digital Filters ◽  
Hardware Implementation ◽  
Digital Filtering ◽  
Number System ◽  
Residue Number System ◽  
Residue Number ◽  
Simulation Results ◽  
Hardware Costs ◽  
Positional Number System

The paper proposes the implementation of digital filtering using residue number system and the modified truncated multiply and accumulate unit. The work was carried out a theoretical analysis of digital filters using residue number system arithmetic and implemented hardware simulation on FPGA. FPGA hardware simulation results show that the use of residue number system allows to increase the frequency of digital filters up to about 4 times and hardware costs reduce up to 3 times compared to using a common positional number system. The obtained results open up the possibility for efficient hardware implementation of digital filters on modern devices (FPGA, ASIC and etc.) to solve practical problems, such as noise reduction, amplification and suppression of the frequency spectrum, interpolation, decimation, equalization and many others.

Wilson frames for ℂL with general lattices

2016 ◽  
Vol 14 (06) ◽  
pp. 1650055
Author(s):  
Minghou You ◽  
Junqiao Yang ◽  
Qiaofang Lian
Keyword(s):  
Digital Signal ◽  
Tight Frame ◽  
Gabor Frame ◽  
Dual Frame ◽  
Dual Frames ◽  
Volume Formula ◽  
Discrete Signals ◽  
Gabor Dual ◽  
Necessary And Sufficient

In digital signal and image processing one can only process discrete signals of finite length, and the space [Formula: see text] is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for [Formula: see text] with general lattices of volume [Formula: see text] ([Formula: see text] even). In this paper, we extend this construction to Wilson frames for [Formula: see text] with general lattices of volume [Formula: see text], where [Formula: see text] and [Formula: see text]. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for [Formula: see text]. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for [Formula: see text], show that a Wilson frame for [Formula: see text] can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Planning and Search in Multi-Stage Risky Decision Making

2011 ◽  
Author(s):  
Jared Hotaling ◽  
Jerry Busemeyer ◽  
Richard Shiffrin
Keyword(s):  
Decision Making ◽  
Risky Decision Making ◽  
Risky Decision ◽  
Multi Stage
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