scholarly journals ANALYSIS OF FAST ALGORITHM OF MATRIX-VECTOR MULTIPLICATION FOR THE BANK OF DIGITAL FILTERS

T-Comm ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 4-10
Author(s):  
Vitaly B. Kreyndelin ◽  
◽  
Elena D. Grigorieva ◽  
Keyword(s):  
Computational Complexity ◽  
Digital Filters ◽  
Matrix Multiplication ◽  
Digital Signal ◽  
Rounding Errors ◽  
Complexity Of Algorithms ◽  
Matrix Vector Multiplication ◽  
Computing Complexity ◽  
Traditional Algorithm ◽  
Digital Filter Banks

Algorithms of implementation of vector-matrix multiplication are presented, which are intended for application in banks (sets) of digital filters. These algorithms provide significant savings in computational costs over traditional algorithms. At the same time, reduction of computational complexity of algorithms is achieved without any performance loss of banks (sets) of digital filters. As the basis for the construction of algorithms proposed in the article, the previously known Winograd method of multiplication of real matrices and vectors and two versions of the method of type 3M for multiplication of complex matrices and vectors are used. Methods of combining these known methods of multiplying matrices and vectors for building digital filter banks (sets) are considered. The analysis of computing complexity of such ways which showed a possibility of reduction of computing complexity in comparison with a traditional algorithm of realization of bank (set) of digital filters approximately in 2.66 times – at realization on the processor without hardware multiplier is carried out; and by 1.33 times – at realization on the processor with the hardware multiplier. These indicators are markedly higher than those of known algorithms. Analysis of sensitivity of algorithms proposed in this article to rounding errors arising by digital signal processing was carried out. Based on this analysis, an algorithm is selected that has a computational complexity smaller than that of a traditional algorithm, but its sensitivity to rounding errors is the same as that of a traditional algorithm. Recommendations are given on its practical application in the development of a bank (set) of digital filters.

scholarly journals Eliminating unwanted signals in sound by using digital signal processing system

2020 ◽  
Vol 18 (2) ◽  
pp. 829
Author(s):  
Amer T Saeed ◽  
Zaid Raad Saber ◽  
Ahmed M. Sana ◽  
Musa A. Hameed
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
Digital Filters ◽  
Processing System ◽  
Digital Signal ◽  
Noise Signal ◽  
Time Range ◽  
Signal Processing System ◽  
Digital Signal Processing System ◽  
Sound Files

<p><a name="_Hlk536186602"></a><span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Unwanted signals or noise signals in sound files are considered one of the major challenges and issues for a thousand users. It is impossible to reduce or remove these noise signals without identifying their types and ranges. Therefore, to address one of the big problems in the digital or analogue communication, which is noise signals or unwanted signals, an adaptive selection method and noise signal removal algorithm are proposed in this research. The proposed algorithm is done through specifying the types of undesirable signals, frequency, and time range, then utilizing digital signal processing system which includes design several types of digital filters based on the types and numbers of unwanted signals. Four digital filters are used in this research to remove noise signals from the sound file by implementing the proposed algorithm using Matlab Code. Results show that our proposed algorithm was done successfully and the whole noise signals were removed without any negative consequence in the output sound signal. </span><span style="font-family: 'Times New Roman', serif; font-size: 9pt;">Unwanted signals or noise signals in sound files are considered one of the major challenges and issues for a thousand users. It is impossible to reduce or remove these noise signals without identifying their types and ranges. Therefore, to address one of the big problems in the digital or analogue communication, which is noise signals or unwanted signals, an adaptive selection method and noise signal removal algorithm are proposed in this research. The proposed algorithm is done through specifying the types of undesirable signals, frequency, and time range, then utilizing digital signal processing system which includes design several types of digital filters based on the types and numbers of unwanted signals. Four digital filters are used in this research to remove noise signals from the sound file by implementing the proposed algorithm using Matlab Code. Results show that our proposed algorithm was done successfully and the whole noise signals were removed without any negative consequence in the output sound signal.</span></p>

scholarly journals Using Rounding Errors in Modern Computer Technologies

2021 ◽  
pp. 43-52
Author(s):  
Valerii Zadiraka ◽  
Inna Shvidchenko
Keyword(s):  
Fourier Transform ◽  
Approximate Solution ◽  
Discrete Fourier Transform ◽  
Information Transfer ◽  
Applied Mathematics ◽  
Digital Signal ◽  
Rounding Error ◽  
Rounding Errors ◽  
Modern Computer ◽  
Computer Technologies

Introduction. When solving problems of transcomputational complexity, the problem of evaluating the rounding error is relevant, since it can be dominant in evaluating the accuracy of solving the problem. The ways to reduce it are important, as are the reserves for optimizing the algorithms for solving the problem in terms of accuracy. In this case, you need to take into account the rounding-off rules and calculation modes. The article shows how the estimates of the rounding error can be used in modern computer technologies for solving problems of computational, applied mathematics, as well as information security. The purpose of the article is to draw the attention of the specialists in computational and applied mathematics to the need to take into account the rounding error when analyzing the quality of the approximate solution of problems. This is important for mathematical modeling problems, problems using Bigdata, digital signal and image processing, cybersecurity, and many others. The article demonstrates specific estimates of the rounding error for solving a number of problems: estimating the mathematical expectation, calculating the discrete Fourier transform, using multi-digit arithmetic and using the estimates of the rounding error in algorithms for solving computer steganography problems. The results. The estimates of the rounding error of the algorithms for solving the above-mentioned classes of problems are given for different rounding-off rules and for different calculation modes. For the problem of constructing computer steganography, the use of the estimates of the rounding error in computer technologies for solving problems of hidden information transfer is shown. Conclusions. Taking into account the rounding error is an important factor in assessing the accuracy of the approximate solution of problems of the complexity above average. Keywords: rounding error, computer technology, discrete Fourier transform, multi-digit arithmetic, computer steganography.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems

2017 ◽  
Vol 22 (2) ◽  
pp. 460-472 ◽  
Author(s):  
Weiwei Li ◽  
Wen Chen ◽  
Zhuojia Fu
Keyword(s):  
Computational Complexity ◽  
Large Scale ◽  
Three Dimensional ◽  
Iteration Step ◽  
Singular Boundary ◽  
Matrix Vector Multiplication ◽  
Boundary Method ◽  
Potential Problems ◽  
Speed Up ◽  
Singular Boundary Method

AbstractThis study makes the first attempt to accelerate the singular boundary method (SBM) by the precorrected-FFT (PFFT) for large-scale three-dimensional potential problems. The SBM with the GMRES solver requires computational complexity, where N is the number of the unknowns. To speed up the SBM, the PFFT is employed to accelerate the SBM matrix-vector multiplication at each iteration step of the GMRES. Consequently, the computational complexity can be reduced to . Several numerical examples are presented to validate the developed PFFT accelerated SBM (PFFT-SBM) scheme, and the results are compared with those of the SBM without the PFFT and the analytical solutions. It is clearly found that the present PFFT-SBM is very efficient and suitable for 3D large-scale potential problems.

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.

EDUCATIONAL PLATFORM FOR REAL-TIME DIGITAL SIGNAL PROCESSING: PRACTICAL APPLICATIONS OF DIGITAL FILTERS

2017 ◽  
Vol 36 (1) ◽  
Author(s):  
Wesley Becari ◽  
Rodrigo B. dos Santos ◽  
André B. Carlos ◽  
Rafael A. Biliatto ◽  
Henrique E. M. Peres
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
Real Time ◽  
Digital Filters ◽  
Digital Signal ◽  
Practical Applications
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