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Mathematics and Digital Signal Processing
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Mathematics and Digital Signal Processing

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Optics and Lasers".

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 29324

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Pavel Lyakhov

E-Mail Website
Guest Editor
Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, 355009 Stavropol, Russia
Interests: high performance computing; residue number system arithmetic; digital signal processing; digital image processing; machine learning; artificial intelligence; medical imaging; custom hardware development
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing, sonar, radar, and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others.

This Special Issue is aimed at wide coverage of the problems of digital signal processing, from mathematical modeling to the implementation of problem-oriented systems. The basis of digital signal processing is digital filtering. Wavelet analysis implements multiscale signal processing and is used to solve applied problems of de-noising and compression. Processing of visual information, including image and video processing and pattern recognition, is actively used in robotic systems and industrial processes control today. Improving digital signal processing circuits and developing new signal processing systems can improve the technical characteristics of many digital devices. The development of new methods of artificial intelligence, including artificial neural networks and brain–computer interfaces, opens up new prospects for the creation of smart technology.

The latest technological developments will be shared through this Special Issue. We invite researchers and investigators to contribute their original research or review articles to this special issue.

Prof. Dr. Pavel Lyakhov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mathematical models of digital signal processing
  • Digital filtering
  • Wavelet analysis
  • Image and video processing
  • Pattern recognition
  • Circuits for digital signal processing
  • Signal processing systems
  • Artificial neural networks
  • Biomedical signal processing
  • Brain–computer interfaces

Published Papers (10 papers)

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Research

14 pages, 3814 KiB  
Article
Wood Defect Detection Based on Depth Extreme Learning Machine
by Yutu Yang, Xiaolin Zhou, Ying Liu, Zhongkang Hu and Fenglong Ding
Appl. Sci. 2020, 10(21), 7488; https://doi.org/10.3390/app10217488 - 24 Oct 2020
Cited by 33 | Viewed by 4155
Abstract
The deep learning feature extraction method and extreme learning machine (ELM) classification method are combined to establish a depth extreme learning machine model for wood image defect detection. The convolution neural network (CNN) algorithm alone tends to provide inaccurate defect locations, incomplete defect [...] Read more.
The deep learning feature extraction method and extreme learning machine (ELM) classification method are combined to establish a depth extreme learning machine model for wood image defect detection. The convolution neural network (CNN) algorithm alone tends to provide inaccurate defect locations, incomplete defect contour and boundary information, and inaccurate recognition of defect types. The nonsubsampled shearlet transform (NSST) is used here to preprocess the wood images, which reduces the complexity and computation of the image processing. CNN is then applied to manage the deep algorithm design of the wood images. The simple linear iterative clustering algorithm is used to improve the initial model; the obtained image features are used as ELM classification inputs. ELM has faster training speed and stronger generalization ability than other similar neural networks, but the random selection of input weights and thresholds degrades the classification accuracy. A genetic algorithm is used here to optimize the initial parameters of the ELM to stabilize the network classification performance. The depth extreme learning machine can extract high-level abstract information from the data, does not require iterative adjustment of the network weights, has high calculation efficiency, and allows CNN to effectively extract the wood defect contour. The distributed input data feature is automatically expressed in layer form by deep learning pre-training. The wood defect recognition accuracy reached 96.72% in a test time of only 187 ms. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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15 pages, 4227 KiB  
Article
Development of Classification Algorithms for the Detection of Postures Using Non-Marker-Based Motion Capture Systems
by Tatiana Klishkovskaia, Andrey Aksenov, Aleksandr Sinitca, Anna Zamansky, Oleg A. Markelov and Dmitry Kaplun
Appl. Sci. 2020, 10(11), 4028; https://doi.org/10.3390/app10114028 - 10 Jun 2020
Cited by 9 | Viewed by 2951
Abstract
The rapid development of algorithms for skeletal postural detection with relatively inexpensive contactless systems and cameras opens up the possibility of monitoring and assessing the health and wellbeing of humans. However, the evaluation and confirmation of posture classifications are still needed. The purpose [...] Read more.
The rapid development of algorithms for skeletal postural detection with relatively inexpensive contactless systems and cameras opens up the possibility of monitoring and assessing the health and wellbeing of humans. However, the evaluation and confirmation of posture classifications are still needed. The purpose of this study was therefore to develop a simple algorithm for the automatic classification of human posture detection. The most affordable solution for this project was through using a Kinect V2, enabling the identification of 25 joints, so as to record movements and postures for data analysis. A total of 10 subjects volunteered for this study. Three algorithms were developed for the classification of different postures in Matlab. These were based on a total error of vector lengths, a total error of angles, multiplication of these two parameters and the simultaneous analysis of the first and second parameters. A base of 13 exercises was then created to test the recognition of postures by the algorithm and analyze subject performance. The best results for posture classification were shown by the second algorithm, with an accuracy of 94.9%. The average degree of correctness of the exercises among the 10 participants was 94.2% (SD1.8%). It was shown that the proposed algorithms provide the same accuracy as that obtained from machine learning-based algorithms and algorithms with neural networks, but have less computational complexity and do not need resources for training. The algorithms developed and evaluated in this study have demonstrated a reasonable level of accuracy, and could potentially form the basis for developing a low-cost system for the remote monitoring of humans. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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29 pages, 10434 KiB  
Article
Multiresolution Speech Enhancement Based on Proposed Circular Nested Microphone Array in Combination with Sub-Band Affine Projection Algorithm
by Ali Dehghan Firoozabadi, Pablo Irarrazaval, Pablo Adasme, David Zabala-Blanco, Hugo Durney, Miguel Sanhueza, Pablo Palacios-Játiva and Cesar Azurdia-Meza
Appl. Sci. 2020, 10(11), 3955; https://doi.org/10.3390/app10113955 - 06 Jun 2020
Cited by 5 | Viewed by 2353
Abstract
Speech enhancement is one of the most important fields in audio and speech signal processing. The speech enhancement methods are divided into the single and multi-channel algorithms. The multi-channel methods increase the speech enhancement performance by providing more information with the use of [...] Read more.
Speech enhancement is one of the most important fields in audio and speech signal processing. The speech enhancement methods are divided into the single and multi-channel algorithms. The multi-channel methods increase the speech enhancement performance by providing more information with the use of more microphones. In addition, spatial aliasing is one of the destructive factors in speech enhancement strategies. In this article, we first propose a uniform circular nested microphone array (CNMA) for data recording. The microphone array increases the accuracy of the speech processing methods by increasing the information. Moreover, the proposed nested structure eliminates the spatial aliasing between microphone signals. The circular shape in the proposed nested microphone array implements the speech enhancement algorithm with the same probability for the speakers in all directions. In addition, the speech signal information is different in frequency bands, where the sub-band processing is proposed by the use of the analysis filter bank. The frequency resolution is increased in low frequency components by implementing the proposed filter bank. Then, the affine projection algorithm (APA) is implemented as an adaptive filter on sub-bands that were obtained by the proposed nested microphone array and analysis filter bank. This algorithm adaptively enhances the noisy speech signal. Next, the synthesis filters are implemented for reconstructing the enhanced speech signal. The proposed circular nested microphone array in combination with the sub-band affine projection algorithm (CNMA-SBAPA) is compared with the least mean square (LMS), recursive least square (RLS), traditional APA, distributed multichannel Wiener filter (DB-MWF), and multichannel nonnegative matrix factorization-minimum variance distortionless response (MNMF-MVDR) in terms of the segmental signal-to-noise ratio (SegSNR), perceptual evaluation of speech quality (PESQ), mean opinion score (MOS), short-time objective intelligibility (STOI), and speed of convergence on real and simulated data for white and colored noises. In all scenarios, the proposed method has high accuracy at different levels and noise types by the lower distortion in comparison with other works and, furthermore, the speed of convergence is higher than the compared researches. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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13 pages, 2758 KiB  
Article
Three-Dimensional (3D) Model-Based Lower Limb Stump Automatic Orientation
by Dmitry Kaplun, Mikhail Golovin, Alisa Sufelfa, Oskar Sachenkov, Konstantin Shcherbina, Vladimir Yankovskiy, Eugeniy Skrebenkov, Oleg A. Markelov and Mikhail I. Bogachev
Appl. Sci. 2020, 10(9), 3253; https://doi.org/10.3390/app10093253 - 07 May 2020
Cited by 3 | Viewed by 3335
Abstract
Modern prosthetics largely relies upon visual data processing and implementation technologies such as 3D scanning, mathematical modeling, computer-aided design (CAD) tools, and 3D-printing during all stages from design to fabrication. Despite the intensive advancement of these technologies, once the prosthetic socket model is [...] Read more.
Modern prosthetics largely relies upon visual data processing and implementation technologies such as 3D scanning, mathematical modeling, computer-aided design (CAD) tools, and 3D-printing during all stages from design to fabrication. Despite the intensive advancement of these technologies, once the prosthetic socket model is obtained by 3D scanning, its appropriate orientation and positioning remain largely the responsibility of an expert requiring substantial manual effort. In this paper, an automated orientation algorithm based on the adjustment of the 3D-model virtual anatomical axis of the tibia along with the vertical axis of the rectangular coordinates in three-dimensional space is proposed. The suggested algorithm is implemented, tested for performance and experimentally validated by explicit comparisons against an expert assessment. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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14 pages, 3007 KiB  
Article
Classification of Hydroacoustic Signals Based on Harmonic Wavelets and a Deep Learning Artificial Intelligence System
by Dmitry Kaplun, Alexander Voznesensky, Sergei Romanov, Valery Andreev and Denis Butusov
Appl. Sci. 2020, 10(9), 3097; https://doi.org/10.3390/app10093097 - 29 Apr 2020
Cited by 7 | Viewed by 2545
Abstract
This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients [...] Read more.
This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients of the harmonic wavelet transform (fast computation), short-time Fourier transform (spectrogram) and Fourier transform using a kNN-algorithm. Classification quality metrics (precision, recall and accuracy) are given for different signal-to-noise ratios. ROC curves were also obtained. The use of the deep neural network for classification of whales’ sounds is considered. The effectiveness of using harmonic wavelets for the classification of complex non-stationary signals is proved. A technique to reduce the feature space dimension using a ‘modulo N reduction’ method is proposed. A classification of 26 individual whales from the Whale FM Project dataset is presented. It is shown that the deep-learning-based approach provides the best result for the Whale FM Project dataset both for whale types and individuals. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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28 pages, 4471 KiB  
Article
Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging
by Nikolay Chervyakov, Pavel Lyakhov and Nikolay Nagornov
Appl. Sci. 2020, 10(4), 1223; https://doi.org/10.3390/app10041223 - 11 Feb 2020
Cited by 28 | Viewed by 4104
Abstract
Denoising and compression of 2D and 3D images are important problems in modern medical imaging systems. Discrete wavelet transform (DWT) is used to solve them in practice. We analyze the quantization noise effect in coefficients of DWT filters for 3D medical imaging in [...] Read more.
Denoising and compression of 2D and 3D images are important problems in modern medical imaging systems. Discrete wavelet transform (DWT) is used to solve them in practice. We analyze the quantization noise effect in coefficients of DWT filters for 3D medical imaging in this paper. The method for wavelet filters coefficients quantizing is proposed, which allows minimizing resources in hardware implementation by simplifying rounding operations. We develop the method for estimating the maximum error of 3D grayscale and color images DWT with various bits per color (BPC). The dependence of the peak signal-to-noise ratio (PSNR) of the images processing result on wavelet used, the effective bit-width of filters coefficients and BPC is revealed. We derive formulas for determining the minimum bit-width of wavelet filters coefficients that provide a high (PSNR ≥ 40 dB for images with 8 BPC, for example) and maximum (PSNR = ∞ dB) quality of 3D medical imaging by DWT depending on wavelet used. The experiments of 3D tomographic images processing confirmed the accuracy of theoretical analysis. All data are presented in the fixed-point format in the proposed method of 3D medical images DWT. It is making possible efficient, from the point of view of hardware and time resources, the implementation for image denoising and compression on modern devices such as field-programmable gate arrays and application-specific integrated circuits. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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8 pages, 1049 KiB  
Article
Maximum Correntropy Criterion Based l1-Iterative Wiener Filter for Sparse Channel Estimation Robust to Impulsive Noise
by Junseok Lim
Appl. Sci. 2020, 10(3), 743; https://doi.org/10.3390/app10030743 - 21 Jan 2020
Cited by 1 | Viewed by 1800
Abstract
In this paper, we propose a new sparse channel estimator robust to impulsive noise environments. For this kind of estimator, the convex regularized recursive maximum correntropy (CR-RMC) algorithm has been proposed. However, this method requires information about the true sparse channel to find [...] Read more.
In this paper, we propose a new sparse channel estimator robust to impulsive noise environments. For this kind of estimator, the convex regularized recursive maximum correntropy (CR-RMC) algorithm has been proposed. However, this method requires information about the true sparse channel to find the regularization coefficient for the convex regularization penalty term. In addition, the CR-RMC has a numerical instability in the finite-precision cases that is linked to the inversion of the auto-covariance matrix. We propose a new method for sparse channel estimation robust to impulsive noise environments using an iterative Wiener filter. The proposed algorithm does not need information about the true sparse channel to obtain the regularization coefficient for the convex regularization penalty term. It is also numerically more robust, because it does not require the inverse of the auto-covariance matrix. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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16 pages, 1151 KiB  
Article
A Division Algorithm in a Redundant Residue Number System Using Fractions
by Nikolay Chervyakov, Pavel Lyakhov, Mikhail Babenko, Irina Lavrinenko, Maxim Deryabin, Anton Lavrinenko, Anton Nazarov, Maria Valueva, Alexander Voznesensky and Dmitry Kaplun
Appl. Sci. 2020, 10(2), 695; https://doi.org/10.3390/app10020695 - 19 Jan 2020
Cited by 2 | Viewed by 3150
Abstract
The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, [...] Read more.
The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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16 pages, 2567 KiB  
Article
Quantification of the Feedback Regulation by Digital Signal Analysis Methods: Application to Blood Pressure Control Efficacy
by Nikita S. Pyko, Svetlana A. Pyko, Oleg A. Markelov, Oleg V. Mamontov and Mikhail I. Bogachev
Appl. Sci. 2020, 10(1), 209; https://doi.org/10.3390/app10010209 - 26 Dec 2019
Cited by 3 | Viewed by 2141
Abstract
Six different metrics of mutual coupling of simultaneously registered signals representing blood pressure and pulse interval dynamics have been considered. Stress test responses represented by the reaction of the recorded signals to the external input by tilting the body into the upright position [...] Read more.
Six different metrics of mutual coupling of simultaneously registered signals representing blood pressure and pulse interval dynamics have been considered. Stress test responses represented by the reaction of the recorded signals to the external input by tilting the body into the upright position have been studied. Additionally, to the conventional metrics like the joint signal coherence Coher and the sensitivity of the pulse intervals response to the blood pressure changes baroreflex sensitivity (BRS), also alternative indicators like the synchronization coefficient Sync and the time delay stability estimate TDS representing the temporal fractions of the analyzed signal records exhibiting rather synchronous dynamics have been determined. In contrast to BRS, that characterizes the intensity of the pulse intervals response to the blood pressure changes during observed feedback responses, both Sync and TDS likely indicate how often such responses are being activated in the first place. The results indicate that in most cases BRS is typically reciprocal to both Sync and TDS suggesting that low intensity of the feedback responses characterized by low BRS is rather compensated by their more frequent activation indicated by higher Sync and TDS. The proposed additional indicators could be complementary for the differential diagnostics of blood pressure regulation efficacy and also lead to a deeper insight into the involved concomitant factors this way also aiming at the improvement of the mathematical models representing the underlying feedback control mechanisms. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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13 pages, 1274 KiB  
Article
Improving Calculation Accuracy of Digital Filters Based on Finite Field Algebra
by Dmitry Kaplun, Sergey Aryashev, Alexander Veligosha, Elena Doynikova, Pavel Lyakhov and Denis Butusov
Appl. Sci. 2020, 10(1), 45; https://doi.org/10.3390/app10010045 - 19 Dec 2019
Cited by 3 | Viewed by 1826
Abstract
The applications of digital filters based on finite field algebra codes require their conjugation with positional computing structures. Here arises the task of algorithms and structures developed for converting the positional notation codes to finite field algebra codes. The paper proposes a method [...] Read more.
The applications of digital filters based on finite field algebra codes require their conjugation with positional computing structures. Here arises the task of algorithms and structures developed for converting the positional notation codes to finite field algebra codes. The paper proposes a method for codes conversion that possesses several advantages over existing methods. The possibilities and benefits of optimization of the computational channel structure for digital filter functioning based on the codes of finite field algebra are shown. The modified structure of computational channel is introduced. It differs from the traditional structure by the fact that there is no explicit code converter in it. The main principle is that the “reference” values of input samples, which are free from the error of the analog-digital converter, are used as input samples. The proposed approach allows achieving a higher quality of signal processing in advanced digital filters. Full article
(This article belongs to the Special Issue Mathematics and Digital Signal Processing)
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