Digital Signal Processing Problems Research Articles

Optimal by the Order of Accuracy Cubature Formula for the Approximate Calculation of Triple Integrals from Fast Oscillating Functions in General View

Introduction. The rapid development of digital technologies encourages scientists to create new or improve existing mathematical models of technical processes. It is time to develop mathematical models with different types of data. In the tasks of digital signal and image processing, the approximate calculation of integrals from rapidly oscillating functions using new information operators makes it possible to build cubature formulas using different types of information: the values of functions on planes, lines and points can be used as data. The purpose is to present and investigate the optimal cubature formula for the approximate calculation of the triple integral from rapidly oscillating functions in the general form on the class of differential functions. Information about functions are traces on systems of mutually perpendicular planes. Results. The study of the problems of digital signal and image processing continued using the example of numerical integration of triple integrals from rapidly oscillating functions in the general form. The values of functions on systems of mutually perpendicular planes are using for constructed cubature formula. The main attention in the research focuses on obtaining the estimations of errors. Proposed cubature formula for the approximate calculation of the triple integral from rapidly oscillating functions in general view is optimal in order of accuracy on the class of differential functions. The conducted numerical experiment confirmed the theoretical results. Conclusions. The obtained results make it possible to build new and improve existing mathematical models of processes with different types of input information. New information operators are a powerful tool in the development of such models. Cubature formulas for the approximate calculation of integrals from rapidly oscillating functions of many variables have been created. Іn the construction of the formulas traces of the function on planes, lines, and points are used. Formulas in their construction use function traces on planes, lines, and points. In this work, a cubature formula for the approximate calculation of the triple integral from a rapidly oscillating function in the general form, which is optimal in order of accuracy, is constructed and investigated on the class of differentiable functions. A feature of the proposed formula is the use of values of functions on systems of mutually perpendicular planes as data. Keywords: integrals of rapidly oscillating functions of many variables, cubature formulas, new information operators, digital signal and image processing.

Inaccuracies due to the frequency warping in simulation of electrical systems using combined state–space nodal analysis

The simulation of electromagnetic transients may suffer from inaccuracies due to a phenomenon known as frequency warping (FW). This paper presents an analysis of the effects of FW on the accuracy of digital simulations, demonstrating that the use of the trapezoidal integration rule (TR), commonly employed in many electromagnetic transients simulators, is the root cause of such inaccuracies. Although FW is considered a major problem in digital signal processing, it is often overlooked when simulating electrical transients. The analysis is carried out in a fourth-order RLC circuit, from which the analytic solution is derived. The circuit is solved using the combined state–space nodal method, considering the TR or recursive convolutions as solution methods for the state–space representation. It was observed that the FW caused a change in the natural oscillation frequency of the system, causing a pulsating behavior of absolute error. The accumulation of errors over time can result in deteriorated solutions when either the time steps are not sufficiently small or the simulation runs for a long enough duration. This paper emphasizes the significance of accounting for the FW phenomenon in digital simulations that rely on integration methods, such as the TR.

Area-Efficient digital filtering based on truncated multiply-accumulate units in residue number system [formula omitted

High resource consumption of digital filtering devices is one of the main practical problems of digital signal processing. Parallel data processing is one of the most effective approaches to improve the quantitative characteristics of such devices. This paper proposes a method for filtering signals using Truncated Multiply-and-Accumulate units (TMAC) in the residue number system (RNS) using moduli of a special type 2n-1,2n,2n+1. These moduli reduced hardware costs and power consumption compared to state-of-the-art approaches for a 32-bit RNS filter by up to 23% and up to 22.3%, respectively, with a delay increase of 131%. The proposed approach allowed to reduce the device area by up to 14% with comparable energy expended for a 48-bit RNS filter, but the device delay increased by 81%. The results obtained open up the possibility of creating area-efficient and power-efficient devices.

Learning based method for near field acoustic range estimation in spherical harmonics domain using intensity vectors

Near-field acoustic range estimation is considered one of the least explored research problems in digital signal processing under noise and reverberant conditions. This letter develops a new learning-based range estimation technique utilizing the spherical harmonics intensity (SH-INT) coefficients. The conventional range estimation in the spherical harmonics (SH) domain relies on the pressure coefficients. However, at high frequencies, these coefficients of different order and range overlap and hinder the accuracy of range estimation. On the contrary, the SH-INT coefficients are well distinguished at high frequencies for various orders and ranges, making these features favorable for accurate range estimation using learning algorithms. Since the SH-INT coefficients in the radial direction are independent of the source signal and vary with range, a convolutional neural network (CNN) model has been adopted to map the SH-INT coefficients with the range classes. The performance of the proposed spherical harmonic intensity (SH-INT) features in the context of near-field range estimation is validated by conducting exhaustive experiments on simulated and real data. Further, the error in near-field source range estimates is characterized using root mean square error (RMSE) criteria. The results are impactful and encourage the use of this method for practical near-field source range estimation applications.

Algorithm for Calculating Primary Spectral Density Estimates Using FFT and Analysis of its Accuracy

Introduction. Fast algorithms for solving problems of spectral and correlation analysis of random processes began to appear mainly after 1965, when the algorithm of fast Fourier transform (FFT) entered computational practice. With its appearance, a number of computational algorithms for the accelerated solution of some problems of digital signal processing were developed, speed-efficient algorithms for calculating such estimates of probabilistic characteristics of control objects as estimates of convolutions, correlation functions, spectral densities of stationary and some types of non-stationary random processes were built. The purpose of the article is to study a speed-efficient algorithm for calculating the primary estimate of the spectral density of stationary ergodic random processes with zero mean. Most often, the direct Fourier transform method using the FFT algorithm, is used to calculate it. The article continues the research and substantiation of this method in the direction of obtaining better estimates of rounding errors. Results. The research and substantiation of the method in the direction of obtaining more qualitative estimates of rounding errors, taking into account the errors of the input information specification, has been continued. The main characteristics of the given algorithm for calculating the primary estimate of the spectral density are accuracy and computational complexity. The main attention is paid to obtaining error estimates accompanying the process of calculating the primary estimate of the spectral density. The estimates of the rounding error and ineradicable error of the given algorithm for calculating the primary estimate of the spectral density, which appear during the implementation of the algorithm for the classical rounding rule for calculation in floating-point mode with τ digits in the mantissa of the number, taking into account the input error, are obtained. Conclusions. The obtained results make it possible to diagnose the quality of the solution to the problem of calculating the primary estimate of the spectral density of stationary ergodic random processes with a zero mean value by the described method and to choose the parameters of the algorithm that will ensure the required accuracy of the approximate solution of the problem. Keywords: primary estimation of spectral density, fast Fourier transform, discrete Fourier transform, rounding error, input error.

VLSI Architecture with a Configurable Pipeline

The analysis carried out in the article shows the possibility of creating a problem-oriented VLSI, fabricated according to the technological standards of 28 nm or less, for at least one family of digital signal processing problems using similar computing nodes in structure. The use of distributed arithmetic allows one to apply a technique based on performing only those multiplication steps for which non-zero digits are set in the corresponding positions of the filter coefficients. Therefore, the performance of 200 nodes executing 2 steps at 1 GHz is equivalent to approximately 80 GMAC/s/mm2 for 16-bit coefficients. The VLSI architecture view opens up the possibility to study the effectiveness of implementing other families of tasks and refine the architectural parameters for their implementation. The proposed functionality of VLSI computing nodes allows them to be used in various fields of technology, which potentially increases the need for the release of such VLSI.

Number systems in modular rings and their applications to "error-free" computations

The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.

Blind signal deconvolution based on pulsed neuron model

In this paper, we consider the vector-matrix model of a pulsed neuron, focused on solving problems of digital signal processing. We extend the application domain of the model to the blind signal deconvolution problem. To achieve this goal we propose an unsupervised learning algorithm, which maximizes the absolute value of the normalized kurtosis of the output signal of the deconvolution filter using vector-matrix model of a pulsed neuron. To show the validity of the proposed learning algorithm, some examples of deconvolution of speech signals distorted by reverberation are presented.

Перспективные методы цифровой обработки многомерных сигналов на основе применения нерегулярных сеток

The article considers sparse representation of signals based on using irregular meshes, which is one of prospective lines in digital processing of multidimensional signals. Application of irregular meshes has been seen for several decades as a promising field of investigations opening the possibility of using high efficiency of representing a signal carrier in combination with well-developed approximation methods used in solving boundary-value problems. However, lack of tools suitable for solving typical digital signal processing problems with the use of irregular meshes (e.g., for computing orthogonal discrete transforms) had resulted in that any noticeable and practically significant results are lacking in this area. Nevertheless, the recent years have seen a growth of interest in using irregular meshes. The article presents the results of investigations in this field that were carried out at the MPEI Chair for Computers, Systems and Networks. Matters concerned with generation of irregular meshes adapted to the specific features of multidimensional signals are addressed. Algorithms intended for carrying out interpolation, for making a shift from a regular carrier (a uniform regular mesh) to an irregular one, and for computing discrete transformations for a signal with an irregular carrier are presented. Solutions for arranging intellectual signal processing, such as pattern recognition and motion detection, are suggested.

A new robust adaptive algorithm based adaptive filtering for noise cancellation

Signal de-noising has been sparked and given a great attention by signal processing community since its applications are found in a diverse range of digital signal processing and computer vision problems. To improve signal quality, phase, frequency and power are the important features that should be preserved during the de-noising process. Adaptive filters have been widely used for this purpose due to their ability to cancel out noise signal from the corrupted one precisely. This paper presents a robust adaptive estimator for solving the problem of signal noise cancellation, based on a new adaptive algorithm derived from a new constrained optimization. Simulation results evaluated using MATLAB show that the proposed algorithm is appropriate for several forms of signals contaminated by diverse levels of noise power. The performance of the proposed algorithm is illustrated to be preferable in terms of the power signal to noise ratio, mean square error and time of speed convergence of filter parameters. It is compared to other conventional approaches such as least mean square and normalized least mean square algorithms with various values of white noise power, variance. It exhibits lower steady-state error and faster convergent time than the other implementations. Finally, an efficient performance is achieved comparable with recursive least square and affine projection algorithms.

Independent component analysis based on quantum particle swarm optimization

One of the Digital Signal Processing problems is a Blind Source Separation (BSS). There are some of methods are employed to solve this problem which are so-called Independent Component Analysis (ICA) which based on the statistical distribution of the signal. Many mechanisms are used to improve the ICA as neural networks, genetic algorithm and particle swarm optimization. In this paper, a new method is introduced to improve the performance of the ICA using Quantum Particle Swarm Optimization (QPSO). A Negentropy is used as the fitness function of the proposed algorithm to maximize the independence of the statistical distribution of mixed signals, easily separated and recover the original signals. The algorithm is implemented with many speech signals under some conditions as the frequency of 8 kHz, the i.i.d. and well-condition. The proposed method is considered the best from the previous method that depending on some measurements as SNR and SDR. The performance of this method has been tested on two metrics Signal-to-Noise Ratio (SNR) and Signal-to-Distortion Ratio (SDR).

Simultaneous estimation of number of signals and signal parameters of superimposed sinusoidal model: A robust sequential bivariate M-periodogram approach

ABSTRACTAccurate estimation of the parameters of superimposed sinusoidal signals is an important problem in digital signal processing and time series analysis. In this article, we propose a simultaneous estimation procedure for estimation of the number of signals and signal parameters. The proposed sequential method is based on a robust bivariate M-periodogram and uses the orthogonal structure of the superimposed sinusoidal model for sequential estimation. Extensive simulations and data analysis show that the proposed method has a high degree of frequency resolution capability and can provide robust and efficient estimates of the number of signals and signal parameters.

Cyclostationary correntropy: Definition and applications

Information extraction is a frequent and relevant problem in digital signal processing. In the past few years, different methods have been utilized for the parameterization of signals and the achievement of efficient descriptors. When the signals possess statistical cyclostationary properties, the Cyclic Autocorrelation Function (CAF) and the Spectral Cyclic Density (SCD) can be used to extract second-order cyclostationary information. However,second-order statistics tightly depends on the assumption of gaussianity, as the cyclostationary analysis in this case should comprise higher-order statistical information. This paper proposes a new mathematical formulation for the higher-order cyclostationary analysis based on the correntropy function. The cyclostationary analysis is revisited focusing on the information theory, while the Cyclic Correntropy Function (CCF) and Cyclic Correntropy Spectral Density (CCSD) are also presented. The CCF has different properties compared with CAF that can be very useful in non-gaussian signal processing, especially in the impulsive noise environment which implies in the expansion of the class of problems addressed by the second-order cyclostationary analysis. In particular, we prove that the CCF contains information regarding second- and higher-order cyclostationary moments, being a generalization of the CAF. The performance of the aforementioned functions in the extraction of higher-order cyclostationary characteristics is analyzed in a wireless communication system in which non-gaussian noise is present. The results demonstrate the advantages of the proposed method over the second-order cyclostationary.

Z Transform and FDTD Method in Unmagnetized Plasma

The Z transform is typically used in digital filtering and signal processing problems. The paper illustrates the use of the Z transform in implementing the FDTD method where it is useful to avoid dealing with convolution integral in the time domain by going immediately to Z domain. This work study the pulse propagation in free space that comes upon a plasma. Plasma is very interesting medium and the results illustrated that at low frequencies, it looks like a metal, and higher frequency, it become transparent just like a dielectric medium.

Атомарные функции в задачах фильтрации и цифровой обработки сигналов

Атомарные функции в задачах фильтрации и цифровой обработки сигналов

Families of atomic functions ch a, n (x) and fup n (x) in digital signal processing

A new class of weight functions constructed on the basis of family of atomic functions and cha,n(x) and fupn(x) is proposed and substantiated. The study consists of three parts. In the first part, the definition of atomic functions and their convolutions are presented. In the second part, a definition of a new family of atomic functions cha,n(x) as convolutions of ha(x) is given. In the third part, a family of weight functions is constructed by truncation of cha,n(x) to the effective support. If smoothening with classical windows is applied after the truncation combined weight functions will be received. The physical characteristics of the weight functions constructed by the direct truncation and in combination with the Hamming and Riesz windows are presented. The found functions can find wide application in problems of digital signal processing, restoration of images, radar, radiometry, radio astronomy, remote probing, and other physical domains.

Some recent work on lattice structures for digital signal processing

This paper is concerned with a review of some recent work on derivation and synthesis of lattice structures for digital signal processing (DSP). In particular, synthesis of canonical structures for both finite impulse response (FIR) and infinite impulse response (IIR) transfer functions is presented in detail. This has been an outstanding problem in DSP, and I demonstrate here how the solution came through very simple ideas and reasoning. Besides a consolidation of results published earlier in various papers, some new results containing refinements and simplifications in the synthesis procedures have also been presented.

Improving convergence for the approximation of non-periodic functions by Fourier series

Approximation of functions by Fourier series plays an important role in many applied problems of digital signal processing. An effective method is presented for the construction of highly accurate mean-square approximations by Fourier series for nonperiodic functions. This technique employs the subtraction of specially selected functions that enhance the smoothness of the periodic extension of the approximated function. The main advantage of the method is that the function-setting interval is taken as a half-period rather than a whole period. This doubles the smoothness of the periodic extension. The efficiency of the method is illustrated by test functions of one and two variables.

A new class of weight and WA systems of the Kravchenko-Kaiser functions

A new class of weight and WA-systems of the Kravchenko-Kaiser functions which showed its efficiency in various physical applications is proposed and substantiated. This publication consists of three parts. In the first the Kravchenko-Kaiser weight functions are constructed on basis of the theory of atomic functions (AFs) and the Kaiser windows for the first time. In the second part new constructions of analytic WA-systems of the Kravchenko-Kaiser functions are costructed. In the third part their applications to problems of weight averaging of the difference frequency signals are considered. The numerical experiment and the physical analysis of the results for concrete physical models confirmed their efficiency. This class of functions can find wide physical applications in problems of digital signal processing, restoration of images, radar, radiometry, radio astronomy, remote sensing, etc.

A unified SVM framework for signal estimation

This paper presents a review in the form of a unified framework for tackling estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The paper formalizes our developments in the area of DSP with SVM principles. The use of SVMs for DSP is already mature, and has gained popularity in recent years due to its advantages over other methods: SVMs are flexible non-linear methods that are intrinsically regularized and work well in low-sample-sized and high-dimensional problems. SVMs can be designed to take into account different noise sources in the formulation and to fuse heterogeneous information sources. Nevertheless, the use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of several properties of Mercerʼs kernels and functional analysis to develop a family of SVM methods for estimation in DSP. Three types of signal model equations are analyzed. First, when a specific time-signal structure is assumed to model the underlying system that generated the data, the linear signal model (so-called Primal Signal Model formulation) is first stated and analyzed. Then, non-linear versions of the signal structure can be readily developed by following two different approaches. On the one hand, the signal model equation is written in Reproducing Kernel Hilbert Spaces (RKHS) using the well-known RKHS Signal Model formulation, and Mercerʼs kernels are readily used in SVM non-linear algorithms. On the other hand, in the alternative and not so common Dual Signal Model formulation, a signal expansion is made by using an auxiliary signal model equation given by a non-linear regression of each time instant in the observed time series. These building blocks can be used to generate different novel SVM-based methods for problems of signal estimation, and we deal with several of the most important ones in DSP. We illustrate the usefulness of this methodology by defining SVM algorithms for linear and non-linear system identification, spectral analysis, non-uniform interpolation, sparse deconvolution, and array processing. The performance of the developed SVM methods is compared to standard approaches in all these settings. The experimental results illustrate the generality, simplicity, and capabilities of the proposed SVM framework for DSP.