Approximate methods for solving amplitude-phase problem for discrete signals

Methods for solving amplitude and phase problems for one and two-dimensional discrete signals are proposed. Methods are based on using nonlinear singular integral equations. In the one-dimensional case amplitude and phase problems are modeled by corresponding linear and nonlinear singular integral equations. In the two-dimensional case amplitude and phase problems are modeled by corresponding linear and nonlinear bisingular integral equations. Several approaches are presented for modeling two-dimensional problems: 1) reduction of amplitude and phase problems to systems of linear and nonlinear singular integral equations; 2) using methods of the theory of functions of many complex variables, problems are reduced to linear and nonlinear bisingular integral equations. To solve the constructed nonlinear singular integral equations, methods of collocation and mechanical quadrature are used. These methods lead to systems of nonlinear algebraic equations, which are solved by the continuous method for solution of nonlinear operator equations. The choice of this method is due to the fact that it is stable against perturbations of coefficients in the right-hand side of the system of equations. In addition, the method is realizable even in cases where the Frechet and Gateaux derivatives degenerate at a finite number of steps in the iterative process. Some model examples have shown effectiveness of proposed methods and numerical algorithms.

Theoretical approaches to the synthesis of discrete signals with necessary properties

Methods for information exchange, formation and processing of data used in information and communication systems (ICS), as well as classes of broadband signals used as a physical data carrier, do not provide the necessary (for individual ICS applications) indicators of cyber and information security, noise immunity of reception signals and secrecy of IKS functioning. Most of the existing systems use signals, the construction of which is based on linear laws, which allows an attacker, based on the establishment of the parameters of the signals used in the system, to carry out deliberate interference in the operation of the ICS with minimal energy consumption. The article presents conceptual approaches to the construction of secure ICS, which determine the need to cover the entire spectrum of information transformations in the complex, and based on the synthesis of signal systems with improved ensemble, correlation, structural properties. A method is proposed for synthesizing discrete derivatives of signals based on nonlinear discrete complex cryptographic signals (CS) and orthogonal signals formed on the basis of the rows of the Hadamard matrix (initial signals),. Based on computer modeling and the performed calculations, it is shown that the derivative signals formed on the basis of cryptographic sequences and rows of the Hadamard matrix have improved properties compared to orthogonal and linear classes of signals. Approaches to the construction are stated and a general characteristic of the hardware-software complex for synthesis, analysis, study of properties, generation, processing of a number of studied signal classes is given. It is shown that the use of such signals will improve such indicators of the system functioning as information security, noise immunity of signal reception and secrecy of functioning.

Fundamental Aspects of Audio and Music Signals

This chapter introduces and explores some basic aspects of audio and music signal processing. It first looks at analogue signals, developing in good detail the concepts of frequency, phase, and amplitude, supported by some mathematics. Simple manipulation of signals is discussed and its effects on sound waveforms are shown. The key concept of discrete signals, and the discretisation process involved in sampling is introduced. The chapter concludes with the definition of digital audio.

Finite-time and spectral-finite methods of optimal filtering of discrete signals

На основе содержания теоремы ортогонального проецирования излагаются методы оптимальных, линейных рекуррентных оценок, в общем случае, не марковских, сигналов, на фоне произвольных помех. Предлагаемые алгоритмы оптимальной обработки дискретных сигналов являются альтернативными методу фильтрации Калмана, не отличающимися заметно от них по точности обработки и являющимися более универсальными и простыми при их реализации. Универсальность исследуемых методов определяется применимостью их к широкому классу моделей сигналов, не требующих марковского свойства оцениваемого сигнала и изменения структуры алгоритма оценки в зависимости от моделей помех измерения в виде случайного коррелированного процесса или белого шума. Более простые структуры алгоритмов рассматриваемых методов по отношению к фильтрации Калмана объясняются отсутствием необходимости представления модели в пространстве состояний и требования решать нелинейное уравнение Риккати для реализации алгоритма. Спектрально-финитный алгоритм оптимальной оценки сигнала осуществляет сжатие информации в спектральном аспекте на основе использования метода нахождения собственных чисел и векторов и позволяет осуществить понижение размерности векторов результатов измерений вплоть до скалярных величин без заметной потери точности оценки. В качестве исходной информации необходимо знание корреляционной функции и математического ожидания оцениваемого дискретного сигнала и дисперсии и математического ожидания дискретной помехи. Based on the content of the orthogonal projection theorem, methods of optimal, linear recurrent estimates of, in general, non-Markov signals, against the background of arbitrary interference, are presented. The proposed algorithms for optimal processing of discrete signals are alternative to the Kalman filtering method, which do not differ significantly from them in terms of processing accuracy and are more universal and simple to implement. The universality of the studied methods is determined by their applicability to a wide class of signal models that do not require the Markov property of the estimated signal and changes in the structure of the estimation algorithm depending on the measurement interference models in the form of a random correlated process or white noise. The simpler structures of the algorithms of the methods under consideration in relation to Kalman filtering are explained by the absence of the need to represent the model in the state space and the requirement to solve the nonlinear Riccati equation for the implementation of the algorithm.

Deterministic Discrete-Time Signals and Systems

Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic discrete-time signals and systems. These discrete signals, which are expressed in the form of functions, including the Kronecker delta function and the discrete rectangular pulse, are used throughout the book for deterministic discrete signal analysis. The chapter also presents the definition of the autocorrelation function and the explanation of the convolution procedure in linear-time-invariant systems for discrete-time signals in detail, due to the importance of these in the analysis and synthesis of discrete communication systems.

Efficient Memory-based Multiplier Technique for SWL DSP Systems

The DSP systems usually deal with a lot of multiplications as it is dealt with many discrete signals. The combinational circuits consume a lot of power as there are many intermediate blocks (i.e., usually full adders & and gates). The combinational circuits take more area and the delay is also more. Usually there is a tradeoff between area and delay. To make the multiplier more efficient we usually prefer memory-based multiplier. Different types of techniques are there in memory-based multipliers like the APC (anti-symmetric product coding), OMS (odd multiple storage) etc. In these techniques LUT based storage is used. The multiplied products are stored efficiently based on the technique used to store the data. To optimize the memory required we combine the APC and OMS technique for better storage and retrieval of data. In this project we show how combined technique increases the performance of multiplier. The suggested combined technique reduces the size of the LUT to one-fourth that of a standard LUT. It is demonstrated that the proposed LUT architecture for tiny input sizes can be used to execute high-precision multiplication with input operand decomposition in an efficient manner.

Optimization for the quick-code methods for the synthesis of discrete signals – physical carriers of data in information-communication systems

The paper presents the theoretical foundations of synthesis and analysis of complex nonlinear discrete cryptographic signals, the basis for the synthesis of which are random (pseudo-random) processes, including algorithms for cryptographic transformation of information, as well as methods for optimizing the synthesis of these signals using decimation and discrete programming. namely, the method of branches and boundaries. In order to improve the performance of signal generation and processing, estimates of the effectiveness of the decimation procedure are proposed and presented. It is shown that the use of the studied signal systems will improve the efficiency of modern ICS (speed of data generation and processing devices, noise immunity, information security, secrecy, protection against input (imposition) of false messages, message falsification, data integrity, etc.).

Noise-like discrete signals for asynchronous code division radio systems

This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous code division systems for radio channels. Asynchrony implies the use of sequences that are statistically uncorrelated for an arbitrary cyclically shifted copy of the signals, i.e. their cross-correlation coefficient for arbitrarily chosen starting points is close to zero. The fundamental theoretical limit for this characteristic is the well-known Welch boundary. In this paper, we compare the correlation properties of various sets (Gold codes, Kasami sequences, etc.) with this fundamental limit. The parameters of different codes are estimated, the corresponding bound is shown and compared with the real correlation characteristics of the codes. For the approximation, the Laurent series expansion and the Puiseau series were used. The asymptotic properties were also estimated. The paper also considers new ensembles of noise-like discrete signals for asynchronous systems. These codes are statistically uncorrelated, asymptotically the square of their cross-correlation for arbitrary starting points tends to the theoretical Welch bound. Moreover, the cardinality (power of the set) of new signal ensembles is much higher than that of Gold codes and Kasami sets. Consequently, the practical use of such noise-like discrete signals will increase the capacity of asynchronous code division systems for radio channels and reduce the cost of communication services. In addition, new sets of spreading signals will be useful for the implementation of the so-called. soft capacity, i.e. when, if necessary, the base station can increase the subscriber capacity with a slight decrease in the quality of service.

METHOD OF OBTAINING THE SPECTRAL CHARACTERISTICS OF THE SCANNING PROBE MICROSCOPE

The article discusses methods and algorithms for digital processing and filtering when carrying out nano-measurements using a scanning probe microscope. The paper discusses frequency methods for improving images, in particular, the use of the Fourier transforms with various filtering methods to improve the quality of the resulting image. Stable computational algorithms have been developed for transforming discrete signals based on the Fourier transform. Methods for the interpretation of the numerical results of the discrete Fourier transform in such packages as Matlab, MathCad, Matematica are presented. It is proposed to use a window transform, developed based on the Fourier transform, which makes it possible to single out the informative features of the signal and to reduce the influence of the destabilizing factors that arise when processing signals from a scanning gold microscope in real conditions.