scholarly journals Periodogram estimating the spectral power density based upon signals’ binary-sign stochastic quantization using window functions

2021 ◽  
Vol 20 (2) ◽  
pp. 341-370
Author(s):  
Vladimir Yakimov
Keyword(s):  
Spectral Analysis ◽  
Discrete Event ◽  
Frequency Resolution ◽  
Dominant Factor ◽  
Stochastic Quantization ◽  
Digital Form ◽  
Complex Signals ◽  
Multiplicative Complexity ◽  
Event Modeling ◽  
Window Functions

Spectral analysis of signals is used as one of the main methods for studying systems and objects of various physical natures. Under conditions of a priori statistical uncertainty, the signals are subject to random changes and noise. Spectral analysis of such signals involves the estimation of the power spectral density (PSD). One of the classical methods for estimating PSD is the periodogram method. The algorithms that implement this method in digital form are based on the discrete Fourier transform. Digital multiplication operations are mass operations in these algorithms. The use of window functions leads to an increase in the number of these operations. Multiplication operations are among the most time consuming operations. They are the dominant factor in determining the computational capabilities of an algorithm and determine its multiplicative complexity. The paper deals with the problem of reducing the multiplicative complexity of calculating the periodogram estimate of the PSD using window functions. The problem is solved based on the use of binary-sign stochastic quantization for converting a signal into digital form. This two-level signal quantization is carried out without systematic error. Based on the theory of discrete-event modeling, the result of a binary-sign stochastic quantization in time is considered as a chronological sequence of significant events determined by the change in its values. The use of a discrete-event model for the result of binary-sign stochastic quantization provided an analytical calculation of integration operations during the transition from the analog form of the periodogram estimation of the SPM to the mathematical procedures for calculating it in discrete form. These procedures became the basis for the development of a digital algorithm. The main computational operations of the algorithm are addition and subtraction arithmetic operations. Reducing the number of multiplication operations decreases the overall computational complexity of the PSD estimation. Numerical experiments were carried out to study the algorithm operation. They were carried out on the basis of simulation modeling of the discrete-event procedure of binary-sign stochastic quantization. The results of calculating the PSD estimates are presented using a number of the most famous window functions as an example. The results obtained indicate that the use of the developed algorithm allows calculating periodogram estimates of PSD with high accuracy and frequency resolution in the presence of additive white noise at a low signal-to-noise ratio. The practical implementation of the algorithm is carried out in the form of a functionally independent software module. This module can be used as a part of complex metrologically significant software for operational analysis of the frequency composition of complex signals.

scholarly journals Digital Spectral Analysis by means of the Method of Averag Modified Periodograms Using Binary-Sign Stochastic Quantization of Signals

2021 ◽  
Vol 12 (3) ◽  
pp. 220-221
Author(s):  
V. N. Yakimov
Keyword(s):  
Spectral Analysis ◽  
Fourier Transforms ◽  
Discrete Event ◽  
Threshold Function ◽  
Method Of Averaging ◽  
Stochastic Quantization ◽  
Event Modeling ◽  
Window Functions ◽  
Algorithmic Support ◽  
Digital Spectral Analysis

The method of averaging modified periodograms is one of the main methods for estimating the power spectral density (PSD). The aim of this work was the development of mathematical and algorithmic support, which can increase the computational efficiency of signals digital spectral analysis by this method.The solution to this problem is based on the use of binary-sign stochastic quantization for converting the analyzed signal into a digital code. A special feature of this quantization is the use of a randomizing uniformly distributed auxiliary signal as a stochastic continuous quantization threshold (threshold function). Taking into account the theory of discrete-event modeling the result of binary-sign quantization is interpreted as a chronological sequence of instantaneous events in which its values change. In accordance with this we have a set of time samples that uniquely determine the result of binary-sign quantization in discrete-time form. Discrete-event modeling made it possible to discretize the process of calculating PSD estimates. As a result, the calculation of PSD estimates was reduced to discrete processing of the cosine and sine Fourier transforms for window functions. These Fourier transforms are calculated analytically based on the applied window functions. The obtained mathematical equations for calculating the PSD estimates practically do not require multiplication operations. The main operations of these equations are addition and subtraction. As a consequence, the time spent on digital spectral analysis of signals is reduced.Numerical experiments have shown that the developed mathematical and algorithmic support allows us to calculate the PSD estimates by the method of averaging modified periodograms with a high frequency resolution and accuracy even for a sufficiently low signal-to-noise ratio. This result is especially important for spectral analysis of broadband signals.The developed software module is a problem-oriented component that can be used as part of metrologically significant software for the operational analysis of complex signals.

Digital Analysis of the Vibration Signals Amplitude Spectrum Based on Fourier Processing of the Binary-Sign Analog-Stochastic Quantization Result

2019 ◽  
Vol 20 (12) ◽  
pp. 723-731
Author(s):  
V. N. Yakimov ◽  
V. I. Batyschev ◽  
A. V. Mashkov
Keyword(s):  
Harmonic Analysis ◽  
Computational Efficiency ◽  
Amplitude Spectrum ◽  
Experimental Studies ◽  
Analytical Calculation ◽  
Frequency Resolution ◽  
Stochastic Quantization ◽  
Complex Signals ◽  
Workload Analysis ◽  
Vibration Signals

The article is devoted to the problem of developing a digital algorithm for operational harmonic analysis of complex vibration signals. The basis for solving this problem was the generalized equation of statistical measurements, which defines the measurement procedure as the sequential execution of interrelated measurement and computational transformations. During the development of the algorithm, special attention is paid to analog-to-digital conversion because it directly affects the computational efficiency of digital procedures for obtaining the final result. As such a conversion, the use of binarysign analog-stochastic quantization is justified, which allows performing two-level quantization without systematic error regardless of the statistical properties of the analyzed signals. The discrete-event model of the binary-sign analog-stochastic quantization result allowed for the analytical calculation of integration operations in the transition to estimating the amplitude spectrum in digital form. As a result, the developed algorithm of harmonic analysis does not require performing digital multiplication operations typical for classical algorithms, which are based on the calculation of the direct discrete Fourier transform. The execution of the algorithm is reduced to the implementation of the addition and subtraction arithmetic operations of the cosine-function values in the time moments determined by the result of the binary-sign analogue-stochastic quantization. The exclusion of digital multiplication operations provided an increase in the computational efficiency of amplitude spectrum estimation. Laboratory studies of the developed algorithm were carried out using simulation modeling. The simulation results showed that the algorithm allows calculating estimates of the amplitude spectrum of complex signals with high accuracy and frequency resolution in the presence of additive noise. In real conditions, the testing of the developed algorithm was carried out during bench studies of the operational status of the MAZ-206067 bus, designed for the transportation of passengers on urban and suburban routes of average workload. Analysis of the results of experimental studies confirmed the possibility of using the algorithm as part of the diagnosability provision for operational monitoring of vibration signals in a complex noise environment.

scholarly journals Spectral Analysis of Stationary Signals Based on Two Simplified Arrangements of Chirp Transform Spectrometer

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 65
Author(s):  
Quan Zhao ◽  
Ling Tong ◽  
Bo Gao
Keyword(s):  
Spectral Analysis ◽  
Frequency Conversion ◽  
Frequency Resolution ◽  
Matching Problem ◽  
System Sensitivity ◽  
Deep Space Exploration ◽  
Spectrum Measurement ◽  
Stationary Signals ◽  
Simulation And Experiment ◽  
Remote Sensing Systems

The classical two-channel push-pull chirp transform spectrometer (CTS) has been widely applied in satellite-borne remote sensing systems for earth observation and deep space exploration. In this paper, we present two simplified structures with single M(l)-C(s) CTS arrangements for the spectral analysis of stationary signals. A simplified CTS system with a single M(l)-C(s) arrangement and a time delay line was firstly developed. Another simplified structure of CTS with a M(l)-C(s) arrangement and a frequency conversion channel was also developed for spectral analysis of stationary signals. Simulation and experiment results demonstrate that the two simplified arrangements can both realize spectrum measurement for the stationary signals and obtain the same frequency resolution, amplitude accuracy and system sensitivity as that of the classical two-channel push–pull CTS system. Compared to the classical CTS structure, the two simplified arrangements require fewer devices, save power consumption and have reduced mass. The matching problem between the two channels can be avoided in the two simplified arrangements. The simplified CTS arrangements may have potential application in the spectrum measurement of stationary signals in the field of aviation and spaceflight.

Discrete-event modeling by system dynamics method

2021 ◽  
Author(s):  
A. N. Medvedev ◽  
V. N. Timokhin ◽  
Yu. A. Nelyubina
Keyword(s):  
System Dynamics ◽  
Discrete Event ◽  
Event Modeling ◽  
Dynamics Method

scholarly journals Redesigned-Scale-Free CORDIC Algorithm Based FPGA Implementation of Window Functions to Minimize Area and Latency

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Supriya Aggarwal ◽  
Kavita Khare
Keyword(s):  
Spectral Analysis ◽  
Fpga Implementation ◽  
Coordinate Space ◽  
Cordic Algorithm ◽  
Scale Free ◽  
Window Functions

One of the most important steps in spectral analysis is filtering, where window functions are generally used to design filters. In this paper, we modify the existing architecture for realizing the window functions using CORDIC processor. Firstly, we modify the conventional CORDIC algorithm to reduce its latency and area. The proposed CORDIC algorithm is completely scale-free for the range of convergence that spans the entire coordinate space. Secondly, we realize the window functions using a single CORDIC processor as against two serially connected CORDIC processors in existing technique, thus optimizing it for area and latency. The linear CORDIC processor is replaced by a shift-add network which drastically reduces the number of pipelining stages required in the existing design. The proposed design on an average requires approximately 64% less pipeline stages and saves up to 44.2% area. Currently, the processor is designed to implement Blackman windowing architecture, which with slight modifications can be extended to other widow functions as well. The details of the proposed architecture are discussed in the paper.

scholarly journals Combined approach architecture development to simulation modeling of systems with parallelism

2021 ◽  
Vol 4 (4(112)) ◽  
pp. 74-82
Author(s):  
Oksana Suprunenko
Keyword(s):  
Petri Nets ◽  
Dynamic Properties ◽  
Discrete Event ◽  
Structural Similarity ◽  
Integral Model ◽  
Combined Approach ◽  
Dynamic Simulations ◽  
Holistic Model ◽  
Event Modeling ◽  
Analytical Tools

Paradigms and graphical-analytical tools for building simulation tools and forming the architecture of a combined approach to studying the dynamic properties of systems with parallelism are described. An extension of the formal language of Petri nets is presented, which has greater modeling power than WF nets. The properties of hierarchical Petri nets are used to synthesize a holistic model. Discrete-event modeling and modeling of dynamic systems, which allow reflecting the quantitative and qualitative characteristics of the elements of the systems under study, served as the basis for the combined approach to the simulation of systems with parallelism. On their basis, graphic-analytical tools are proposed that provide the ability to describe the modeled system, adhering to the principle of structural similarity. They have dynamic simulations that make it easy to visually analyze and correct the model. Also, the proposed toolkit provides for the analysis of the dynamic properties of the model, which makes it possible to identify accumulated phenomena that can lead to unpredictability of the system’s functioning. A conceptual model for the synthesis and analysis of systems with parallelism is proposed, which provides for the construction of the components of the model based on the architecture. Their step-by-step analysis and the formation of an integral model of the software system are carried out using a network representation, according to the matrix description of which invariants are calculated. The analysis of invariants allows one to obtain the dynamic properties of the model and determine the localization of structures that lead to critical situations when they are detected. The architecture of the combined approach to the simulation of systems with parallelism is built, which provides the study of their dynamic properties to improve the reliability of the functioning of software systems

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