Digital Signal Processing

Scientific & Technical

ôDigital Signal Processingö No. 2-2014

In the issue:

- parametric energy Fourier spectrums;
- empirical mode decomposition;
- waveform envelope extraction;
- adaptive signal processing;
- algorithm of matching pursuit;
- analysis of time relation;
- analysis of signals on multicore processors.

Use of Hartley Transform to Solve the Integral Equation of Convolution Type
Egorov V.V., JSC "Russian institute for power radiobuilding"
Maslakov M.L., JSC "Russian institute for power radiobuilding",

Keywords: integral equation of convolution type, ill-posed problem, calculation of impulse response of the communication channel, correction, Fourier transform, Hartley transform.

The calculation of unknown impulse response of the communication channel is one of the most important task for adaptive signal correction. Consider a signal S(t) transmitted through the system with the impulse response h(t), where the received output signal U(t) is presented by the following formula:

The above shown equation refers to a linear integral equation of convolution type, or it is also called a Fredholm integral equation of the first kind, where there the function h(t) is unknown.
Various methods of solving this equation, concerning time or frequency domain, are practically known. One of the most effective methods for the numerical solution of integral equations of convolution type are those based on the transition to frequency domain. For this purpose it is supposed to use the discrete Fourier transform (DFT), for there are a variety of algorithms for the fast Fourier transform (FFT). This significantly reduces the computational cost. However, the Fourier transform uses complex numbers, that is why it is recommended to use Hartley transform, which makes possibility to avoid complex numbers in calculation. Unfortunately, the Hartley transform is rarely used in practice.
The authors have presented the new formulae provided for the solution of the integral equation of convolution type in the Hartley basis. The advantage of discrete Hartley transform (DHT) compared to the DFT is proved and illustrated. The results of the simulation and computational efficiency evaluation of the algorithms are presented.
The calculation of the impulse response of the communication channel is provided using DHT for adaptive signal correction. The provided numerical solution of integral equations using DHT is more effective than the DFT, since there are algorithms fast Hartley transform (FHT), which can be easily implemented and require lower computational cost, moreover, all the performed operations are real. At the same time the obtained numerical results practically are not worse than the results obtained using the Fourier transform. Therefore, the use of FHT allows to reduce the number of operations for the solution of integral equation as good as twice.


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Invariance of Current Parametric Energy Fourier Spectrums of Discrete Real Signals on Finite Intervals
Ponomareva O.V. Ph.D. (technical science), associate professor of Kalashnikov Izhevsk State Technical University,

Keywords: discrete signal, finite interval, sliding spectral measurement, basis, parametric discrete exponential functions, non-invariance, energy Fourier spectrum, tonal components.


In such fields of research as radar, speech recognition and synthesis, passive sonar, biomedicine, it is often necessary to solve the problem of detection and measurement of tonal components (problem of detecting the hidden periodicities). One of the effective methods of detecting hidden periodicities in the signals of such kind is a measurement of their sliding Fourier spectra on finite intervals. In this case, the method of discrete Fourier transform (DFT) uses basis of discrete exponential functions (DEF). While method of parametric DFT (DFT-P), proposed by the author, uses basis of parametric DEF (DEF-P). The essence of measurement of sliding Fourier spectra of signals on finite intervals is to determine the Fourier spectrum of the signal in the time window (having N samples), which shifted by one sample before spectral re-measurement. Papers on digital spectral analysis relies, by default, that the sliding energy Fourier spectrum of tone signal in the DEF basis is invariant to time shift of tone signal. Experimental researches on simulated signals, made by the author of this paper, showed that the assumption of the invariance of the sliding energy Fourier spectrum of tone signal to its time shift is generally untrue in both DEF basis and DEF-P basis.
We have studied the relationship of discrete-time Fourier transform (DTFT) and DFT-P signal defined on a finite interval with DFT signal defined on a finite interval and zero padded. For real applications it is important that the DFT of sequence defining the DTFT values at points , does not answer the question, what are values of DTFT between these points, creating so-called stockade effect. To avoid this unwanted effect in the spectral digital signal processing (DSP) (of both one-dimensional and multidimensional sequences), the operation of zero padding (OZP) has been widely used. However, despite the undoubted advantages of this operation, it has two major drawbacks. Practical use of OZP requires significant additional memory and significant useless computational operations due to the need for a large number of operations with zero samples. DFT-P (proposed by the author) allows while calculating Fourier spectra with OZP, not to increase the amount of required memory, to reduce extra computational operations and to find the DTFT signal at any frequency, varying parameter of DFT-P. This makes it possible to increase significantly (compared to OZP) distinguishing harmonics in the frequency domain. We studied the methods and algorithms of sliding spectral measurements on finite intervals. The theoretical principles of measurement of sliding energy Fourier spectra of digital signals in the basis of discrete exponential functions and parametric discrete exponential functions. We got theoretical and practical results of the evaluation of non-invariance of sliding energy Fourier spectra of tonal components on finite intervals in the DEF-P basis.
The results allow: to increase the spectral efficiency of the DSP in solving problems on the detection and identification of hidden periodicities, to further develop a methodology to determine the errors of spectral measurements of tone signals on finite intervals, taking into account the effect of the non-invariance.

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5. Petrovsky, Alexey. Hydrid signal decomposition dased on instantaneous harmonic parameters and perceptually motivated wavelet packets for scalable audio coding / Alexey Petrovsky, Elias Azarov, Alexander Petrovsky, Elsiver, Signfl Processng, Special issue "Fourier Related Transform for Non-Stationary Signals"/- Vol. 91/-Issue 6/-June 2011.- P/ 1489-1504.

6. ╬. V. Ponomareva, "Development of the Theory of Spectral Analysis of Discrete Signals on Finite Intervals in the Basis of Parametric Exponential Functions," Tsifrovaya Obrabotka Signalov, No. 2, 7-12 (2010).

7. ╬. V. Ponomareva, "Probabilistic Properties of Spectral Estimates Obtained by Parametric Discrete Fourier Transform," Intellektual'nye Sistemy v Proizvodstve, No. 2(10), 36-42 (2010).

8. V. A. Ponomarev and ╬. V. Ponomareva, "Theory and Application of the Parametric Discrete Fourier Transform," Tsifrovaya Obrabotka Signalov, No. 1, 2-6 (2011).

9. ╬. V. Ponomareva, "Fast Parametric Discrete Fourier Transform of Real Sequences," Tsifrovaya Obrabotka Signalov, No. 2, 2-5 (2012).

10. ╬. V. Ponomareva, A. V. Ponomarev, and N. V. Ponomareva, "Sliding Parametric DFT in Detecting Tonal Components," Tsifrovaya Obrabotka Signalov, No. 4, 2-7 (2012).

11. V. A. Ponomarev and ╬. V. Ponomareva, "Modification of the Discrete Fourier Transform for Solving Problems of Interpolation and Convolution of Functions," Radiotekhnika i Elektronika, 29 (8), 1561-1570 (1984).

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14. ╬. V. Ponomareva, A. V. Ponomarev, and N. V. Ponomareva, "A Fast Method for. Computing the Discrete Fourier Transform of Real Sequences," Tsifrovaya Obrabotka Signalov, No. 2,10-15 (2013).

15. V. A. Alekseev, V. A. Ponomarev, and ╬. V. Ponomareva, "Methodology for Determining Measurement Errors of Probability Characteristics of Random Processes Implemented by Measuring Processing Means" Intellektul,nye Sistemy v Proizvodstve, No.2(10), 91-99 (2010).

16. ╬. V. Ponomareva, V. A. Alekseev, and V. A. Ponomarev, "Digital Periodogram Analysis and Problems of its Practical Application," Vestn. IzhGTU, No 2, 130-133 (2013)

17. ╬. V. Ponomareva and N. V. Ponomareva, "Modification of a Filter Based on Frequency Sampling for Solving Problems of Digital Processing of Stochastic Processes with Hidden Periodicities," Intellektual'nye Sistemy v Proizvodstve, No. 2(20), 122-129 (2012).

18. ╬. V. Ponomareva, A. V. Ponomarev, and V. A. Ponomarev, "Generalization of the Goertzel Algorithm for Detecting Hidden Periodicities," Intellektual'nye Sistemy v Proizvodstve, No. 1(21), 41-46 (2013).

19. V. A. Ponomarev and ╬. V. Ponomareva, "Vibroacoustic Diagnostics of the Machine Gearboxes by Digital Methods," Stanki i Instrument, No. 9, 18-21 (1983).

20. ╬. V. Ponomareva and N. V. Ponomareva, "Improving the Accurace and Extending the Functionalite of Digital Filters Based on Frequency Sampling," Pribory Metody Izmerenii, No. 2, (5), 114-119 (2013)

21. ╬. V. Ponomareva and V. A. Ponomarev, "Measurement of current energy Fourier spectrum of complex and real discrete signals on finite intervals," Intellektual'nye Sistemy v Proizvodstve, No. 2(22), 149-157 (2013).

22. ╬. V. Ponomareva, V. A. Ponomarev and A. V. Ponomarev, Hierarchical morphlogicflly-information model diagnosis of functional objects based on digital signal processing, Sensors and Systems, 2014, No.1(176), 2-8.

23. V. A. Ponomarev, ╬. V. Ponomareva, A. V. Ponomarev and N. V. Ponomareva, "The summary of the Goertzel algorithm and the sliding parametric discrete Fourier transform," Tsifrovaya Obrabotka Signalov, No. 1, 3-11 (2014).

24. V. A. Ponomarev, ╬. V. Ponomareva and A. V. Ponomarev, "Method for Effective Measurement of a Sliding Parametric Fourier Spectrum," Avtometria. 2014, Vol 50, No.2,. 31-38.

25. V. A. Ponomarev and ╬. V. Ponomareva, "The invariance of current energy Fourier spectrums of discrete real signals on finite intervals," Technology and Design in Electronic Equipment, 2014, No.1, pp.15-22

Loss in Signal-to-Noise Ratio for Communication System with Binary Differential Shift Keying and Orthogonal Coding
Zaytsev G.V.,

Keywords: binary differential phase shift keying, orthogonal code, soft metrics, bit error probability, loss in signal-to-noise ratio.

The paper analyzes digital communication system which uses binary differential phase shift keying and orthogonal coding with Hadamard matrix. The system is intended for transmission of short messages. In the channel additive white Gaussian noise is present. The purpose of the paper is to estimate loss caused by differential modulation/demodulation.
Several algorithms for soft differential demodulation are deduced from the concept of logarithm likelihood ratio. Formula for exact calculation of log-likelihood ratio is derived but it requires calculation of Bessel function and proved to be rather complex for practical purposes. Two simple approximations are described as follows. Let , be the sequence of numbers at the demodulator input, resulting from optimal reception of transmitted bits. Then simple forms of soft differential demodulation are given by the formula
, .
Nonlinear operations in these formulae cause loss in signal-to-noise ratio. It is shown that this loss can be evaluated by the expression
where is signal-to-noise power ratio in the sequence Z. For small signal-to-noise ratio this loss may be up as high as 10 dB. For considered orthogonal codes, optimal correlation reception is possible, additional losses are absent, and presented formula is valid for decoder output.
Computer simulation of the considered communication system was performed in C++ language. The method of simulation is described and main parameters of the program are given. Bit error rate Pb vs signal-to-noise ratio is calculated and is displayed graphically for Pb>10-8 . The simulation confirmed that performance of simple demodulation method, described above, is in close agreement with performance of exact method. It is also shown that total code gain in described communication system is rather small (2 3 dB) for the range Pb>10-8 and code lengths n≤1024.
From the results of the paper it is obvious that the above mentioned heavy loss may take place for any code with large redundancy. For different reception methods, other than correlation, some additional losses may arise. Analytical estimation of these losses is difficult because probability density function of the noise after differential demodulation is not Gaussian.


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Problems and Methods of Communication Systems Spectral Efficiency Increasing: Orthogonal Transmission
Bakulin M.G, Kreindelin V.B., Shumov A.P.

Keywords: spectral efficiency, wireless communication systems, OFDM, many carriers, multicarrier modulations, inter-carrier interference.

Spectral efficiency is a key design issue for all wireless communication systems. Orthogonal frequency division multiplexing (OFDM) is a very well-known technique for efficient data transmission over many carriers overlapped in frequency. Recently, several papers have appeared which describe spectrally efficient techniques for multi-carrier systems where the condition of orthogonality is dropped. Proposed techniques suffer from high complexity or high error rates because of the inter-carrier interference. This work addresses to problems of transmitter and receiver architectures whose design is based on using high efficient OFDM technologies.
There can be several approaches to realize transmission of FTN modulated symbols. One approach is considering in the first part of the article. Efficient implementations for multicarrier modulations already exist in the form of IFFT, as used in OFDM-based systems. Hence an effort is made to retain this attractive option. However, using only the IFFT introduces complexity in a different dimension. In order to use IFFT for multicarrier modulation the Gaussian pulses are to be represented in an orthonormal set of basis functions. Each FTN symbol is represented on the basis functions spanning both time and frequency. The number of basis functions required in time can be different. The process of representing the FTN symbols in the orthogonal basis is referred to as mapping and a block realizing it is referred to as a mapper. The mapper produces outputs by processing the incoming FTN symbols. Data processing at the receiver is implemented in a reverse way. This approach allows spectral efficiency increasing.
Another approach is considering in the second part of the work. Recently many authors have proposed non-orthogonal systems or Spectrally Efficient Frequency Division Multiplexing (SEFDM) systems. OFDM symbols are sent on carrier frequencies separated by F and the symbols remain constant for time T (the symbol period) with TF = 1. This ensures no sub-channel interference. For SEFDM, TF < 1 and, while there will necessarily be sub-channel interference, the key advantage is that the available spectrum can be used more efficiently. This approach suggests design for a simple to implement transmitter and receiver/decoder for SEFDM systems. The transmitter design and the decoder design are interlinked. The key insight is to see SEFDM as a small number of interleaved OFDM systems. The design can increase spectral efficiency by 20% using similar techniques to traditional OFDM and with little compromise to the required signal to noise ratio for the system. The designs require only slightly more complexity in the receiver and transmitter.

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Empirical Mode Decomposition in Geophysical Multivariate Time Series Short-Term Forecasting
Zaporozhtsev Ivan Fedorovich, Murmansk State Technical University, Department of Higher Mathematics and Computers Software, postgraduate student,
Sereda Algirdas-Vladimir Ignatyevich, Murmansk State Technical University, Department of Higher Mathematics and Computers Software, Doctor of Engineering, Professor,

short-term forecast, spatial distribution of geophysical characteristics, clustering, sea level anomalies, Arctic.

The article is concerned with multivariate time series forecasting based on multivariate singular spectrum analysis and preprocessing with empirical mode decomposition concepts. We assume that particular time series originates from the observations of geophysical parameters with time-based variety. Geophysical characteristic values are calculated in planar uniform grid nodes on basis of regularly obtained satellite and/or surface measured data. Each node provides time series with the same start point, time step and length (time points number). These conditions are necessary to form multivariate time series. The problem is to make accurate short-term forecast of grid nodes values while input data is multivariate time series of the same characteristic and the same grid for previous time span.
Main forecast tool is K-continuation technique described by D.A. Stepanov and N.E. Golyandina. It is developed in connection with multivariate singular spectrum analysis (MSSA).
Forecast accuracy can be enhanced by applying appropriate preprocessing steps to multivariate time series already constructed. In processing raw data it is advantageous and often necessary to make abnormal values removal, smoothing, numerical differentiation, etc. It is also important to mention additive decomposition: original multivariate time series is to be replaced with a system of new multivariate time series each of which is obtained as a result of combination of additive components with the same number extracted from different original univariate series. It should be noted that linear regression models, such as MSSA, are extremely efficient for stationary time series. Therefore, most univariate time series of new multivariate series have to indicate greater stationarity than original ones. According to previous statements, authors of this article choose suggested by N.E. Huang empirical mode decomposition (EMD) to be essential preforecast step. The so-called sifting process as iteratively repeated EMD stage is intended to extract orthogonal additive components (with predetermined accuracy) except last summand being a time series residue with arbitrary properties. Sifting requires construction of upper and lower time series envelopes interpolating its local extrema. Current time series analysed is renovated at each stage.
Being originally designed for univariate time series, the EMD technique was widely accepted as promising treatment in multivariate series processing. The method is unreasonable to use for each univariate series separately because it is not supposed to insure the same number of additive components extracted. Furthermore, the main obstacle of the EMD generalization is that multivariate series being referred to as vector-function of time is not provided with extremum definition.
Some possibilities analysed in details by some authors for method adoption in multivariate case are used in the article. The obvious concept (principle 1, P1) is discarding of sifting (and the refusal of orthogonality) to replace it with some procedure finishing on predetermined number of component extracted criterion. Another idea (principle 2, P2) is formulated by J. Fleureau et al and is based on the so-called oscillation extrema definition. They are local minima of vector-function time derivative norm. The latter provides usage of the same joint points for envelopes construction in the meaning of univariate EMD. This fact is crucial to obtain the same number of additive components for all the univariate time series as a result of applying numeric method called multivariate EMD (MEMD).
Both EMD and MEMD problem that arises in connection with interpolation features is named end effect. Some experts suggest to use the first and the last envelopes joint points outside the analysed time series domain. Obviously, the concept is questionable in case of forecast task solution. Therefore in this article two variants of spline end conditions (additional principle, PA) are used: zero value of the first or the second univariate time series derivative.
According to principles mentioned, there are three preforecast EMD based methods (two for P1 and one for P2) in the article. In addition, PA branching doubles the number of methods used in the article. The series of numerical experiments is carried out with a set of sea level anomalies maps corresponding to particular area in the Barents Sea. A map is defined as spatial distribution of the characteristics reconstructed in specified grid nodes at chosen time point. Thus, maps time array is exactly the same as multivariate time series. Area is restricted by 71░N - 76.4░N and 25░E - 44.7░E. Time period to deal with contains 365 sequential time points ended with August, 12th, 2013. Data source is international project Aviso which have been distributing altimetry data worldwide since 1992. Nowadays reference portal located in France provides data, articles, news and tools to satisfy users requests concerning altimetry domain. Particular sea level anomalies can be obtained if you know the mapping between degrees and Aviso counters. In our research, we used 764 - 823 for latitude and 75 - 134 for longitude (60 by 60 nodes uniform grid). Grid nodes are divided into clusters according to its definition (set of nodes corresponding to simply connected subregion of area studied which time series have similar temporal variability) and clustering method suggested by authors of this article. Time series values vary from -15 to +15 with precision of one hundred-thousandths. Calculations are made for 4 multivariate time series. Each series is constructed as cluster time series corresponding to stable cluster of grid nodes. These clusters have 21,15,15 and 25 nodes respectively.
In conclusion, error values estimated via experiments are analysed and some proposals are formulated concerning applying models assembly based on MSSA and EMD/MEMD combination.

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Error Decreasing Method of Waveform Envelope Extraction in Digital Spatial Correlation Processing Chain
Oroshchuk I. M., professor ,
Suchkov A. N.,
Vasilenko A.M.,

Keywords: spatially-correlation signal processing, noise-immunity, cross-correlation function, time delay, digital detector, quadrature component, phasing error, pulsation, pulsation averaging, root-mean-square error, compensation factor.

The paper deals with the operation principle of spatial correlation of signal processing chain (SCSPC) in a decameter range. This processing chain consists of the antenna array (AA), multichannel direct amplifier and analog-to-digital converter (ADC), time delay unit, correlation processing chain, decision taken device.
The mapping is carried out by introducing compensation time delay in the input signals. It virtually locates the AA elements on one line orthogonally to the signal arrival direction that results to ensuring high spatial selectivity of the whole signal processing chain.
Then in the correlation processing chain the signal cross-correlation function (CCF) is being assessed from the outputs of all the couple elements of array antenna. After that the output voltage is summed up. The decision on signal detection is made in the decision taken unit, depending on the assigned probability characteristics.
Spatially-correlation signal processing chain is characterized by enhanced noise immunity and spatial resolution selectivity at low level signal. The antenna array comprises 30-40 identical direct amplifier. To make them identical is difficult. In case of partial identities of array antenna elements and amplifier tracks, or if phasing minor errors occur in signal time delay unit CCF significance can be reduced to a great value. This phasing hardware error results in significant reduction of spatially-correlation signal processing chain noise-immunity.
To eliminate such errors the evaluation of CCF based on waveform envelope is proposed. Waveform envelope computation is carried out with the Hilbert's transform by the adjustment of a quadrature component. To exclude additional phase distortions in the SCSPC direct amplifiers are used. In this kind of receivers signal carrier frequency changes within a decameter range at a fixed sampling frequency of ADC. As a result errors while adjusting the quadrature signal component occur. This is displayed in the form of pulsations in the specified envelope. The amplitude of pulsations enhances with the increase of the quadrature component errors. Pulsations also result in inaccurate evaluation of the CCF that in general reduces noise-immunity and other characteristics of SCSPC.
To reduce the impact on the above-mentioned drawbacks the error decrease method of specifying waveform envelope in the spatial correlation processing chain is offered. The method is based on smoothing pulsations due to averaging samplings massif within pulsations period. It leads to the fact that the envelope has become smoothed, but the constant deviation from the maximum values of amplitudes is observed depending on the ratio of the signal carrier frequency to the sampling frequency of ADC. To eliminate these deviations compensating coefficient at the evaluation of final values of cross-correlation function is used with the analytical method. As a result, the final inaccuracy of cross-correlation function of the specified waveform envelope is not more than 0.1%.
The application of this method allows to reduce the phasing inaccuracy emerging due to incomplete identity of array antenna channels and pulsations compensation error. This results in SCSPC use that will have the greatest noise-immunity at processing low-level signal.
The proposed method can be used in other digital radio engineering systems of direct amplifying as well as for the channels with signal phase jitter.

1. Dolgikh V.N., Oroshchuk I.M., Prishchepa M.N. Probabilistic characteristics of signal detection by a spatial correlation filter // Acoustical Physics. 2007. Ď. 53. ╣ 2. Đ. 190-196.

2. Oroshchuk I.M., Dolgikh V.N., Suchkov A.N. Spatial correlation method probabilistic characteristics of signal acquisition in decameter range // Journal of radio electronics. 2013. ╣ 12. http://jre.

3. Oroshchuk I.M., Dolgikh V.N., Suchkov A.N. The measuring device for estimating spatially - and frequency-correlation properties of signals and disturbances in decameter range // Izvestiya Volgogradskogo gosudarstvennogo tehnicheskogo universiteta. 2013. ╣ 23 (126). Đ. 95-99.

4. Oroshchuk I.M., Suchkov A.N. Spatial correlation method of signal processing in decameter range // The 16th International Conference "Digital signal processing". Section 4 "Signal processing in radio engineering system". March 26 - March 28, 2014 Moscow, Russia.

5. Oroshchuk I.M., Suchkov A.N. Error estimate of waveform envelope extraction in digital processing chains // The International Conference "The radio-electronic devices and systems for the infocommunication technologies. May 21 - May 23, 2014 Moscow, Russia.

Detecting Changes of State of the Complex Source in the Absence of Parametric Models
Chuvilina E. V.,
Gryzlova T. P., Solovyev Rybinsk State Aviation Technical University,

Keywords: diagnostics states of bearings of transmission, detecting changes, threshold algorithm, measure of the complexity of the signal's blocks.

Technical state of GTE largely determines reliability and safety of the aircrafts. Device IVU-1M is used in operating tests of aircraft engines D30/KU for transmission bearings control. It is an analog meter of vibration's amplitude [1]. If level of the amplitude exceeds value, determined by the test method, engine has to be taken out of service. A large number of engines are removed unjustifiably, that leads to economic loss. Digital processing of diagnostic signals is implemented in device VDK-44(MIC - 200), but its quality is not enough for introduction into service [2].
Development of algorithms of digital signal processing (DSP) for diagnostics states of bearings of transmission GTE is actual not only for practical issues. Its solution based on structural analysis, detecting local inhomogeneities leads to new class of algorithms DSP, the theory of which is currently being actively developed [3].
For evaluation of informativity of features it is selected the ratio of the average interclass distances to the average intra-distance [4].
Problem of detecting changes in the properties of random processes formulated by VV Mottl [5], was used for detecting changes of the source state. It is required to detect in realization of a random process G moments of abrupt change in the parameter,and estimate its moments: θ(S)={t1,...,tG}.

Detecting a change of state of the source is performed using a threshold algorithm based on the calculating of the change the measure of the complexity of the signal's blocks. Realization is represented as a sequence of overlapping blocks length b. For each block calculated measure of the complexity of the block of the signal in accordance with an algorithm coating which is commonly used for calculating the fractal dimension.
The change of the measure of complexity between adjacent blocks ΔRi=Ri-Ri-1is compared to value of measure of complexity in previous clock. It is considered that local heterogeneity is detected if

where hR - predetermined threshold.
Separately calculated the total number of inhomogenities and the number of inhomogenities associated with increasing or decreasing of measure of complexity - we call them positive and negative, respectively.

It is proposed to use as diagnostic sequences the frequency of conditional and unconditional increment signal modules within blocks [6]. The set of values of the entire signal S is partitioned into n ordered ranges, the range of modules divided into m increments ranked ranges. For each block at a fixed level signal the matrix of conditional increments is calculated, then rows of the matrix are summed, so we have unconditional frequency increments: vector drift coefficients for the block of the signal.
Investigated sample are provided by "NPO" Saturn "and the center of Intelligent Maintenance Systems, University of Cincinnati [7].
The first sample is divided into three classes: B - faulty, C - conditioning, (correctly recognized using the device IVU-1M) and N - wrongly taken (conditioning, but incorrectly identified as a bad bearing device IVU-1M).
The second sample was obtained in the tests on the reliability of the bearings. The sample is split into two classes: B - faulty, C - conditioning.
The results show that the use of algorithms for detecting local inhomogeneities in the vibrosignal provides more informative features. Informativity of features depends on the block's size, threshold, matrix's growth statistics size. It is sufficient for linear separability wrongly taken and faulty bearings. The most informative are combinations of the dissimilar features, ie results of nonparametric processing and estimating parameters of rough linear model.

In [8] proposed a segmentation signal based nonparametric approach to the problem of detecting moments of change of probability characteristics of random processes.
It has been shown that the detection of any changes in the distribution function or any other characteristics of the probability can be reduced to the detection of changes in expectation of some new random sequence generated from the original (diagnostic sequence). In this paper it is offered to use sequences of local measures of complexity as diagnostic sequences.
In the absence of parametric models, like the fractal dimension, measure of the complexity of the signal's blocks are estimated. Under the assumption that within a block can be taken a linear model of the signal, the algorithms of rough statistical estimation of its parameters are developed. Change conditional and unconditional statistics increment signal is more informative than the known solution of bearings diagnostics. It is Shown that the complex processing of diagnostic signals is effective for the analysis of signals of bearings. Algorithms can be adapted for the analysis of signals in a wide class of applications, such as medical.

1. Kuzmenko M. L., Porter A. M., Komarov B. I., Karasev V. A. Vibrodiagnostics of bearings of D30KU-family engines: scientific and technological collection edited M. L. Kuzmenko, V. F. Bezyazichny, V. N. Vernigor, A. L. Mikhailov. M.: CIAM. 2001. part. 4. Non-destructive testing of materials and structures of damage GTE. - p. 221.

2. Shepel V. T., Komarov B. I., Gryzlova T. P. Feature selection for the diagnosis of the technical state of transmission bearings GTE // Aerospace Engineering and Technology. - 2005. - ╣8(24). - Pp. 97-100.

3. Kolesnikova S. I. Problem-oriented model recognition and estimation of states of complex objects: dissertation of the doctor of technical sciences: 05.13.01/Kolesnikova S.I; [place of defense: Tomsk State University].-Tomsk, 2011. - 364 p.

4. Glyzlova T. P. Methods of evaluation of the informative digital signal processing in tasks of classification analysis. - 15-th International Conference "Digital Signal Processing and its Applications" - DSPA - 2013", Moscow, Russia. Pp.149 - 152.

5. Mottl V.V., Muchnik I. B. Hidden Markov models in the structural analysis of signals. - M.: FIZMATLIT, 1999. - 352 p.

6. Chuvilina E.V. Informative features for diagnostics of bearings by detection of local inhomogeneities // Machine learning and data analysis. 2013. V. 1, ╣ 6. Pp. 695-704.

7. J. Lee, H. Qiu, G. Yu, J. Lin, and Rexnord Technical Services 'Bearing Data Set', IMS, University of Cincinnati. NASA Ames Prognostics Data Repository URL:

8. Brodsky B.E., Darkhovsky B.S., Kaplan A.Ya., Shishkin S.L. Nonparametric segmentation of brain electrical signals. - Automatics and teleautomatics. - 1998. - ╣ 2. - Pp. 23-32.

Adaptive Refining Matching Pursuit Algorithm For Combined Dictionaries In The Analysis Of The Geoacoustic Emission Signals
Tristanov A.B, Lukovenkova O.O.,

sparse approximation; matching pursuit; geoacoustic emission; time-frequency analysis; geophysical signals.

Annotation Active investigation of geoacoustic emission (GAE) at different stages of seismic activity has been carried out at Kamchatka peninsular since 1999. GAE characteristic signal is compound of a sequence of relaxation pulses with the length of not more than 200 ms, 0.1-1 Pa amplitude, with shock excitation and the basic frequency from units to the first tens of kHz. Besides pulses, GAE signals may contain noise of different nature, acoustic noise hereafter.
In 2011 a method of sparse approximation was suggested for the analysis of GAE signal inner structure at the Laboratory of Acoustic Research in the Institute of Cosmophysical Research and Radio Wave Propagation (IKIR) FEB RAS. The task of sparse approximation was to construct a signal model containing the least number of elements.
In general case, minimization of L0-norm is a computationally intensive task which is not solved within the polynomial time. Algorithms of pursuit decrease the computational complexity of the task and allow us to find an effective solution for ||RN|| minimization, but not an optimal one. In the course the experiments, the authors showed that the algorithm of Matching Pursuit, suggested by Mallat S and Zhang S., is the most appropriate from the algorithms of sparse approximation to analyze GAE signals.
In comparison to the methods of classical time-and-frequency analysis which result in redundant decomposition of signals, including all atoms of a dictionary, the sparse approximation constructs compact presentations composed of only the most significant dictionary elements, not loosing the accuracy. One more advantage of the sparse approximation approach is the possibility to make signal decomposition into nonorthogonal dictionaries, in general case, described by different mathematic functions, which gives wider possibilities to interpret signal models and to explain the physics of signal generation processes. The quality of approximation, further analysis, and interpretation depend on the choice of a dictionary D.
In the first approximation, GAE signal elements may be described by modulated functions. It was shown, that the dictionary composed of scaled, modulated and shifted Berlage functions is the most adequate in comparison to Gabor dictionary, since Berlage functions have a similar structure with GAE elementary pulses, thus, they approximate better the parts of a signal containing a pulse. To improve the quality of GAE signal approximation, we decided to apply a joint dictionary including both Berlage and Gauss functions.
In the course of a series of the experiments, parameter distributions the most frequently occurring in atom decompositions were analyzed, and the ranges of dictionary parameters were chosen so to ensure the appropriate quality of approximation. Application of a joint dictionary reduced the approximation error by about 5-10%.
The most laborious part of the Matching Pursuit algorithm is the calculation of scalar products of dictionary atoms with a signal on every iteration. One of the ways to improve the quality of approximation in the conditions of limited calculation resources, not requiring dictionary growth, is to add a refinement in the parameter space of the algorithm. The essence of the Matching Pursuit adaptive algorithm with a refinement is to find a new, more significant element of decomposition at every algorithm iteration in the vicinity of the selected atom. The detected atom and all its shifts are added into the dictionary, adopting it to the specific features of the signal.
Application of a refinement allows us to decrease the size of computational resources.
Modification of the classical Matching Pursuit applying joint dictionaries and algorithms of refinement in parameter space considerably improves the quality of GAE signal approximation. It is reasonable and effective to use the suggested algorithm in the systems for GAE signal processing and analysis.

1. Mallat S. A Wavelet Tour of Signal Processing: The Sparse Way. 2009 // Acad. Burlingt. 2009.

2. Marapulets Yu.V., Tristanov A.B. Using The Sparse Approximation Method For The Problems Of Geoacoustic Emission Analysis //Digital Signal Processing. 2011, ╣2, P.13-17 (in Russian)

3. Marapulets Yu.V., Tristanov A.B. Acoustic Time Series Sparse Approximation with Berlage's time-series dictionary // Proceedings of RNTORES. Digital Signal Processing. 2012. ╣XIV, Vol. 1, P. 91-94 (in Russian)

4. Marapulets Yu.V., Shevtsov B.M. Mesoscale Acoustic Emission. - Vladivostok: Dalnauka, 2012 (in Russian)

Comparative Analysis of the Two Autoregressive Methods in Computing Weighting Coefficients for the Adaptive MTI
Bartenev V. G., Kutepov V. E. ,

Keywords: adaptive Doppler filtering, autoregressive methods, moving targets indicators.

One of the most important design stages of modern radar is development of the MTI system working in severe clutter environment. The classical solution of this problem using MTI with constant binomial weighting coefficients on the base of a small number processed impulses is not effective. It is possible to consider alternative option of the multichannel Doppler filtering with more number processed impulses using FFT algorithm and weighing for example, Hamming's function [1]. However both simple MTI and multichannel Doppler filter having fixed weighting coefficients, give insufficient efficiency of suppression of echo signals from multimode clutter, with Doppler shift.
The progress in the field of the parametric spectral analysis with high resolution and high-performance means of digital processing of signals gave the chance to approach to the realization of more perfect algorithms.
The purpose of this article is the comparative analysis of two methods of realization of adaptive MTI system on the basis of autoregressive approach. Two methods were considered: adaptive filtering with weight coefficients estimated with use of Yule-Walker method [2] and adaptive filtering with weight coefficients estimated using Burg's method [2].
The mathematical modeling which has been carried out in MATLAB system, gave the chance to compare two options of realization of adaptive system based on autoregressive approach.
Results of modeling show that adaptive MTI system using autoregressive coefficients calculated by Burg's method most preferable.


1 . Bartenev V. G., Tanygin A.A. "Radar radio control systems". M, MIREA, 2010.

2 . Sergiyenko A.B. "Digital processing of signals". St. Petersburg, 2003.

3 . Bassem R. Mahafza & Atef Z. Elsherbeni "MATLAB simulations for radar systems design". Chapman & Hall/CRC Press LLC, 2000 N.W. Corporate Blvd. Boca Raton, Florida 33431, 2004

4 . Gaspare Galati. "Advanced radar techniques and systems". Peter Peregrinus Ltd., on behalf of Institution of Electrical Engineers, London, UK, 1993.

5 . Vyacheslav Tuzlukov "Signal processing in radar systems" Talor & Francis Group LLC/CRC Press LLC, 2000 N.W. Corporate Blvd. Boca Raton, Florida 33431, 2013.

Parallel Algorithm of Matching Pursuit and its Application for the Analysis of Acoustic Emission Signals
Marapulets Yu. V.,
Kim A. A.,

Keywords: acoustic emission, time-and-frequency analysis, sparse approximation, parallel algorithm of matching pursuit.

During the last years, methods of sparse approximation have been actively used for time-and-frequency analysis of signals. They are widely applied in the studies of complicated processes of different nature, in particular, in the analysis of seismic signals [1], hydro-acoustics [2], tasks of nondestructive testing [3, 4]. The results have been obtained which show the efficiency of application of sparse approximation for the analysis of acoustic emission (AE) signals in the sound frequency range [5, 6]. Investigation of emission in this range is urgent to evaluate the hardness of landscapes, mountain slopes, glaciers, snow mantles and large technical constructions. They are very important in the study of the physics of earthquake precursors [7]. An acoustic emission signal consists of a series of relaxation oscillations (geoacoustic pulses) with shock excitation, 0.1-1 Pa amplitude, with the length of not more than 200 ms, and the frequencies from units to the first tens of kilohertz [7]. Pulse repetition frequency is determined by rock deformations and changes within a wide range, from single pulses on some second time interval during calm periods to tens and even hundreds per a second during anomalies before earthquakes [7]. One of the main tasks of AE signal processing is the automatic detection and time-and-frequency analysis of geoacoustic signals, the frequencies of which contain the data on their source size and dynamics. Sparse approximation methods with basic dictionaries constructed on Gabor [5] and Berlage [6, 8] functions were used for that purpose. To realize the sparse approximation, a matching pursuit method, suggested by Mallat S. and Zhang Z [9, 10] was applied, it was considered in detail in [5, 6].
The significant disadvantage of the matching pursuit method is its computational complexity; time for signal analysis is dozens of times longer than the signal length. To make the calculation faster, it is reasonable to apply the methods of parallel estimations in SIMD (Single Instruction stream/Multiple Data stream) architecture format, which allows one to perform one arithmetic step for much data at once [11]. One of the most popular technologies, based on SIMD conception, is CUDA hardware-software platform used to organize parallel calculations on graphic processors (GPU) [12]. The basics notion of CUDA program model is the Thread. Threads are joined into blocks and blocks, in their turn, form a grid. Grid and blocks may be one-, two- and three-dimensional. The number and the size of grid components are determined by a video card family and version. Application of such a group allows one to launch millions of threads, and it saves the programmer from the necessity to scale the computed blocks. If a GPU does not have enough resources, blocks are processed sequently. It is just necessary to determine the size of a launching grid. Let the number of threads nt, launching in every block, be 256. This number gives the optimal relation of memory and delays [13]. Consequently, the number of blocks nb, necessary to calculate the covariance matrix is determined as nb = k/256.
To realize the parallel algorithm for matching pursuit method, MS Visual Studio 2010 programming environment and CUDA 5.0 package were used. A fragment of geoacousstic emission record with the length of 400 counts was sent to the input of a standard matching pursuit method (sequential algorithm) and of the developed parallel algorithm. A laptop with Intel Core i3-2330M, 2.2 GHz central processor and NVIDIA GeForce 410M (48 kernel CUDA, 73 Gflops performance) video card was used in the experiment. In the result of tests it was established that computational time decreased by more than 10 times, when applying the parallel algorithm. The results of time-and-frequency analysis for geoacoustic emission signals were the same. We should note that, in spite of CUDA platform support, the applied video card has quite low performance. Application of a more powerful card, for example, NVIDIA GeForce GTX 760 (1152 kernel CUDA, 2258 Gflops performance) will allow us to decrease the time of calculation more significantly and to synthesize a system for time-and-frequency analysis of acoustic emission, operating in real-time regime.

1. Chakraborty A., Okaya D. Frequency-time decomposition of seismic data using wavelet-based methods// Geophysics. Vol.60, 6, P.1906-1916.

2. Josso N. F., Zhang J. J., Papandreou-Suppappola A. et al. On the Characterization of time-scale underwater acoustic signal using matching pursuit decomposition // Proceedings of the IEEE of OCEANS Conference. P. 6, Biloxi, Miss, USA, 2009.

3. Ebenezer S. P., Papandreou-Suppappola A., Suppappola S. B. Classification of acoustic emissions using modified matching pursuit // EURASIP Journal on Applied Signal Processing. N.3, P. 347-357.

4. Kovvali N., Das S., Chakraborty D., Cochran D., Papandreou-Suppappola A., Chattopadhyay A. Time-frequency based classification of structural damage //AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 23 - 26 April 2007, Honolulu, Hawaii, P. 2007-2055.

5. Marapulets Yu.V. Tristanov A.B. Application of sparse approximation method in the tasks of analysis of geoacoustic emission signals // Digital Signal Processing. 2011. ╣2. P.13-17

6. Afanaseva A. A., Lukovenkova O. O., Marapulets Yu. V., Tristanov A. B. Using the sparse approximation and clustering methods for the time series structure description of acoustic emission // Digital Signal Processing. 2013. ╣2. P.30-34.

7. Marapulets Yu. V., Shevtsov B. M. Mesoscale acoustic emission. Vladivostok: Dal'nauka, 2012, 125 p.

8. Afanaseva A. A., Lukovenkova O. O. Application of matching pursuit method to detect acoustic emission pulses in the sound range // Proceedings of 15-th International Scientific Research Conference "Digital Signal Processing and its Applications" (DSPA'2013). Moscow, Russia, Issue: XV., V. 1., 2013. P. 86-89.

9. Mallat S., Zhang Z. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing. N. 41(12), P.3397-3415.

10. Mallat S. A Wavelet Tour of Signal Processing. Academic Press; 3rd edition, 2008. 832 p.

11. Voevodin V. V., Voevodin Vl. V. Parallel computations. St.Petersburg.: BVH-Peterburg, 2002. 608 p.

12. Boreskov A. V., Kharlamov A. A. Operation basis for CUDA technologies. M.: DMK Press, 2010. 232 p.

13. Sanders J., Kandrot E. CUDA by Example: An Introduction to General-Purpose GPU Programming. Addison-Wesley Professional, 2010. 312 p.

The features of data plotting in MATLAB
Rybolovlev A. A., Associate Professor, Ph. D. The Academy of Federal Security Guard Service of the Russian Federation,
Rybolovlev D. A., research associate, Ph. D. The Academy of Federal Security Guard Service of the Russian Federation,

Keywords: processing of results, plot, diagram, MATLAB, Russian unified system for design documentation.

At the final stage of any research work, special attention is paid to the presentation of the results in one form or another. There are different ways of presenting information: verbal form (text, speech), symbolic (signs, formula), graphics (charts, diagrams, graphs), subject-shaped (layouts, models, movies, etc.).
This paper is devoted to processing the calculation results obtained in the MATLAB computing environment. The authors believe that the visibility (and hence clarity, persuasiveness) of presented plots and diagrams is determined not only by possession of elementary methods of processing the calculation results, but also by researcher ability to use MATLAB opportunities competently.
Special attention is paid to the issue of compliance with plotting rules that are defined in the recommendations of Russian unified system for design documentation (ESKD) P 50-77-88. As in other systems, such information is not found in the general case. So, it is specially noted that the construction of plots should be guided by the rules of ESKD. It should be emphasized that the research works (according to Russian national standard GOST 7.32-2001 and GOST 2.105-95), dissertations and theses (according to GOST 7.0.11-2011) are also performed in accordance with the ESKD standards.
All samples are prepared in MATLAB R2012a computing environment. Plots and diagrams are performed in a rectangular coordinate system of two dimensions (plotting in other coordinate systems is described in detail in ESKD).
The initial data used to plot the curves includes the basis functions (carrier waves) of VDSL communication system (Very high speed Digital Subscriber Line).
Mastering this method will help the researcher to enhance the visibility and readability of presented plots and diagrams. In addition it will help to get a general appreciation of the work by the experts.

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6. GOST 7.0.11-2011. System of standards on information, librarianship and publishing. Thesis and dissertation. Structure and design rules. Moscow : Standartinform, 2012. 12 p.

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10. GOST 2.307-2011. Unified system for design documentation. Dimensioning and tolerances. Moscow : Standartinform, 2012. 37 p.

Analysis of Time Relation for Signals in Design Digital Modules and Availability Estimation
Kuzin A.A.,
Pluzhnikov A.D.,
Pribludova E.N.,
Sidorov S.B.,

Keywords: multiprocessor systems; high-speed; route; synchronous exchange.

Technique of route singularity accounting with analysis of time relation for signals propagating in high-speed digital modules with synchronous data exchange is devised. The matrix route definition for the system highway and the system clocking is proposed. The application example of devised technique for the analysis of multiprocessor cluster designed with purpose of the use for advanced processing of the large information volume is considered.
For the choosen example, cluster contains the four advanced digital signal processors, the four SDRAM chips and the flash memory chip. The listed cluster components are connected among themselves by system highway that contains three multiplexed system buses: address bus and con-trol bus, high-order bit transfer bus (from 63th to 32th) of datum and low-order bit transfer bus (from 31th to 0) of datum. Though four processors are connected to all three system buses and every of the rest five components is connected to two of three system buses only (every to own).
Singularity of route such that the system highway may imagine as closed in the ring formally. Formality of such presentation defines with what none of three highway buses above physically do not close in the ring, i.e., every form these bus is opened or it is the opened ring. However, a mutual displacement of the three similar closed ring (three buses) in point of fact a mutual displacement of the sections their opening with sufficiently near placement of the printed conductors (lines) of the three bus on multilayer board allows to tell about the system highway structurally closed (formally, but no physically) in the ring.
So far as the current task is assigned so that should analyze the synchronous data exchange, in which flash memory does not share, when this component ignores with an analysis. For realization of synchronous exchange serves the synchronization buffer containing in cluster and connected with eight components (four processors and four SDRAM chips) lines of the unilateral transfer of the clock pulses from the synchronization buffer to the listed eight components.
Singularity of the considered multiprocessor cluster is the possibility of interprocessor data ex-change when any from four processors (master processor, Master) has access to internal memory and registers of other (slave, Slave) or all other (in the regime of broadcast exchange, Broadcast).
The timing analysis made for comparing project variants will allow to avoid the crude errors in the design process.
The made analysis shows that the route of system highway is potential source of system nonser-viceability as a whole.
Developed in the given work the technique of route singularity accounting with the timing analy-sis for signals propagating in high-speed digital modules with synchronous data exchange ensures the availability estimation capability for the selected design variant.

1. Kyle Castille. TMS320C6000 EMIF-to-External SDRAM Interface. Application Report SPRA433D. Texas Instruments, March 2004. P. 76.

2. CDCLVC11xx Data Sheet. Texas Instruments, May 2010. P. 2.

Spectrum analysis of signals on multicore processors
Musayev M.M.,
Kardashev M.S.,

Keywords: multi-core processors, algorithms of spectral analysis of signals, parallel processing cycles, the matrix-vector calculation, thread processing, the acceleration of parallel algorithms.

This article focuses on the implementation procedures of spectral analysis of signals on multicore processors. To estimate the resulting acceleration of calculations a few basic systems of the Fourier transform are taken: a fast Fourier transform, discrete cosine transform and Hadamard transform.
Acceleration of digital signal processing procedures can be achieved both by optimizing algorithms or recursive computation in the fast Fourier transforms, and by using of threads on multicore processors.
Thread processing in the signal processing tasks should be considered as a new technology, including the following elements of the preparation and execution of programs:
- analysis of the numerical methods and algorithms for the creation of independent computational threads;
- choice of effective programming language for writing programs;
- implementation of forming threads technologies using modern tools;
- estimation of parallel solutions efficiency.
Performance of the parallel algorithm depends on the software implementation environment: processor parameters, mechanisms for creating computational threads in the operating system, the number of threads.
In this paper the parameters of the acceleration of parallel algorithms performed for various numbers of threads on processors Intel Core i3, i5 are discussed. As a tool for the implementation of created parallel algorithms of spectral analysis the library of Open MP, Intel TBB and API Win32 Native Threads is used.
To compare the efficiency of these algorithms the graphs of acceleration of each parallel algorithm are shown relative to the sequential version of the same algorithm, as well as a parallel algorithm is shown relative to another at different numbers of threads.
Research results show that the main parameter that affects the scalability and final acceleration of application when migrating to multi-core platform is the number of source signal samples. Usually dependence of acceleration from number of samples has the character of a power function with horizontal axis, thus this maximum value of acceleration tends to the number of processors.
Another important estimation parameter is a minimum amount of data, which can be processed without a loss of performance. The optimal value for this parameter is the quotient obtained by dividing the total number of iterations to a number of computing threads.
Comparison of programming libraries shows when the number of samples in the signal fragment is a small, the usage of compiler directives Open MP is more efficient (acceleration occurs when the number of samples of signal fragment is from 16 to 64) and when the number of samples in the processed fragment is more than 128, the usage of Intel TBB algorithms is more efficient.
The best areas of using developed parallel processing algorithms are speech processing algorithms, spectra construction of small plots of the signals, spectrogram, digital filters.

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