Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 2-2015

In the issue:

- adaptive signal processing

- evaluation of the NMR signal parameters
- multirate processing of ECG signals
- tomographic reconstruction of radiation
- pulse classification of acoustic emission
- estimation of the IIR-filter self-noise
- analysis of I/Q signal parameters
- linear precoding for the MIMO systems

- processing on DSP

Algorithms of Linearly Constrained Blind Adaptive Signal Processing in Digital Arrays with Odd Symmetry
Victor I. Djigan, e-mail:
National Research University of Electronic Technology, Moscow, Russia

Keywords: adaptive array, RLS algorithm, LMS algorithm, Linear Constraints, Constant Modulus, real-valued arithmetic, complex-valued arithmetic.

Today the Linearly Constrained (LC) adaptive signal processing is widely used in Adaptive Arrays (AA) of radio communication systems, where a direction to the receiving signal source is a priory known. The direction is used to provide a linear constrain on radiation pattern toward the source. However, it is known, that LC AA loses performance, if correlated information signal and interferences are received. Besides, if blind signal processing is used, when AA receives Constant Modulus (CM) signals, a so-called tone capture phenomenon can be arisen. It is when the main beam of AA is steered toward an interference and a notch is created toward the information signal source.

The using of the linear constrains in AA allows to receive the information signals in the correlated interference conditions without tone capturing.

Unfortunately, cost function of AA with blind processing is multiextreme one and this does not allow to use the efficient Recursive Lest Square (RLS) adaptive filtering algorithms in this application.

The given paper proposes to use a quadtatized cost function of the CM AA and to use the radiation pattern constraints in multy-beam AA. These constraints are incorporated not only towards known information signal source of the AA under the consideration, but also towards the information sources of the neighbor AAs of the multy-beam array, which are the sources of interferences with known directions for the considered AA.

As the signals, received by AA, have some amplitudes and phases, the adaptive algorithms have to use complex-valued arithmetic. If to use AA with odd symmetry (when an arrays has geometrical symmetry and its phase canter is the same as geometrical one), then it is possible to reduce adaptive algorithms complexity (number of arithmetic operations per iteration) about twice comparing with that of the algorithms in complex-valued arithmetic.

The paper present basic details of such real-valued RLS and Least Mean Square (LMS) algorithms, their computations procedures and simulation results of the symmetrical 8 elements and 3 beam AA, relieving 3 different CM information signals with PSK-4, PSK-8 and PSK-16 modulations.

According the simulation, the LC RLS adaptive algorithm, based on the real-valued arithmetic, provides 1.5 … 2 times shorter transient response and 2 … 3 dB deeper notches in radiation pattern toward the interferences sources in steady-state comparing with the complex-valued one.

The LC LMS adaptive algorithm, based on real-valued arithmetic, also provides 2 … 3 dB deeper notches in radiation pattern toward the interferences sources in steady-state comparing with complex-valued one. However, the transient response duration is the same for both AA.

The simulation demonstrates the developed algorithms efficiency. They can be used in diversity of communication systems, where arrays with digital beamforming are used as receiving antennas.


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NMR compound signal parameters evaluation by maximum likelihood method
1E.V. Korotey, e-mail:
1E.V. Volkhonskaya, e-mail:

2V.A. Pakhotin, e-mail:
1K.V. Vlasova, e-mail:
2V.I. Strokov, e-mail:
1Baltic state academy of fishery fleet
2Baltic Federal university of I. Kant, Russia, Kaliningrad

Keywords: nuclear magnetic resonance, nuclear quadrupole resonance, method of maximum likelihood, assessment of parameters, Rao-Kramer's dispersion.


The results of maximum likelihood method application to processing of compound nuclear magnetic resonance (NMR) or nuclear quadrupole resonance (NQR) signals in the presence of noise are presented in this work. On the basis of this method authors created algorithm of processing of such signals. The expression for a credibility function logarithm containing signal model on a receiver entrance is the basis of the created algorithm. Research of this function on a minimum allows to define values of the evaluated parameters for two NMR (or NQR) signals in mix which are closest to true values.

Working range of the maximum likelihood method was estimated with use of expression for Rao-Kramer's dispersion. Elements of information matrix of Fischer were for this purpose defined. Diagonal elements of a matrix, the return to Fischer's matrix, give dispersions of signal parameters estimates.

By authors it is established that the maximum likelihood method gives adequate values of NMR (or NQR) signal parameters estimates, as in the field of orthogonality of signals when their coefficient of correlation is equal to zero, and in the field of their nonorthogonality when the coefficient of correlation is other than zero (to values about 0,9).

According to this algorithm the program code allowing to work as with a model NMR (or NQE) signal with the set parameters, and to carry out processing of experimentally received signals or their spectra on the basis of nuclear magnetic resonance spectrometers was developed.

The conducted preliminary model researches showed that satisfactory estimates of parameters of two signals it is possible to receive in the range of the signal to noise ratio over 10 dB at a difference of resonant frequencies over 0,4 kHz and at the relation of amplitudes of signals in mix from 0,05 to 20. At the same time the classical analysis on the basis of a spectral method allows to receive satisfactory estimates at the signal to noise ratio over 15 dB at a difference of frequencies over 2,5 kHz and at the relation of amplitudes of signals in mix from 0,2 to 5.

The results of processing of experimentally received 14N NQR signals for urotropin (C6H12N4, hexamethylenetetramine), 2H NMR spectra for cetylpyridinium chloride/hexanol/0,2 M (NaCl) and 35Cl NQR spectrum for a paradichlorbenzene (C6H4Cl2) are presented in this work. The results received by authors confirm results of model researches of a program code: the offered algorithm of a nuclear magnetic resonance compound signal processing on the basis of a maximum likelihood method realized in the form of a program code really possesses the increased resolution in comparison with classical methods of signals processing and allows to receive adequate estimates of a NMR (or NQR) compound signal parameters.

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HRV Analysis Filter Optimal Design

T.A. Vityazeva, e-mail:
S.V. Vityazev, e-mail:

A.A. Mikheev
Ryazan State Radio Engineering University, Ryazan, Russia

Keywords: multirate signal processing, optimal design, narrowband filtering, ECG, heart rate variability.

The problem of heart rate variability (HRV) analysis is considered in this paper. The analysis consists in signal power estimation in three frequency subbands and is usually accomplished in frequency domain. In previous works it was offered to perform HRV-analysis in time domain. This approach gives better opportunities for the detection of events in ECG signal related to the events in patient’s behavior (activities or emotions). However, finite impulse response filtering of the very big order (about several hundred thousand taps) is required in this case, because of very narrow subbands. Huge computational requirements become necessary in this situation which is not allowable in practical implementation.

In this paper it is offered to use multirate signal processing approach to decrease computational complexity of the problem. Sample rate is decreased 500 times. Multistage downsampling structure is designed. Optimal combination of the number of stages and downsampling coefficients is chosen. The optimum is found according to the computational costs minimization. Optimization procedure is taken from [8].

One-, two- and three-stage downsampling structures are considered. All possible combination of downsampling coefficients are taken into account. The required number of calculations and memory size are estimated for each case. It is shown, that for the considered task two-stage downsampling structure with coefficients 50 and 10 is the best choice. It requires 200- and 400- taps FIR decimating filters. Computational costs are about 10280 multiply operations per second and the required memory size is 1514 words. This approach gives more than 30 thousand times computational cost reduction related to the processing at original sampling frequency. The computer modeling approves the functionality of the approach.


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Visualization of Three-Dimensional Kohonen Self-Organizing Maps with Hexagonal Grid
A.V. Shadrin, e-mail:
Cosmophysical Research and Radio Wave Propagation Far Eastern Branch of Russian Academy of Sciences

Keywords: visualization, hexagonal grid, two-dimensional Kohonen self-organizing maps, clusterization, multidimensional data, rectangular grid, three-dimensional Kohonen self-organizing maps, unified distance matrix, U-arrays, U-matrix.

Methods for visualization of Kohonen self-organizing maps, which are widely applied for multidimensional data analysis and visualization, are considered. Techniques for calculating the unified array (U-array) hexagonal two-dimensional map is suggested. It is based on the estimation of unified distance matrix (U-matrix). To visualize the three-dimensional map proposed interpolation unified array into a regular three-dimensional network. The map is displayed after interpolation in the form slices and isosurfaces. Unlike existing methods of visualization three-dimensional maps, the proposed visualization method allows to analyze the data using the architectures with rectangular and hexagonal lattices. This method expands the toolkit of the researcher, allowing clear and simple to visualize multidimensional data in the three-dimensional Kohonen maps with rectangular and hexagonal architecture.

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Dependence of tomography reconstruction accuracy on noise correlation function involved in projection data

A. V. Likhachov, e-mail:
Yu. A. Shibaeva
Institute of Automation and Electrometry of the Siberian Branch of RAS (IAE SB RAS) Russia, Novosibirsk

Keywords: two-dimensional tomography, correlation function of noise, projection data smoothing.

We consider the problem of two-dimensional tomography based on the inverse formula of the two-dimensional Radon transform. This problem is known to be ill-posed since in the process of reconstruction the Fourier image of each projection is multiplied by the module of frequency (so-called ramp-filtration). The filtration leads to increasing of high frequency components of noise that is ever present in the measured signals. In accordance with the Wiener-Khintchine theorem the power spectral density of a stationary random process is the Fourier transform from the correlation function. Thus, the latter can have a significant impact on the quality of the reconstruction. However, in the available literature, when studying the stability of algorithms, the only type of distortions is usually considered. It is white noise that has no correlations by definition.

This paper investigates the random distortions of the projection data having arbitrary correlation functions. The mathematical relations between the characteristics of stationary noise before and after ramp-filtering are obtained. In particular, as a result of this operation, the power spectrum is multiplied by the square of the frequency characteristic of ramp-filter approximation. Three types of random noise with equal variance are modeled: white noise, Gaussian noise and a telegraph signal. In the latter two cases the autoregressive models from first to third order are used. The obtained standard deviation between the exact and simulated correlation functions is 10-30% for Gaussian noise and 4-20% for the telegraph signal.

According to the results of the computational experiment it to be proved that the reconstruction error is greater, the greater the variance of the filtered noise. The latter, in turn, decreases with increasing width of the correlation function. For example, for the correlation radius of telegraph signal changing from 5 to 100 steps of the grid the normalized mean root square error reduces from 1.222 to 0.335, i.e. almost four times. Such result is not obvious a priori since the angle integration, which is a part of the Radon transform inversion, to be applied to strongly correlated noise, could lead to the emergence of regular structures in the image, similar to the origin of the interference pattern. This would have a negative impact on the quality of the tomogram.

In addition, for Gaussian noise the variance value after filtering is found to be about four times lower than for telegraph signal (the noise variance in the input data in the both cases is equal). It appears from the above that when designing regularizing filters the criterion of minimizing the residual between the correlation function of the smoothed noise and a Gaussian function with the appropriate parameters can be used. The paper also examines two procedures of projections smoothing: the averaging in a sliding window, and the regularizing splines. It is shown that the splines compared with averaging significantly stronger reduce the variance of the noise and provide a broader correlation function.

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The sound range acoustic emission pulses classification based on symbolic representation of time-frequency structure
A.B. Tristanov1,2, e-mail:
O.O. Lukovenkova1,3
1Institute of Cosmophysical Research and Radio Wave Propagation of the Far Eastern Branch of Russian Academy of Science, Russia, Kamchatka region, Elizovskiy district, Paratunka
2Kaliningrad Technical State University, Russia, Kalinigrad
3Vitus Bering Kamchatka State University, Russia, Petropavlovsk-Kamchatskiy

acoustic emission, geoacoustic signal, time-frequency analysis, sparse approximation, matching pursuit.

This paper is devoted the classification of the geoacoustic emission (GAE) pulses based on symbolic representation of time-frequency structure.

The acoustic emission in solids is elastic vibrations arising as the result of dislocation changes in the environment. The characteristics of pulsed radiation excited in this case are directly concerned with the characteristics of plastic processes. This dictates the interest in emission research in order to develop methods of acoustic diagnosis of environments.

The authors proposed using the method of sparse approximations for the formation of attributive descriptions of isolated pulses of the emission process. GAE pulse model based on sparse approximation schemes is offered. This model reveals the internal structure of the pulse, captures local features, and reduces the dimension of the signal. To identify the model, the matching pursuit (MP) algorithm proposed by S. Mallat and S. Zhang and showing good results in the analysis of real GAE signals was selected.

A GAE pulse classification algorithm based on the symbolic representation of elements of the attributive space is assumed. The symbolic approximation involves the replacement of the original signal by a sequence of characters, each of which corresponds to a local signal behavior. The symbolic representation can be given in different ways and correspond to different local models. In our case, the local model is described by the filling frequency of the atom. Thus, the sequence of symbols describes the dynamics of the frequency–time signal structure, thereby giving an isolated class of pulses.

1. Yu.V. Marapulets and B.M. Shevtsov, Mesoscale Acoustical Emission // Dal’nauka, Vladivostok, 2012, p.126.

2. A.B. Tristanov and Yu.V. Marapulets, The way to apply thin approximation in the problems for analyzing heteroacoustic emission signals // Tsifrovaya Obrabotka Signalov, No. 2, 2011, pp.13–17.

3. S.G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries // IEEE Transactions on Signal Processing, 41(12), 1993, pp.3397–3415.

4. Yu.V. Marapulets and A.B. Tristanov, Sparse approximation of acoustic time series with Berlage time-frequency dictionary // Proceedings of Russian Scientific and Technical Society of radio engineering, electronics and communication named by A.S. Popov, No. XIV, Vol. 1, 2012, pp.91-94.

5. A.B. Tristanov and Yu.V. Marapulets, The way to apply thin approximation in the problems for analyzing heteroacoustic emission signals // Tsifrovaya Obrabotka Signalov, No. 2, 2011, pp. 13–17.

6. A.A. Afanaseva, O.O. Lukovenkova, Yu.V. Marapulets and A.B. Tristanov, Using the sparse approximation and clustering methods for the time series structure description of acoustic emission // Tsifrovaya Obrabotka Signalov, No. 2, 2013, pp. 30–34.

7. O.O. Lukovenkova and A.B. Tristanov, Adaptive refining matching pursuit algorithm for combined dictionaries in the analysis of the geoacoustic emission signals // Tsifrovaya Obrabotka Signalov, No. 2, 2014, pp. 54–57.

Own noise estimates of recursive digital filter structures and their MATLAB calculation
A.I. Solonina, e-mail:
Saint Petersburg State University of Telecommunications named after prof. M. A. Bonch-Bruevich (SPbGUT), Russia, Saint Petersburg

structure, multiplier, adder, rounding, own noise, equivalent linear model, vector, variance, algorithm.

Nonlinear quantization procedures in digital fixed point systems are accompanied by quantization errors. Multipliers of the digital system structure provide some quantization errors known as the round-off noise or the own noise. In the DSP theory the own noise is analyzed separately from any other quantization errors. In this case certain assumptions, concerning noises of multipliers, are introduced.

The own noise of FIR filters is estimated on the base of a linear model, where the integral effect of all multiplier’s noises is represented by some equivalent noise. In the structure of IIR filters the noises of multipliers are processed by different parts of the structure, therefore in this case for estimation of the own noise a specific equivalent linear model, depending on the structure of second order sections, should be created.

This paper proposes the general equivalent liner model, which forms vectors of input eÓâõ(n) and output eÓâûõ(n) noises of multipliers, as well as a vector-column of equivalent system functions Hý(z) of structure parts, processing eÓâõ(n) vector’s components.

Estimates of the own noise depend on a digital filter structure and digital device architecture. The structure determines a configuration of multipliers, and the architecture – characterization of multiplications: rounding each local product or rounding the sum of local products. In the last case, a modification of the equivalent liner model is the linear model with post-accumulation. In the equivalent liner model, parts of input multiplier noises eÓâõ(n) are formed from additive multiplier noises at inputs of adders, but in the linear model with post-accumulation they are formed at outputs of the adders.

It is especially considered the general equivalent liner model and the linear model with post-accumulation of the cascade structure of IIR filters. The paper determines vector components of models for different structures of second order sections, analyses influence of section system function zeros and poles on the own noise variance. Based on this models, it is derived analytical formulas for the own noise variance of IIR filters with different structures of second order sections and also with rounding each local product and the sum of local products.

Simple MATLAB algorithm for calculation of the own noise variance of the cascade structure is proposed. The cascade structure of IIR filters with known structures of second order sections is described as the dfilt object with the corresponding coefficient matrix. Coefficient matrixes of equivalent system functions are formed within the cycle by consecutive nullification of initial matrix elements. Equivalent impulse responses of cascade structure parts are calculated within the cycle with automatic limitations up to equal length.

Finally, the paper illustrates the proposed theoretical approach by results of own noise variance calculations for FIR and IIR filters.

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I/Q signal parameter analisys for digital television system DVD S2
D.Sc. Prof. Dvorkovich V.P., e-mail:
D.Sc. Prof. Dvorkovich A.V., e-mail:
Ph.D. Basiy V.T., e-mail:
Moscow Institute of Physics and Technology 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation

Keywords: digital signal processing, digital television, OFDM constellation, digital measurements, DVB-S2.

Currently no suitable international norm exists, standardizing the metrology of modest satellite television broadcasting system DVB-S2. This state has been got because of the complexity of structures of circular constellation of I/Q diagrams used in the DVB-S2 system.

The straightforward use of the distortion evaluation algorithms implemented in the related terrestrial television broadcasting DVB-T2 system, leads to a number of problems, as listed below:
- the problem of correct constellation center bias evaluation;
- the problem of correct System Target Error Mean (STEM) and System Target Error Deviation, (STED) evaluation;
- the problem of correct Amplitude Imbalance (AI) evaluation;
- the problem of correct Quadrature Error (QE) evaluation;
- the problem of correct Error Vector Magnitude (EVM) evaluation;
- the problem of correct Phase Jitter (PJ) evaluation.

The issue is that it is impossible to establish unambiguous measurement tolerances, since the definition of parameters listed above does not provide the mutual independence of their values.

The method of measurement considered in this paper uses the consequent distortion exclusion to eliminate these problems.

The following signal processing sequence is proposed:
- determination of the mean values of the star vectors in the constellation and I/Q-component standard deviation.
- measurement and subsequent correction of constellation distortion due to the quadrature error QE.
- measurement of the average resulting error STEM and of its deviation value STED.
- measurement and subsequent correction of constellation distortion due to the amplitude imbalance AI.
- separation, correction of mutual influence and measuring the fluctuation parameters of the constellation - MER (EVM) and PJ.

In this research for the first time algorithms have been considered for evaluation of parameters of I/Q signals of digital satellite broadcasting system DVB-S2 (for QPSK, 8PSK, 16APSK and 32APSK modulation types). In addition, the measurement procedure has been developed that allows to set independent unambigouos tolerances for error qualification of the positions of constellation points, amplitude imbalance, quadrature errors, relative phase modulation error and jitter.

1. ETSI TR 101 290 V1.3.1. Measurement Guidelines for DVB Systems (07/2014).

2. ETSI EN 300 744 V1.6.1. Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for digital terrestrial television (01/2009).

3. ETSI EN 302 755 V1.3.1. Digital Video Broadcasting (DVB); Frame structure channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2) (04/2012).

4. ETSI TR 101 290 V1.3.1. Measurement Guidelines for DVB Systems (07/2014).

5. Victor P. Dvorkovich, Alexander V. Dvorkovich, Digital video information systems (theory and practice). p.1008. Technosphere, Moscow 2012

6. Victor P. Dvorkovich, Alexander V. Dvorkovich, Measurements in digital video information systems (theory and practice). p.788. Technosphere, Moscow 2015

7. ETSI EN 302 307 V1.3.1. Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2). (2013-03)

8. ETSI TR 102 376 V1.1.1.Digital Video Broadcasting (DVB). User guidelines for the second generation system for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2). (2005-02)

9. DVB Document A83-1. Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications. Part I: DVB-S2. March 2014

10. DVB Document A83-2. Digital Video Broadcasting (DVB);Second generation framing structure, channel coding and modulation systems for Broadcasting, InteractiveServices, News Gathering and other broadbandsatellite applications. Part II: S2-Extensions (DVB-S2X) - (Optional). March 2014.

A Two-Element Linear Precoding for MIMO Spatial Multiplexing
V.B. Kreindelin, email:
M.Yu. Starovoytov, email:
Moscow Technical University of Communications and Informatics " MTUCI", Russia, Moscow

Single User MIMO, linear precoding, SVD, Spatial Multiplexing, LTE

The paper describes a new simple precoding for the mode of Single-User Multiple Input Multiple Output with Spatial Multiplexing (SU MIMO SM) - for the architecture of Radio Access Network referred to as “Centralized RAN”, with all Cellular Base Stations (“BS”) synchronized and BS data processing centralized.

The term "MIMO" addresses an established sphere of research and applications in fixed and mobile wireless communications, employing the use of multiple transmit and multiple receive antennas together with effective processing algorythms to get the additional gain on the radio link.

The term “precoding” means operations on the transmitter side that shall lead to improved channel performance.

The proposed precoding consists of two elements. The first matrix element is taken from the Singular Value Decomposition (SVD) of the channel matrix; it accounts for the individuality of the ongoing session and acts as a ”key”, opening the way for the second element to directly working on the channel matrix spectrum. The second matrix element is used in a ready precalculated form, it is taken on protocol request from the Central Database where it is stored. Real-time calculations on the Mobile Station and the BS are reduced essentially to the SVD transform of channel matrix. For the cases of MIMO2x2 and MIMO4x4 the matrix representations for the second elements of precoding are proposed, that allows for an economy and convenience in coping with the precoding, but at the same time saves a good performance effect.

The performance of the method is shown in comparison with the linear precoding based on 3GPP standard: with 1-bit codebook for MIMO2x2 and 4-bit codebook for MIMO4x4. Channel model was taken also from 3GPP standard. Modeling showed that despite the simplicity and minimum of calculations applied in real time, the proposed precoding gives a considerable effect, from 0.5 to 2 dB, compared to the 3GPP codebooks on the plot Symbol Error Rate vs Signal to Noise Ratio (SER/SNR). Among all the known precoding methods for SU MIMO SM for Maximum Likelihood demodulation, the proposed method applies for a minimum of extra computational effort in real time spent for the unit dB gain.

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Multiprocessor clusters based on signal processors with static super-scalar architecture
Å.À. Bukvàråv, email:
A.A. Kuzin, email:
E.N. Pribludova, email:

À.G. Ryndyk, email:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Russia, Nizhny Novgorod

Keywords: digital processing, signal processor, multiprocessor clusters, integrated module.

In this paper two structures of multiprocessor clusters on basis of signal processors with static super-scalar architecture are presented. Some design features are considered, configuration and appearance of the multiprocessor cluster are shown and characteristics of cluster are provided.

Generally, calculating cluster is collection of calculating units, connected by some communication network. Each computing unit has the random access memory and works under control of the operating system. The most widespread is uniform clusters use where all units are absolutely identical on the architecture and productivity. Feature of a cluster is component application of serial production.

For problems of digital signal processing use as units of a cluster of specialized high-performance processors is represented perspective. As a rule, DSP processors have the built-in memory, and communications between processors in a cluster are provided with the built-in means of processors.

Development of a multiprocessor cluster on the basis of DSP processors is a private problem of the integrated DSP module design with possibility of productivity scaling.

The chosen option of the integrated module configuration in the form of basic (the bearing board) with the submodules (attics) installed on it assumes installation from one to five multiprocessor clusters that provides change of productivity over a wide range.

The submodule represents functionally and structurally finished four-processor cluster. Besides, the submodule has special signal distribution of high-speed LINK-ports on sockets for the purpose of trace simplification of a basic board.

The developed multiprocessor clusters are intended for use into integrated module in stationary and mobile systems of high-performance digital signal processing.


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4. Kuzin A.A., Pluzhnikov A.D., Pribludova E.N., Sidorov S.B. Analysis of time relation for signals in design digital modules and availability estimation // Digital signal processing, ¹ 2, 2014, pp. 70-77.

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