Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 1-2023

In the issue:

- adaptive filters
- signals modulation and demodulation
- parametric spectral analysis
- stochastic modeling of pulse signal
- classification of endoscopic images
- optimization of rejection filters
- narrow-band interference rejection
- formation of meteorological product in X-range

- voice activity detector
- ADC L-card E-502 dynamic libraries

Djigan V.I., e-mail:

Institute for Design Problems in Microelectronics of Russian Academy of Sciences, Moscow, Russia

Keywords: acoustic echo cancellation, room impulse response, Affine Projection (AP) algorithm, Fast Affine Projection (FAP), Recursive Least Squares (RLS) algorithm, Least Mean Square (LMS) algorithm, Normalized LMS (NLMS) algorithm.

The paper considers the problem of the identification of the multichannel linear system with the long impulse responses of its channels. An example of such task is the multichannel cancellation of the acoustic echo signals in the closed spaces. Depending on the size of the room, its decoration, the sampling rate, the duration of the acoustic impulse responses might take a several thousands of the sampling periods. In this case, to solve the identification problem, it is required to use a multichannel adaptive filter with the large number of weights. The implementation of such filters is not an easy task because the computational complexity of the adaptive filters depends on the number of their weights. Due to this reason, the efficient adaptive filters based on the Recursive Least Squares (RLS) algorithm are rarely used in the acoustic echo cancellers even in its fast (computationally efficient) forms. Instead of these algorithms, the simple from the computational point of view adaptive filters based on the Least Mean Square (LMS) algorithm or based on the Normalized LMS algorithm (Normalized LMS, NLMS) are usually used. However, these simple adaptive filters have a number of known disadvantages. One these disadvantages is a slow convergence when the correlated or non-stationary signals, like speech, are processed. Adaptive filters based on the LMS/NLMS algorithms in the frequency domain make it possible to decorrelate the processed signals. Such filters have the less computational complexity than their time domain counterparts. However, because signals are processed using the blocks of the samples, the frequency domain adaptive filters introduce the delay of the output signal and exhibit a slow convergence because their weights are updated only once per block. This reduces the tracking properties of such adaptive filters. The tracking property is important one for the adaptive filters in the problem of the acoustic echo cancellation because the acoustic medium is usually not stationary. The use of adaptive filters based on the Fast Affine Projection (FAP) algorithm is a compromise between the efficiency of an acoustic echo canceller and its computational complexity. Such adaptive filters are widely used today in the single-channel acoustic echo cancellers. This paper discusses the usage of the adaptive filters based on the FAP algorithm in the multichannel echo cancellers. The paper presents a computational procedure for the calculation of the weights of a multichannel adaptive filter based on the FAP algorithm and considers an example of the simulation of the two-channel echo canceller based on this algorithm. Simulations show that the characteristics of such an adaptive filter in the steady-state are close to those of an adaptive filter based on the RLS algorithm or based on the NLMS algorithm in the time or frequency domain. The convergence of the adaptive filter based on the FAP algorithm is several times faster compared to that of the adaptive filter based on the NLMS algorithm. Due to this feature, the adaptive filter based on the FAP algorithm can be used in the multichannel echocancellers ensuring the low requirements to the implementation resources and ensuring an ability to track the changes in the statistics of the processed signals and/or to track the changes in the acoustic environment.


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Methods for modulation and demodulation of multidimensional ensemble signals
M.A. Bykhovskiy, e-mail:

Keywords: Formation of optimal multidimensional signals, demodulation of optimal multidimensional signals, energy efficiency, spectral efficiency, noise immunity of signal reception.


The paper presents an algorithm for converting the specific number of a transmitted message m into modulation indices necessary for generating signals belonging to surface-spherical signal ensembles (SSAS). Functional diagrams of modulators and optimal demodulators of SSAS are also discussed.

It is noted that the SSAS generation procedure is similar to the convolutional code generation procedure, and the demodulation procedure is similar to the sequential decoding procedure of a convolutional code using the Viterbi algorithm. It is shown that the number of operations required to generate SSAS signals in modulators and processing operations of these signals in demodulators increases linearly with an increase in the duration of signals in SSAS. Therefore, the complexity of the technical implementation of communication systems with SSAS turns out to be comparable to the complexity of the implementation of communication systems which use two-dimensional signal ensembles such as QAM and APSK to increase the reliability of message reception. It is noted that the use of SSAS allows the creation of communication systems with high energy and spectral efficiency.

Parametric spectral analysis of piece-stationary radioengineering signals taking into account the effect of noise on correlation properties
V. G. Andrejev, e-mail:
V. A. Tran,
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: piecewise-stationary noise, non-stationary noise, weight vector, adaptive algorithm, autoregressive model, change-point, spectral estimation, power spectral density.

We proposed and investigated a method of spectral analysis of piecewise-stationary processes with correction of estimates of correlation matrices to take into account the influence of changing power of additive noise.

The aim of the work is to increase the computational efficiency of analysis algorithms and the accuracy of spectral estimation of radioengineering signals on the background of piecewise-stationary noises. Based on an estimate of the optimal value of the correction value based on an estimate of the noise power Pn, the proposed method makes it possible to reduce the influence of non-stationary noise and improve the accuracy of spectral estimates by correcting the autocorrelation coefficients of piecewise stationary random processes. The qualitative indicators of the proposed modified spectral analysis method are compared with the conventional parametric autoregressive method.

Experimental studies have shown that when using the proposed approach for spectral estimation, when compared with known autoregressive methods, it is possible to reduce the discrepancy between the control and estimated spectra by 7.4...9 times. When conducting a comparative analysis with a conventional autoregressive model, the decrease in the order of p can reach 2.5...3 times while maintaining the same spectral estimation accuracy. It is confirmed that for the analysis of the spectrum of the studied narrowband radioengineering signals, the relative deviations ΔF of the estimate of dominant frequency are significantly (up to 6 times) reduced by using the proposed modified method in comparison with the autoregressive method. Winnings are achieved through the use of a priori information about the time-varying power of the interfering process.

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Stochastic modeling of geoacoustic emission pulse signal

Yu.I. Senkevich, e-mail:
M.A. Mishchenko, e-mail:
A.A. Solodchuk, e-mail:
O.O. Lukovenkova, e-mail:
M.I. Gapeev, e-mail:
Institute of cosmophysical research and radiowave propagation FEB RAS (IKIR FEB RAS), Russia, Kamchatka region, Paratunka

Keywords: seismic activity, geoacoustic emission, pulse signal stochastic model, anomalies in the parameters distribution, structural-linguistic analysis.

The development of approaches and methods for warning about the danger of earthquakes and tsunamis in short-term periods (from several hours to several tens of days) is the most serious task of ensuring the safety of human life and technical structures. Research practice shows that there are no universal scientific approaches and methods applicable to solving this problem anywhere in the world. The reasons for this are the nonlinearity of the tectonic process, the influence of solar-terrestrial and other planetary-gravitational processes, the dependence of the lithosphere states and the Earth's magnetic field on the geographic location, etc.

This work is carried out within the framework of the study of processes occurring at different stages of seismic activity in the Kamchatka region. The source of information for the performed observations is the acoustic field. In particular, one of the indicators of seismic activity is a change in the characteristics of geoacoustic emission, which is generated by near-surface sedimentary rocks. Changes in these signals are connected with earthquake preparation. However, the study of these changes is associated with certain difficulties in processing and analyzing geoacoustic emission signals. These signals are flows of pulses of various shapes, durations, with different interpulse intervals. At the same time, these characteristics change noticeably over short time intervals in a wide range of values.

In order to better understand the behavior of pulses in group dynamics, the authors proposed a stochastic model of the geoacoustic emission signal. The signal is recorded by a point receiver in a homogeneous and isotropic medium. The model parameters are three random variables. These are pulse amplitude, interpulse interval, and pulse duration.

To analyze the proposed model, a technique for constructing three-dimensional graphs of the distributions of each of the parameters was developed. It makes it possible to reveal the features of their behavior over time. Approbation of the technique was carried out on an artificial signal with different laws of parameters distribution.

Applying the developed technique to real data, the authors revealed anomalies in the parameters distribution of geoacoustic pulses flow. As a result, new knowledge was obtained about the effect of seismic processes on the acoustic field in near-surface sedimentary rocks.

This work is carried out within the framework of the State task on the topic (2021-2023) «Physical processes in the system of near space and geospheres under solar and litospheric impact», registration number AAAA-A21-121011290003-0.

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A. I. Gladyshev1, e-mail:
A. M. Telegin2, e-mail:
E. A. Shchelokov2, e-mail:
1Russian New University (RosNOU), Moscow, Russia
2Samara University, Samara, Russia;

microparticles, Mie theory, laser beam, scattering.

The problem of constructing a mathematical model of an optical system for recording the parameters of high-speed microparticles (micrometeoroids and space debris particles) is considered. To find the distribution of light fluxes caused by the scattering of laser radiation on microparticles, the Mie theory is used. The aim of the work is to develop recommendations for constructing an optical system for recording microparticle parameters

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Optimization of rejection filters when wobbling the repetition period
D.I.Popov, e-mail:

The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: adaptation, weight vector, repetition period wobble, minimax criterion, optimization, clutter, rejection filter.

Non-recursive rejection filters with weighting coefficients optimized for the case of processing a wobbled sequence in the range of a possible change in the width of the interference spectrum are considered. The criterion of optimization of the vector of the weight coefficients of the rjection filter is given, which ensures the maximum coefficient of improvement of the signal-to-noise ratio in each period of the wobbled sequence.

The application of the minimax principle to the magnitude of relative losses in marginal efficiency leads to the determination of a weight vector in each period of repetition, in which minimal losses are provided over the entire optimization range compared to optimal processing. The numerical results of optimization are given, from which it follows that the vector of weight coefficients in each period is asymmetric and varies from period to period.

For different values of the noise/clutter ratio, the gains in marginal efficiency provided by a filter with optimized weighting coefficients compared to known non-optimized coefficients are determined. The principles of implementing an optimized filter based on a system function in the form of cascading inclusion of 1st and 2nd order links with time-variable weighting coefficients are considered, and a block diagram of the filter with partial adaptation to the Doppler phase of passive clutter and switching from period to period of weighting coefficients is presented.

According to the criterion determining the effectiveness of interference suppression, a comparative analysis of the effectiveness of optimized filters was carried out and the volume of the training sample was estimated in case of their adaptation to the Doppler phase of clutter.

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Quality indicators of the DFT-based algorithm for narrow-band interference rejection under various functions of the preliminary weighing
E.V. Kuzmin, e-mail:
Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: narrow-band interference, interference rejection, weight function, discrete Fourier transform, spread spectrum signal, signals searching, interference suppression coefficient, signal power loss factor.

The efficiency of the narrow-band interference rejection algorithm based on direct and inverse discrete Fourier transform of a weighted realization has been studied. The possible behavior of the quality indices of interference rejection with different number of removed frequency samples and with weighing of the realization by different weight functions: rectangular, sine-window, Hann, Blackman, Parzen, and cubic variation of the Henning weight function was studied. A color graphical visualization of the interference suppression gain with controlled element-by-element removal of frequency samples is given, and the resulting deformation of the useful output effect of quadrature correlation processing is demonstrated. Interference suppression coefficient and signal power loss factor are obtained, as well as the subinterference visibility coefficient for which the dependence on the frequency position of the interference is demonstrated. Families of statistical dependencies of aggregate processing, including the considered DFT-rejection of interference and subsequent a spread spectrum signal searching based on quadrature correlation processing of a «cleaned» from interference realization, are presented.

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A functionally-oriented model of the formation of a meteorological product in the x-range from hydrometeors of a supercooled liquid with full polarization reception
O.V. Vasiliev, e-mail:
S.A. Zyabkin, e-mail:
A.V. Nikonenko, e-mail:
D.S. Chirov, e-mail:
Moscow State Technical University of Civil Aviation, Russia, Moscow
JSC Concern International Air Navigation Systems, Russia, Moscow
Moscow Technical University of Communications and Informatics

Keywords: Meteorological radar complex, near airfield zone, classification of hydrometeors, aircraft icing, simulation modeling, polarimetry, radar meteorology.

The task of classifying hydrometeors of dangerous weather phenomena can significantly contribute to the study of microphysics of clouds, the detection of hail and areas of probable icing of aircraft, which in turn will ensure an increase in the safety of their operation. Polarimetric meteorological radar systems make it possible to detect and identify various classes of hydrometeors in liquid, mixed and icy phases. Recently, X-band meteorological radars of the near airfield zone have been widely developed and distributed, processing only a horizontally polarized signal. One of the promising areas of modernization of such complexes is the transition to antenna systems with full polarization reception. The article describes the developed algorithm for simulation of polarimetric products of the X-band meteorological radar complex under conditions corresponding to the phenomenon of aircraft icing. Classes of drizzle, rain, dry and wet snow and oriented ice crystals were considered as hydrometeors. Hydrometeors are put down by spheroids with dimensions, shape, orientation and dielectric composition depending on the class. Direct calculation by the T-matrix method was used as a method for calculating the reflections of a single particle. Simulation of polarimetric products from an ensemble of hydrometeors is based on Monte Carlo methods. The adequacy of the simulation model was evaluated by comparing the histograms obtained with the accessory functions obtained on the basis of experimental data in the S-range. According to the results of the conducted studies, the probabilities of correct modeling in the X-range for the classes of drizzle, rain, oriented ice crystals, dry and wet snow are 0.987, 0.967, 0.914, 0.951 and 0.929, respectively.

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