Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 2-2021

In the issue:

- ñreating low-speed communication systems
- roundoff errors in allpass chain
- cochlear implantation systems stimulation
- trajectory instability of flight carier small-size SAR
- adaptive rejection filters
- analyzing of the adaptive interpolated IIR filters
- mathematical models of multi-packet message delivery
- detecting polyps on endoscopic images

Possibilities of creating low-speed communication systems with high spectral and energy efficiency (Part 2)
M.A. Bykhovskiy, Moscow Technical University of Communications and Informatics, Russia, Moscow, e-mail:

Keywords: low-speed communication systems, signal transmission methods, spectral and energy efficiency, noise-resistant codes.

In this paper, we consider the possibility of creating low-speed communication systems in which messages are transmitted using signals with permutation modulation (PM) with extremely low power, and to correct errors that occur when demodulating such signals, the use of error-correcting codes (ECCs) with the maximum achievable code distance (MACD). As such ECCs, Reed-Solomon (RS) codes or low-density parity-check code (LDPC) codes can be used.

The paper describes two algorithms for the formation of ensembles of signals from the PM, analyzes the noise immunity of receiving signals from the PM, and discusses in detail issues related to the selection of ECC parameters for low-speed communication systems that can ensure high reliability of message reception and their high spectral efficiency.

It is shown that, in contrast to high-speed communication systems, in which two-dimensional AS with quadrature-amplitude modulation and ECCs with MACD are used for message transmission, in the studied low-speed systems, the optimal choice of their parameters allows their energy and spectral efficiency to be very close to the limiting ones - those that have the "perfect" Shannon system. It is also shown that the ECC used in these systems can have a relatively small length and its implementation is quite simple in technical terms.


1. Bykhovskiy M.A. Possibilities of creating high-speed communication systems with high spectral and energy efficiency (Part 1) (Vozmozhnosti sozdaniya vysokoskorostnykh sistem svyazi s vysokoy spektral'noy i energeticheskoy effektivnost'yu (chast' 2))//Cifrovaja obrabotka signalov (Digital signal processing), 2021, no. 1, pp. 20–31.

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3. John G. Proakis. Digital communications/ New York : McGraw-Hill, 1989. p. 608

4. Slepian D. Permutation modulation. Proc. IEEE, vol. 53, Mar. 1965. pp. 228-236

5. Bykhovskiy M.A. Giperfazovaya modulyatsiya – optimal'nyy metod peredachi soobshcheniy v gaussovskikh kanalakh svyazi. (Hyperphase modulation is the optimal method for transmitting messages in Gaussian communication channels) M.: Tekhnosfera, 2018. p. 310

6. W. Wesley Peterson and E. J. Weldon, Jr. Error-Correcting Codes, Second Edition, The MIT Press, 1972. p. 576

7. A.A. Frolov, V.V. Zyablov, Granitsy minimal'nogo kodovogo rasstoyaniya dlya nedvoichnykh kodov na dvudol'nykh grafakh, Problemy peredachi informatsii, (Boundaries of the minimum code distance for nonbinary codes on bipartite graphs, Problems of Information Transmission) 2011, vypusk 4, pp. 27-42

8. Frolov A.A. Korrektiruyushchiye svoystva nedvoichnykh kodov s maloy plotnost'yu proverok. Correcting properties of non-binary codes with low density of checks). Dissertation for the scientific degree of fis.-mat. sciences. IPPI named after Kharkevich. RAS, 2012. p. 117

9. Osipchuk S.A. Povysheniye informatsionnoy effektivnosti besprovodnykh sistem peredachi na osnove pereraspredeleniya resursov kanala svyazi. KPI, (Improving the information efficiency of wireless transmission systems based on reallocation of communication channel resources). KPI, Dissertation for the degree of candidate of technical sciences, Kiev, 2015 p. 182

10. Uryvsky L., Osypchuk S. The analytical description of regular LDPS codes correcting ability. Institute of Telecommunication Systems National Technical University of Ukraine “Kyiv Polytechnic Institute”. Transport and Telecommunication Vol. 15, ¹ 3, 2014

11. Bykhovskiy M.A. Metod formirovaniya mnogochastotnykh shirokopolosnykh signalov i vozmozhnosti ikh primeneniya v sistemakh svyazi. (Method of formation of the multifrequency broadband signals and possibilities of their application in communication systems)//Cifrovaja obrabotka signalov (Digital signal processing), 2019, no. 1, pp. 10–13.

Roundoff errors analysis in fixed-point allpass chain implementation
M.I. Vashkevich, Belarusian State University of Informatics and Radioelectronics (BSUIR), Belarus, Minsk, e-mail:

Keywords: allpass transform, quantization, roundoff error, rounding, probabilistic rounding, error spectral shaping, allpass chain, fixed-point implementation.


The necessity of allpass chain (cascade) implementation is emerged in the realization of audio signal processing systems based on allpass transformation. The use of allpass transformation makes it possible to obtain discrete systems (e.g. filter banks) in which representation of spectral information in close correspondence with that in the human ear. The purpose of this work was to study the quantization noise and roundoff errors in fixed-point implementation of allpass chain. Various schemes for quantizing the results of arithmetic operations were investigated: truncation, deterministic and probabilistic rounding, as well as the error spectral shaping method. Quantization schemes are compared by the ratio of mean square error (MSE) to quantization step q. The error signal is calculated as difference between outputs of reference allpass chain model and the model of allpass chain with quantization of the results of arithmetic operation. The MSE computed for the four different test signals: unit impulse, unit-step, sinusoid and pulse-train. Experiment carried out for data wordlength 10,12,14 and 16 bits. In average lowest MSE is achieved when using the error spectral shaping method; the highest MSE is achieved when using truncation. The deterministic and probabilistic rounding are shows very close results. The highest MSE are observed for a sinusoidal input signal (near 31 dBq), and the lowest for a unit impulse (new 14 dBq).

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History of the development of cochlear implantation systems stimulation strategies
Korotkov À. S., e-mail:
Glukhovskiy Å. Ì.,
Egorov A. I.
, e-mail:
Moscow Institute of Physics and Technology (MIPT), Medical Instrumentation Laboratories, 9 Institutskiy Alley, Dolgoprudny, Moscow Region, 141701, Russian Federation

Keywords: cochlear implantation, stimulation strategies, virtual channels, future developments.

Modern medicine is aimed both at preserving the patient's life and to maintaining and improving his quality of life. Hearing impairment is not a new problem, but it is relevant and significant today. Integration of people with hearing impairments into today's dynamic society is a difficult task without restoring lost sensory function. The presented review focuses on pacing strategies in a cochlear implant system. Authors have considered strategies that reproduce the original spectrum through fixed and virtual channels. The history of the cochlear implantation development and the stages of development of stimulation strategies in cochlear implantation systems were studied, the principles of operation of the main stimulating strategies used in modern implants were studied. The authors have identified promising directions for the development of new strategies and considered the problems currently faced by researchers of cochlear implants. This article describes both strategies that have found application in the implant market and fundamentally new but have not used yet. The basic principles of improving the accuracy of the sound spectrum and, as a consequence, the key directions in the development of new stimulation strategies are explained by the authors. And the results of clinical studies are presented in the manuscript.

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Research on the effect of trajectory instability of flight carier small-size SAR on quality of gen-erated radar images

G.A. Gulyaev, e-mail:
M.V. Ivannikova, e-mail:
L.B. Ryazantsev, e-mail:
A.V. Unkovsky, e-mail:
MESC «Zhukovsky–Gagarin Air Force Academy», Russia, Voronezh

Keywords: FMCW SAR, trajectory instability, resolution, trajectory instability, phase errors, optimal aperture synthesis time, autofocus.

The article is devoted to the study of the influence of the trajectory instabilities of the flight of the carrier of a small-sized synthetic aperture radar on the quality of the generated radar images. On the basis of the research, a method for preliminary fast autofocusing of the generated radar images is proposed, which consists in determining the optimal synthesis time based on the analysis of the statistical characteristics of trajectory instabilities.

To assess the degree of influence of trajectory instabilities on the quality of the generated radar images and to determine the optimal value of the synthesis time, the following steps were performed: calculation of the statistical characteristics of trajectory instabilities recorded by onboard sensors during flight for various types of aircraft; flight simulation of aircraft in the presence of trajectory instabilities, taking into account the calculated statistical characteristics; the integration of mathematical models of the flight of the aircraft into the algorithms for forming the radar image, followed by the calculation by the simulation method of the optimal time for synthesizing the aperture, which ensures the best quality of the radar image.

To calculate the statistical characteristics of trajectory instabilities, a number of flight experiments were carried out using various types of aircraft: unmanned aerial vehicles of the aircraft type Skywalker 1880 and Phoenix (NPP New Technologies of Telecommunications LLC, St. Petersburg), piloted helicopter Robinson R44, as well as the Il-114ll manned aircraft (JSC NPP Radar mms, St. Petersburg). The registration of flight parameters was carried out on straight sections of the trajectory by the Ublox NEO-M8 SRNS receiver, the data from the output of which were stored at a frequency of 10 Hz in the form of coordinates, speed and altitude readings of the carrier for sub-sequent statistical processing.

On the basis of the obtained statistical characteristics, the modeling of trajectory instabilities was carried out, which was carried out by passing white Gaussian noise through a shaping filter, the impulse response of which is calculated on the basis of an autocorrelation function with a given spectral width.

The calculation of the value of the optimal synthesis time, which provides the best quality of the radar image, is based on the formation of a radar image, a test scene consisting of a single point reflector with known coordinates typical for the observation conditions of a small-sized high-resolution radar with the subsequent calculation of the resolution along the track range in the width of the response from point reflector.

Thus, based on the assessment of the statistical characteristics of trajectory instabilities of various types of unmanned and manned aerial vehicles, as well as the degree of influence of trajectory instabilities on the quality of the generated radar images, a new approach is proposed for estimating the optimal synthesis time in the presence of trajectory instabilities based on the analysis of their statistical characteristics. The inclusion of procedures for evaluating the optimal synthesis time in the algorithms for forming the radar image will ensure the achievement of the maximum permissible quality of the radar image at their are automatically formation on board the carrier while reducing computational costs.

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3. Kulakova V.I., Nozdrin S.A., Soharev A.YU., Carik D.V. Sistema mikronavigacii dlya podderzhki radiolokatora s sintezirovannoj aperturoj na bortu malogaba-ritnogo BpLA (Micronavi-gation system to support synthetic aperture radar on board a small-size UAV) // Giroskopiya i navi-gaciya. Vol 27. No (107), 2019. pp. 130-146.

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5. Gur'yanov M.A., Prokof'ev A.A. Avtopodbor parametrov sinteza radiolokaci-onnogo izo-brazheniya, poluchennogo s radiolokatora s sintezirovannoj aperturoj (Automatic selection of the synthesis parameters of the radar image obtained from the synthetic aperture radar) // Izve-stiya vuzov. Elektronika. Vol 20, No 2, 2015. pp. 161-167.

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Principles of constructing adaptive rejection filters
D.I.Popov, The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan, e-mail:

auto compensation, adaptation, repetition period wobble, doppler phase, clutter, construction principles, rejection filter, synthesis.

The features and principles of constructing adaptive non-recursive rejection filters are considered. The system functions in the z-plane of canonical and cascade ARFs are given for equidistant and non-equidistant input of the processed samples. A method for analyzing the system functions of filters that function with a non-equidistant input of processed samples is proposed.

The general principles of ARF construction for both constant and variable repetition periods are outlined. The fundamental differences in the synthesis of ARF during the wobbling of the repetition period and the associated features of the structural schemes of filters are highlighted. The considered ARFs with complex weight coefficients and ARFs with auto-compensation are classified as ARFs with full adaptation and partial adaptation when performing each of these ARFs in a canonical or cascading form.

For the above variants of ARF construction, the principles of their implementation are considered, taking into account the properties of the correlation matrix of passive interference when the repetition period is wobbled. The features of ARF synthesis during the repetition period wobble are described, including the estimation of the interperiod phase shift of the clutter in each period, the asymmetry of the weight coefficients, and the estimation of the corresponding number of modules of the interperiod correlation coefficients of the clutter.

Enlarged block diagrams of ARF with complex weight coefficients and with an auto-compensator are presented. The problem of optimization of non-recursive rejection filters (RF) of high orders by the probabilistic criterion is considered. The statement of the optimization problem is formulated and an expression is given for the average probability in the Doppler interval.

1. Skolnik M.I. Introduction to Radar System, 3rd ed., New York: McGraw-Hill, 2001. – 862 p.

2. Richards M.A., Scheer J.A., Holm W.A. (Eds.). Principles of Modern Radar: Basic Principles. New York: SciTech Publishing, IET, Edison. 2010. – 924 p.

3. Melvin W. L., Scheer J.A. (Eds.). Principles of Modern Radar: Advanced Techniques. New York: SciTech Publishing, IET, Edison, 2013. – 846 p.

4. Radar Handbook / Ed. by M.I. Skolnik. 3rd ed. McGraw–Hill, 2008. 1352 p.

5. Popov D.I. Adaptive notch filter with complex weight // Vestnik Kontserna PVO «Almaz – Antej». 2015. no 2 (14). pp. 21-26. (in Russian).

6. Popov D.I. Autocompensation of the Doppler phase of clutter // Cifrovaja obrabotka signalov. 2009. no 2. pp. 30–33. (in Russian).

7. Popov D.I. Adaptive suppression of clutter // Cifrovaja obrabotka signalov. 2014. no. 4. pp. 32-37. (in Russian).

8. Popov D.I. Adaptivnije regektornjie filtrij kaskadnogo tipa // Cifrovaya obrabotka signalov. 2016. no. 2. pp. 53-56. (in Russian).

9. Popov D.I. Adaptive notch filter with real weights // Cifrovaya obrabotka signalov. 2017. no. 1. pp. 22-26. (in Russian).

10. Popov D.I. Optimizacja nerekursivnjih regektornjie filtrov s chastichnoj adaptaciej // Cifrovaya obrabotka signalov. 2018. no. 1. pp. 28-32. (in Russian).

11. Popov D.I. Rezhektirovanie passivnyh pomeh pri vobuljacii perioda povtorenija // Radiotehnika. 2015. no. 5. P. 97-101. (in Russian).

12. Popov D.I. Ocenivanie korreljacionnyh parametrov passivnyh pomeh // Radio-promyshlennost'. 2017. no. 1. P. 57-62. (in Russian).

13. Patent na izobretenie no. 2579998 RF, MPK H03H 7/12. Adaptivnyj rezhektornyj fil'tr / D.I. Popov, opubl. 10.04.2016, Bjul. no. 10. – 12 p. (in Russian).

14. Patent na izobretenie no. 2599621 RF, MPK H04B 1/10. Adaptivnyj rezhektor passivnyh pomeh / D.I. Popov, opubl. 10.10.2016, Bjul. no. 28. 16 p. (in Russian).

Robust algorithms for clutter rejection
D.I.Popov, The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan, e-mail:

Keywords: adaptation, weight vector, repetition period wobble, minimax criterion, clutter, rejection, robust al-gorithms, synthesis.

A qualitative definition of robustness is considered in relation to the MTI problem and a criterion for the synthesis of robust algorithms for adaptive rejection of clutter in the form of a modified minimax approach is introduced.

Based on the qualitative determination of robustness in relation to the MTI problem and the introduced criterion for the synthesis of robust algorithms, the synthesis and analysis of adaptive robust algorithms for clutter rejection are carried out. The problem of synthesis of adaptive algorithms for clutter rejection resistant to measurement errors is solved for all possible values of the es-timated parameters for the cases of equidistant and non-equidistant receipt of processed clutter samples.

The synthesis and analysis of adaptive robust algorithms for clutter rejection, the main properties and advantages of which are analyticity and comparative simplicity, is carried out; as well as the possibility of achieving the maximum or close to it efficiency in the absence of measurement errors of unknown parameters of the correlation matrix of the clutter, while the maximum loss value due to not taking into ac-count the shape of the energy spectrum of the clutter, in comparison with the ex-act optimal algorithms is only a fraction of dB (in particular, for the second-order notch filter (RF) is 0.16 dB).

It is shown that the existence, continuity, and modulo-boundedness of the derivatives of the vector of weight coefficients reduces the influence of a methodological or systematic measurement error. The synthesized robust algorithms for clutter detection neutralize the influence of random errors caused by various objective destabilizing factors on the calculation of the RF weight vector.

1. Skolnik M.I. Introduction to Radar System, 3rd ed., New York: McGraw-Hill, 2001. – 862 p.

2. Richards M.A., Scheer J.A., Holm W.A. (Eds.). Principles of Modern Radar: Basic Principles. New York: SciTech Publishing, IET, Edison. 2010. – 924 p.

3. Melvin W. L., Scheer J.A. (Eds.). Principles of Modern Radar: Advanced Techniques. New York: SciTech Publishing, IET, Edison, 2013. – 846 p.

4. Radar Handbook / Ed. by M.I. Skolnik. 3rd ed. McGraw–Hill, 2008. 1352 p.

5. Popov D.I. Adaptacija nerekursivnyh rezhektornyh fil'trov // Izvestija vuzov. Ra-diojelektronika. 2009. vol. 52. no. 4. P. 46-55. (in Russian).

6. Popov D.I. Autocompensation of the Doppler phase of clutter // Cifrovaja obrabotka signalov. 2009. no 2. pp. 30–33. (in Russian).

7. Popov D.I. Adaptive suppression of clutter // Cifrovaja obrabotka signalov. 2014. no. 4. pp. 32-37. (in Russian).

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Analyzing of the adaptive line enhancement of narrowband signal using adaptive interpolated IIR filters
Goriushkin R.S., e-mail:
Vityazev V.V., e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: digital signal processing, adaptive filtering, interpolated IIR filters, adaptive line enhancement, RLS.

Digital adaptive filtering has found application in many areas of digital signal processing: communication systems, radar, audio- and video data processing. A typical challenge is adaptive amplification of spectral lines in the presence of broadband noise. This paper investigates the use of digital adaptive interpolated filters with infinite impulse response in the problems of digital adaptive filtering of narrowband signals.

When the signal passes through the structure of the interpolated filter, additional spectral components appear. To exclude additional spectral components, a low-order smoothing filter is used. Therefore, the use of an interpolated filter assumes the construction of a two-stage system, including an interpolated IIR adaptive filter and an FIR or IIR smoothing filter.

Experimental studies were carried using the NumPy library. The research was carried out using the RLS algorithm for both basic and two-stage adaptive filter structures. It has been shown that, when using the same adaptation algorithm, interpolated IIR filter has an advantage in both speed and convergence accuracy.

The price for the improvement is the increase of the data memory in the delay line for storing intermediate samples of the signals, as well as the need to implement a smoothing filter.

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Mathematical models of delivering multi-packet messages via asymmetric communication channels with the LLC procedure
V.A. Tsimbal, e-mail:
S.E. Potapov, e-mail:
A.A. Potapova, e-mail:
Military Academy of the Peter the Great Strategic Missile Forces, Russia, Serpukhov

Keywords: duplex communication channels, markov processes, mathematical models, multi-packet messages, temporary characteristics, transition probabilities, the fundamental matrix.

The article presents the main provisions of mathematical models of the processes of delivering multi-packet messages via duplex communication channels with the LLC procedure.

At the control level of the logical channel, there is no provision for correcting errors that occur during transmission, but only checking their absence in the received frame by the checksum, so any distortion of the bits of the received frame will entail its retransmission in the future. At the same time, the longer the frame length in bits (bytes), the higher the probability of its distortion during transmission over the communication channel with interference.

The transmitted information frame of any duration contains a mandatory service part of a fixed size. Therefore, the smaller the information part of the transmitted frame, the more of these frames will need to be transmitted to deliver the entire message and more service information of the frame headers will be transmitted along with the useful message.

Consequently, an increase in the size of the transmitted information frames of the message on the one hand reduces the total time of its transmission by reducing the share of the transmitted service information of the headers, and on the other hand increases the probability of incorrect delivery of these frames, and the number of their repeated transmissions. This increases the total time to deliver the message. Therefore, an urgent task is to choose the optimal value of the volume of the information part of the message packets, which ensures the minimum average time of its delivery over the communication channel.

To determine the optimal value of the volume of the information part of the message packets, a mathematical model of this process is developed and studied on the basis of the apparatus of homogeneous absorbing finite Markov chains (PCMC).

Moreover, channels with different logical forward and reverse channels are considered. The first of the above mathematical models takes into account the worst quality in terms of the probability of a bit error of a direct logical data transmission channel. The second of the models under consideration allows us to determine the timeliness of delivering messages over a connected virtual connection with handshaking at the transport layer of the OSI model.

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Development of an algorithm for detecting polyps on endoscopic images using convolutional neural networks
A.A. Lebedev, e-mail:
V.V. Khryashchev, e-mail:
A.S. Srednyakova, e-mail:
E.M. Kazina, e-mail:
P.G. Demidov Yaroslavl State University, Russia, Yaroslavl

Keywords: deep learning, convolutional neural network, augmentation, neural network algorithm, basic network, endoscopic image analysis, colonoscopy, polyp detection, interlacing, deinterlacing, polyp video database, post- processing of results, algorithm quality assessment metric.

The purpose of this paper is the development of an algorithm for detecting polyps on endoscopic images of the colon using a convolutional neural network based on the SSD architecture.

For research, we have collected our own database of colonoscopy images. The work was carried out jointly with endoscopist doctors of the Yaroslavl Regional Clinical Oncological Hospital. Today this base is closer to a real practice situation. Videos and images were taken from the Olympus CF-Q180AL and Olympus CF-Q190AL video colonoscope models, which were used with the Olympus EVIS EXERA II and EXERA III video system centers. In the course of the work, 67 video fragments of colonoscopy of 64 patients were received and processed. The average length of one video clip was 15 minutes. 6430 images of polyps with a resolution of 626x532 pixels were obtained from video fragments.

A modified version of input data augmentation is proposed. When using it, the image is converted from the RGB color space to HSV, the brightness, contrast, saturation, and hue are randomized within the specified limits, the image is also randomly rotated by 90, 180, and 270 degrees with a probability of 0.5, horizontal and vertical mirroring, cut out patches from the image at random and resize them with different aspect ratios. The best results of the SSD neural network were obtained using the developed modified version of augmentation.

The developed neural network algorithm has a performance sufficient for analyzing the video stream in real-time and also has relatively high values of the algorithm quality assessment metrics. The highest metric value F1 = 81.53 was obtained for the SSD algorithm with a VGG-512 backbone network.

For assessing the performance of the trained neural network models, a test was carried out on a personal computer with the following characteristics: CPU AMD Ryzen 7 3800X, RAM 64 GB, GPU GeForce GTX 1080 Ti. The test measured the processing time of a short video fragment, consisting of 1249 frames. For the algorithm based on SSD VGG-300, the processing speed was 62 frames per second, for SSD VGG-512 - 55 frames per second, and for SSD MobileNet-300 - 84 frames per second. Thus, the proposed algorithms can be used to process an endoscopic video stream in real-time.

A promising direction for further research is improving the quality of the proposed algorithm by post-processing the results using additional information from adjacent frames of the video stream, as well as improving the quality of the input image through the use of deinterlacing algorithms.

The reported study was funded by RFBR, project number 19-37-90153.

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