Digital Signal Processing

Scientific & Technical


“Digital Signal Processing” No. 3-2022

In the issue:

- two-dimensional fast fourier transform

- multichannel equalizers of acoustic channels
- modeling of radio reflections systems
- visualization of hyperspectral images
- classification of reference micromarks images
- application of convolution neural networks
- edge detection of objects on earth imagery
- detection visual similarity of images
- synthesis of non-recursive rejection filters
- multidimensional signal structures forming
- wavelet introscopy of human biosystems

Two-dimensional fast fourier transform with variable parameters
O.V. Ponomareva, e-mail: ponva@

A.V. Ponomarev, e-mail:
N.V. Ponomareva, e-mail:
Kalashnikov Izhevsk State Technical University (Kalashnikov ISTU), Russia, Izhevsk
Sevastopol State University, Russia, Sevastopol

Keywords: information technology, Fourier processing, finite signal, parametric discrete Fourier transform, two-dimensional discrete Fourier transform with variable parameters, separability of the transform kernel.

The development of information technologies has significantly expanded the scope of application of digital Fourier processing of finite discrete signals. Among them are such subject areas as tomography, active and passive sonar, radar, seismology, technical diagnostics, medicine, forensic cybernetics, and artificial intelligence.

The complication of problems solved by digital Fourier processing in information technology has stimulated the transition from one-dimensional to two-dimensional digital Fourier processing. A systematic analysis of the transition from the one-dimensional discrete Fourier transform (DFT) to the two-dimensional discrete Fourier transform (2D DFT) showed that, firstly, such a transition is far from trivial and, secondly, the transition is primarily qualitative, not quantitative character. At the same time, the generalization of the results of the two-dimensional case to the multidimensional one, as a rule, does not cause difficulties, since it is mainly quantitative, not qualitative.

As is known, for the practical application of Fourier processing methods, expanding the scope of their application, an important role belongs to the procedures for the rapid implementation of the corresponding Fourier transforms. The story of the FFT algorithm, proposed in 1965, is a vivid confirmation of this.

The article deals with the solution of an important and urgent problem of developing fast algorithms for implementing a new discrete Fourier transform: a two-dimensional discrete Fourier transform with variable parameters (2D DFT-VP). In this paper, the following three groups of methods for improving the speed of 2D DFT-VP are proposed and studied.

The first group of methods for improving the speed of 2D DFT-VP is based on the separability property of the core of 2D DFT-VP and the use of one-dimensional parametric DFTs (DFT-P). The second group of methods for improving the performance of 2D DFT-VP is based on the separability property of the 2D DFT-VP kernel and the use of one-dimensional parametric fast Fourier transforms (1D FFT-P). The third group of methods for improving the performance of 2D DFT-VP is based on the 2D Fast Fourier Transform (2D FFT-VP) in vector base 2, with space decimation.

A comparative analysis of the effectiveness of the proposed three groups of methods for improving the speed of 2D DFT-VP based on a computer complex developed in the fourth generation language MATLAB (4GLS) was carried out.


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Multichannel Equalizers of Frequency Response of Acoustic Channels
V.I. Djigan, e-mail:

Institute for design problems in microelectronics of Russian Academy of Sciences, Moscow, Russia

Keywords: room response, equalization, adaptive filter, LMS, NLMS, RLS, traditional x-filtered algorithm, modified x-filtered algorithm.


This paper considers the adaptive equalizers of the frequency responses of the acoustic wave propagation channels. The equalizers use the so-called traditional and modified x-filtered adaptive signal processing algorithms. Comparing to the traditional x-filtered algorithms, the modified ones allow to accelerate the equalizer convergence if the computationally simple gradient algorithms like the Least Means Square (LMS) or the Normalized LMS (NLMS) are used for the equalizer weights computation. Besides, the modification allows to use the computationally complex but efficient Recursive Least Squares (RLS) adaptive algorithms in the x-filtered equalizers because the algorithms cannot be used in the traditional x-filtered equalizers. The multichannel equalizer architectures and the computational procedures of the traditional and modified adaptive filtering algorithms are presented. The results of computer simulation demonstrate the efficiency of the equalizers in terms of such quality indicators as: the ripple of the amplitude-frequency characteristic of the equalized acoustic channel, the distance between the curves of the graphs of the power spectral densities of the undistorted speech signal and the same signal that passed through the equalizer and the acoustic channel, the duration of the adaptive filter transient response and the value of its steady state error signal. The equalizers unsure about 2 dB ripples in the main part of the equalized frequency response of the acoustic channel except the low and high frequency regions. The equalization quality degrades in the high frequency region in the case of the NLMS algorithm usage. The proposed solution can be easily extended to the Multi-Input and Multi-Output (MIMO) equalizers. The MIMO equalizers allow to improve the quality of the sound listening in the selected area of a room.

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Visualization of hyperspectral images in the task of decoding small-sized, low-contrast objects
V.V. Shipko, e-mail:
S.M. Borzov

MESC AF «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy», Russia, Voronezh
Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sci-ences, Russia, Novosibirsk

Keywords: hyperspectral images, contrast, probability of detection, decryption.

As is known, modern samples of hyperspectral equipment cover the visible and infrared spectral range with the formation of hundreds of spectral images with a spectral resolution of a unit of nanometers. Processing of hyperspectral images (HSI) allows for decryption and recognition of objects based on spectrum analysis. However, in a number of tasks, information about the spectra may not be enough. In this case, the visualization of the GIS is carried out, which allows the use of spatial features during decryption. Considering all spectral images sequentially is a time–consuming and inefficient task. Basically, this task is solved at the post-processing stage of the already formed GSI by synthesizing a new image.

The article analyzes the main approaches to the visualization of GIS, highlights their advantages and disadvantages. A new approach is proposed and an appropriate algorithm for contrast visualization of small-sized, low-contrast objects is developed. The developed algorithm is based on calculating the contrast coefficient of the specified spectral characteristics of the object and background, finding local maxima of the spectral contrast function, selecting a set of spectral images from the corresponding maxima and synthesizing a grayscale or color image from this set. Examples and results of numerical studies confirming the effectiveness of the proposed approach are presented.

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Binary classification of reference micromarks images in probe microscopy using conventional processing methods

P.V. Gulyaev, e-mail:
Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, Russia, Izhevsk

Keywords: micromarks, reference labels, probe microscopy, image processing, recognition, binary classification.

Reference micromarking is used to define the boundaries of a certain area of the surface, to identify products or the location of protective nanomarkings. The marking may consist of individual imprints or a series of adjacent imprints, continuous lines or geometric shapes. The task of binary classification (recognition) of microlabeling images and background surface relief obtained in the process of micromarks searching for using a probe microscope is considered. The reference marking and its images were obtained using a probe microscope. For this purpose, the modes of semi-contact force microscopy and nanolithography were used. Typical images of markings consisting of segments oriented to each other at right angles are presented. These images are distinguished by the following features:

1. low-frequency components that reduce the contrast of marking elements;
2. background elements of the surface relief near the marking, leading to preferential registration of straight line segments along their borders;
3. interference, contamination or suboptimal settings of the probe microscope, reduce the contrast of the marking;
4. fragmentation of the marking and the segments approximating it.

The analysis of the possibilities of conventional processing methods for recognizing markings on images is carried out. In particular, the Fourier-Mellin transform, the Sift detector-descriptor together with the Ransac method, the contour extraction method, and the Hough transform were considered. A classification algorithm based on Erosion operation, threshold filtration and Hough transform is described. The need for an erosion operation, threshold filtration is due to the above-mentioned features of micro-labeling images. The classification used structural analysis of the Hough transform results, configured to search for straight line segments. As recognition criteria, it is proposed to use the proportion of registered segments with specified angles of mutual orientation or the local predominance of such segments in the histogram of the distribution. The efficiency of the proposed methods is established on different types of images of markings and background relief. Metrics for evaluating the effectiveness of the proposed solutions are given.

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Application of convolution neural networks for identification of structurally homogeneous areas on Earth remote sensing images
V.A. Eremeev, e-mail:
A.A. Makarenkov, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

remote sensing, identification of homogeneous areas, texture features, convolutional neural network U-Net.

The analysis of different approaches to automatic identification of objects with uniform brightness and structure on Earth remote sensing images is presented. Marking of homogenous areas on the satellite images is crucial for such important tasks as radiometric calibration, signal-to-noise level estimation, adaptive compression, etc. This article evaluates an application of convolutional neural networks for the segmentation of satellite image into two classes: homogenous and non-homogenous areas. U-net is chosen as the appropriate neural network architecture because of comparatively low requirements for the training set size and good identification performance. Due to the notably big variation of brightness and structure of the areas which could be considered as homogenous augmentation of the U-net input is proposed: additional channel with texture feature is added to the satellite image. The texture feature is chosen amongst Haralick features and during performance evaluation the “Sum of square” is selected.

Proposed approach of using U-net with an addition of texture feature is assessed on the real images from Russian remote sensing system “Resurs-P”. Results of the performance evaluation showed that proposed approach produces from 5% to 14% increase (F-measure) of homogenous areas identification compared to the U-net network processing data without texture feature.

1. Ronneberger O., Fischer P., Brox T. Convolutional Networks for Biomedical Image Segmentation // Medical Image Computing and Computer-Assisted Intervention (MICCAI), Springer, LNCS, vol. 9351, 2015, pp. 234-241.

2. Haralick, R. M., Shanmugam, K. & Dinstein, I. Textural Features for Image Classification // IEEE Trans. Man, and Cybernetics 3, 1973. pp. 610-621.

3. Marina Sokolova, Guy Lapalme. A systematic analysis of performance measures for classification tasks // Information processing and management, 2009, vol. 45, no. 4, pp. 427-437.

Algorithm for detecting visual similarity of images
M.B. Nikiforov:

V.Y. Tarasova:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: visual search, visual similarity, convolutional neural networks, hash.

The article considers an algorithm for visual search of images similar in content. The search is carried out in the local database. The article discusses the comparison of the developed algorithm with the existing ones.

The article reveals the algorithm for generating query metrics by content. Currently, there are metric and non-metric algorithms for assessing the similarity of images. Content evaluation was carried out using the MobileNet v2 convolutional neural network. The last layer of the neural network was used, convolution and subsampling operations were used, which allow you to convert images into a hash that is invariant to various distortions, which allows you to find identical images in the search database with high efficiency. The algorithm makes it possible to increase the probability of finding images based on their content by hashing each image from the search base using convolutional neural networks. The developed algorithm for detecting visual similarity of images does not use a priori information, but takes into account only image pixels. It can be used in solving problems of visual search, classification, as well as software for systems for searching attractions from photographs in travel companies, in text and image search systems, in open access electronic catalogs (local history museums, cadastral maps).

The results of the algorithm presented in the article show its effectiveness. The comparison was carried out with known content search algorithms. The short running time and high efficiency of the presented algorithm make it possible to use such an application on a personal computer. To reduce the operating time of the algorithm for detecting moving objects, it is planned to use parallel computing technologies.

1. Tarasov A.S., Tarasova V.Yu. Development of a search system for similar images in local storages // In the collection: Neuroinformatics-2020. Collection of scientific papers. XXII international scientific and technical conference. - 2020. - S. 286-293.

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4. Babenko A., Lempitskiy V. Effektivnyy algoritm poiska blizhayshikh sosedey pri bolshikh obyemakh poiskovoy bazy // Trudy 54-oy nauchnoy konferentsii MFTI. Innovatsii i vysokiye tekhnologii. Dolgoprudnyy: 2011. – S. 16-17.

5. El-saban M.A., Tavfik A.I., Chalabi A.A.M.T., Sayyed S.KH. Poisk izobrazheniy na yestestvennom yazyke // Patent na izobreteniye RU 2688271 C2, 21.05.2019. Zayavka ¹ 2016144699 ot 14.05.2015.

6. Noa Garcia, George Vogiatzis Learning Non-Metric Visual Similarity for Image Retrieval the IEEE International Conference on Computer Vision Workshops (ICCVW) – 2017

7. Venice Erin Liong, Jiwen Lu, Gang Wang, Pierre Moulin, and Jie Zhou. Deep hashing for compact binary codes learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition – 2015.

8. Albert Gordo, Jon Almazan, Jerome Revaud, and Diane Larlus. Deep image retrieval: Learning global representations for image search. In Proceedings of the IEEE European Conference on Computer Vision – 2016.

9. Wenjie Luo, Alexander G Schwing, and Raquel Urtasun. Efficient deep learning for stereo matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition – 2016.

10. Laurens van der Maaten Geoffrey Hinton Visualizing non-metric similarities in multiple maps. The Author(s) 2011. This article is published with open access at DOI 10.1007/s10994-011-5273-4

11. Tomas Skopal On Fast Non-metric Similarity Search by Metric Access Methods. (Eds.): EDBT 2006, LNCS 3896, pp. 718–736 – 2006.

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16. Tarasova V. YU., Tarasov A. S., Grinchenko N. N. Algoritm obnaruzheniya sovpadeniy v kollektsii izobrazheniy // v sbornike trudov Mezhdunarodnogo nauchno-tekhnicheskogo foruma STNO-2019. – Tom 4. – S. 164-168.

17. Bodrov O.A., Tarasov A.S., Tarasova V.Y., Bodrova I.V. IMAGE SEARCH ALGORITHM IN LOCAL DATA BASE 8th Mediterranean Conference on Embedded Computing, MECO 2019 - Proceedings. – 2019. – Ñ. 453-455.

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19. F. Sabahi; M. Omair Ahmad;MNS Swamy Content-based Image Retrieval using Perceptual Image Hashing and Hopfield Neural Network. 2018 IEEE 61st International Midwest Symposium on Circuits and Systems (MWSCAS)

Synthesis of non-recursive rejection filters high orders
D.I.Popov, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: sub-interference visibility coefficient, clutter transmission coefficient, quantization errors, clutter, rejection filter, synthesis.

A method for the synthesis of non-recursive rejection filters is considered, based on the separate formation of the cutting band and the passband and allowing, with a limited filter order, to pro-vide the specified requirements for the cutting band, a given unevenness in the passband and the minimum possible width of the transition band of the frequency response.

The formation of the cutting band is based on the placement of mutually displaced zeros of the system function on the unit circle. The formation of the bandwidth is based on the methods of linear programming from the condition of minimizing the transition bandwidth of the filter at a given value of the maximum error in the bandwidth.

As a result, the proposed method for the synthesis of digital non-recursive rejection filters allows for a given filter range to obtain the specified parameters of passband and notch at the minimum possible width of the transition band. A comparative analysis of the quality of interference rejection by filters synthesized by the proposed and known methods according to the criteria of the interference transmission coefficient and the coefficient of subsurface visibility is carried out.

The comparative analysis confirmed the possibilities of the proposed method to synthesize effective rejection filters with high indicators of the quality of Doppler signal isolation against the background of correlated interference. The simplest synthesis method based on the Fourier series expansion with the subsequent introduction of a weight function, due to its simplicity, can be used in the absence of strict requirements for filter parameters, while providing acceptable results.

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

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The method of forming optimal multidimensional signal structures and their properties
Bykhovskiy M.À., e-mail:

Keywords: Formation of optimal multidimensional signals, error-correcting codes, message transmission rate, energy efficiency, noise immunity of signal reception.

The article proposes a method of forming ensembles of multidimensional signals with hyperphase modulation (HPPM) for transmitting messages with a certain number. The dependence of the specific rate of transmission of messages with HPPM on the value of the minimum distance between the signals, as well as issues related to the structure of this ensemble are investigated. A method for estimating the energy losses of communication systems using two-dimensional signal ensembles and error-correcting codes for the transmission of messages is considered, in comparison with systems in which HPPM are used for this. Formulas are obtained that make it possible to determine the dependence of the specific signal transmission rate on the normalized value of the minimum distance between the signals belonging to the HPPM, and the issues of the formation of signal modulation indices when transmitting messages with a certain number are considered. It is shown that, using HPPM, it is possible to ensure high reliability of message reception without the use of error-correcting codes (ECC). Estimates of the energy losses of communication systems with a ECC are given in comparison with systems in which signals from HPPM are used, as well as an increase in the duration of signals in them to ensure the required communication reliability. The results of the article show that it is advisable to use ensembles of signals with HPPM in new systems that must ensure the transmission of messages over communication channels at a high speed.

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A Modification of YOLO Object Detector for Real-Time Implementation on FPGA
D.A. Vasilev, e-mail:
T.V. Levkin, e-mail:
P.N. Skonnikov, e-mail:
D.V. Trofimov , e-mail:
Bauman Moscow State Technical University, JSC «S&P Complex «Alpha-M», Russia

Keywords: digital image processing, artificial neural networks, YOLO, backpropagation.

The principle of YOLO object detector operation is considered. The functions of processing the array elements coming from the last convolutional layer are analyzed, the most difficult operations implemented on FPGAs have been identified.

It is shown that three different types of functions are used to process various parameters: the logistic sigmoid is used to predict the positioning accuracy and the bounding boxes vertical and horizontal offsets, the exponent is used to predict the height and width of boxes, and the SoftMax function is used to predict class probabilities. Formulas for the derivatives of these functions, which are required when training the network, are given.

The multiple execution of given transformations, required for the YOLO detector operation, needs the calculation of an exponential function values. Methods of calculus mathematics make it possible to obtain a fairly accurate approximation of the exponential for a certain number of terms of the corresponding series taken into account.

Nevertheless, to ensure the necessary accuracy of the correspondence between these transformations and operations performed on hardware, an unacceptably high computing power is required. We propose a different approach that does not require an exact approximation of given transformations. The logistic function is replaced by a rational sigmoid, the exponent is replaced by a shifted fourth-order parabolic curve. The modified SoftMax function also uses a shifted parabola.

For the proposed transformations, formulas for calculating the loss back-propagation are analytically derived.

Using the obtained formulas, a YOLO detector based on a modified neural network was trained. The modified YOLO detector with the proposed functions is implemented on a specially designed Xilinx FPGA board. Experimental studies of the board showed the high speed of the detector (more than 60 frames per second) and the high quality of object detection and classification. When processing typical video recordings, the values of the output array of floating-point numbers obtained on the video card of a personal computer coincided with the corresponding values calculated by hardware on the board with an error of less than 1%. The effectiveness of the proposed transformations is confirmed by the qualitative characteristics of object recognition, which are not inferior to the characteristics of the original detector.

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