Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 1-2014

In the issue:

- generalization of the Goertzel algorithm;
- multirate adaptive filter;
- regeneration of frequency;
- methods of modulation recognition;
- image compression;
- wavelet transformation of EEG;
- multichannel jammer canceller;
- hardware realization on the FPGA and GPU.

Generalization of the Goertzel algorithm and the sliding parametric discrete Fourier transform algorithm
Ponomarev V.A. Doctor of Technical Sciences, professor of the Kalashnikov Izhevsk State Technical University,
Ponomareva O.V. Ph.D. (technical science), associate professor of Kalashnikov Izhevsk State Technical University
Ponomarev A.V. Ph.D. (economy), chief of staff of Central Election Commission of Udmurt Republic
Ponomareva N.V. Director of software testing "NPO Computer" Ltd.,

Keywords: parametric discrete Fourier transform, slide parametric discrete Fourier transform, detection, harmonic component, Goertzel algorithm, comb filter.

In this paper we introduce a new procedure for digital block processing, which is called by the authors as procedure of digital block processing with accumulation. On the basis of the procedure two generalizations of Goertzel algorithm were proposed.
First generalized Goertzel algorithm, unlike standard Goertzel algorithm allows simultaneous provide:
- high resolution digital spectral processing;
- stability of the filter.
Second generalized Goertzel algorithm, unlike standard Goertzel algorithm allows simultaneous provide:
- high resolution digital spectral processing;
- stability of the filter;
- full control over the resonant frequency of Goertzel filter.
The paper considers the generalized algorithms of one-bin sliding DFT (SDFT) and parametric one-bin sliding DFT (SDFT-P). The proposed algorithms significantly reduce, in comparison with traditional SDFT and SDFT-P algorithms, the number of operations required to force SDFT and SDFT-P algorithms work in a sliding measurement mode.
Advantage, which is provided by the proposed generalized algorithms, is approximately to 4 times reduce the number of real multiplications and 2 times reduce the number of real additions.
In addition, by applying the proposed generalized Goertzel algorithms in SDFT and SDFT-P structures (first and second, respectively), possible to achieve a high-resolution sliding spectral analysis while maintaining the stability of the filters.

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

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

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

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

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

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

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Cascade connection optimal linear phase FIR filters
N. O. Vzduleva, Post-graduate, Kalashnikov Izhevsk State Technical University,
V. B. Gitlin, DSc in Engineering, Professor, Kalashnikov Izhevsk State Technical University,

Keywords: chromatograph, FIR filter, cascade connection, optimal, signal/noise ratio, software package MATLAB.

Chromatographic analysis methods [1] are sufficiently accurate methods of determining the presence of a substance component in the sample, and calculating its concentration [1]. Chromatographic assay sensitivity is determined by the relation of energy useful chromatograph signal to background noise [1]. To increase the signal / noise ratio filtering signal having a corresponding frequency response can be used. FIR filters with linear phase [2] are preferable as chromatographic analysis is based on accurate timing measurements of output chromatographic signal. Designing filter is preferably carried using Chebyshev approximation ensures the minimum order filter [2]. Experiments with the chromatographic signals has been shows that the order of the designed FIR filter should have rather high [3]. Trying to estimate the parameters of the filter Remez algorithm , by finding optimal solutions of equations by Gauss [4 ] has been show that the solution diverges already at odds filter order N = 51. Using an algorithm Pakrsa - McClellan [5] is also not allowed to increase the order of the calculated filter. Limited accuracy of calculations , even at higher bit number representation requires special methods for calculating FIR filters using of a Chebyshev approximation [4]. To create the optimal FIR filter with linear phase of high order , it was decided to construct a FIR filter by cascading number of optimal FIR filters with the same lower order. Such filters can be attributed to the quasi-optimal . Ones preserve phase linearity, require significantly less computation for calculating the parameters of the filter. Ones are not inferior about quality signal filtration by the optimal FIR filters of the same order, calculated using the software package MATLAB. Application of FIR filter with linear phase, consisting of the cascade of two optimal FIR filters 51-th order , allowed to increase the signal / noise ratio at the output of the Chromatographic is almost eight times.

1. Sacodinsky R.I., Brajhnikov B.B. Volkov S.F. Analytical chromatography. Moscow: Chemmistry, 1993.

2. L.R. Rabiner, B. Gold. Theory and Application of Digital Signal Processing. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, USA., 1975/

3. N.O. Vzduleva, V.B. Gitlin. Selection of noise chromatograph filter parameters / Information Technology of Science, Industry and Education. Publishing House ISTU, Izhevsk, 2014. - P. 40-42.

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Optimization of the multirate adaptive filter with least-mean-square algorithm in equal-width subbands
Linovich A.Yu.,

Keywords: multirate adaptive filter, least-mean-square algorithm, optimization, computer simulation, equal-width subbands.

The main subject is solving of the optimization problem for the multirate adaptive filter with least-mean-square algorithm in equal-width subbands. Analytical estimations for the best values of the main parameters of the multirate adaptive filter are derived. The results of the computer simulation which confirm the theoretical study are supplied. The analysis of the theory and experiments results in the next decisions. First, while the optimal ratio between the decimation ratio and quantity of channels holds true, large changes of the quantity of channels tends to insignificant increase in the computational complexity. So this ratio may be considered as the main condition of optimality. Second, for the little quantity of channels the discreteness of the quantity of channels and decimation ratio should be taken into account. That is, in the neighborhood of the theoretical minimum point it is necessary to choose those couples of numbers which are closer to the optimal ratio.

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Peculiarities and characteristics of frequency regeneration with the RF signals recording-reproducing digital functional devices in the multisignal mode
Kozlov S.V., Doctor of Engineering, the deputy chief of chair of radio engineering and antenna and feeding devices of Air Force Education and Research Centre “The Zhukovsky and Gagarin Air Force Academy”
Mazilov S. L., Candidate of Technical Sciences, the senior teacher of chair of radio engineering and antenna and feeding devices of Air Force Education and Research Centre “The Zhukovsky and Gagarin Air Force Academy”
Uskov A.V., graduated in a military academy of chair of radio engineering and antenna and feeding devices of Air Force Education and Research Centre “The Zhukovsky and Gagarin Air Force Academy”,

digital device of record and reproduction of radio signals, frequency restoration, range.

In a number of practical appendices of signal's processing the problem of restoration (reproduction) of frequency on the basis of supervision of radio signals on a limited interval of time is solved. For the solution of this task digital devices of record and reproduction of radio signals (digital radiofrequency memory - DRFM) now are widely used. Standard are a situation of functioning of DRFM in a multisignal (multifrequency) mode in the presence of noise and harmonious hindrances.
Research of the main regularities and receiving quantitative estimates of influence of a multifrequency mode and hindrances on quality of restoration of bearing frequencies of radio signals with use of digital devices of record and reproduction were carried out with use of methods of statistical radio engineering and imitating modeling.
The case formation of harmonious fluctuation from the written-down short digital sample by duration was considered , where - the period of the digitization consisting from complex counting with estimates of phases of counting , with method use " sewing together of phases". The essence of a method consists in: allocation of a short site - an analysis interval from the first , duration ; search among counting of a copy of a radio signal at , , groups from the counting which estimates of phases have the minimum average square of a deviation from estimates ,; calculation of average shift of phases between counting during signal reproduction ; formation of demanded number counting of restored harmonious fluctuation by cyclic rewriting (reproduction) of the written-down site with the reproduction period and shift on frequency on .
For a case of existence of the unique harmonious fluctuation and noise for a mistake's square root restoration of frequency of a look is received. The expression connecting parameters of algorithm of restoration of frequency (Tb, Ta), spectral density of capacity N0 noise in a strip of frequencies of DRFM and capacity Pñ harmonious signal.
The main regularities of a multifrequency operating mode are revealed on an example of biharmonic fluctuation by methods of the spectral theory and imitating modeling. It is shown that:
in a case when the period of reproduction is chosen equal to the period of multifrequency fluctuation, exact restoration of frequency of each harmonious component from structure of multifrequency fluctuation will take place;
if the condition of equality of the period of reproduction and the period of multifrequency fluctuation is not carried out, errors of restoration of frequency of each harmonious component and enrichment of a range of the restored fluctuation will take place;
at equality of amplitudes of harmonious components of biharmonic fluctuation, an error of reproduction of their frequencies are equal on the module and have a different sign; at increase in the relation of amplitudes of harmonious components of biharmonic fluctuation the error of reproduction of frequency of a bigger component on amplitude decreases approximately in proportion to the relation of amplitudes, and the error of reproduction of frequency of a smaller component on amplitude slightly increases;
with increase in time of record and increase in a rating of frequencies of an error of reproduction of frequencies of harmonious components of multifrequency fluctuation decrease.
It is shown that at restoration of frequencies with use of digital devices of record and reproduction on short samples situations of a multialarm mode are the most dangerous at small frequency off-tuning of signals. The received results can be used at justification of characteristics and research of efficiency of functioning of digital devices of record and reproduction of radio signals.

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Estimation method for interaction of local extremum for matrices of coefficients in continuous wavelet transforms of EEG signals

Turovskij Ya.A., Kurgalin S.D., Semjonov A.G. , Voronezh state university

electroencephalogram, continues wavelet analysis, local spectrum, chain of the local maximum.

Application of wavelet transformations for analysis of biomedical signals has helped to expand the volume of useful information, obtained from processing of data recorded from humans or animals during clinical or physiological studies. However, the currently applied methods, based on continuous wavelet transformations, in most cases do not use an approach based on a dynamic estimation of the spectral characteristics of the time series of the analyzed data. Consequently, it is important to establish such methods, which take into account that biomedical signals, including electroencephalograms (EEG), are the result of complex nonlinear interaction of a large number of oscillators, which generate electrical signals from the studied organs and systems. The resulting data are also influenced by features of organs and tissues, through which the signal passes before it reaches the transducer. Therefore, we need an approach aimed at all-round analysis of biomedical signals, including EEG data, based on the continuous wavelet transformation, which will help to identify the features of processes taking place in the studied organs and systems. These features, as it was already noted, are reflected in the form of specific dynamics of behaviour in the chains of local maxima (CLM) or minimum (ClMin) matrices of squares of coefficients of a continuous wavelet transformation. The given paper is aimed at developing a research method for studying the dynamics of local extrema for matrices of second powers of coefficients for continuousEEG signals wavelet transformations to identify areas in which there is a high concentration of local maxima and minima chains. An analysis of these areas will allow to evaluate the performance of the processes occurring in organs and systems that generate these signals.
In this paper we propose a method of analysis of biomedical signals on the example of the EEG based on evaluation of structures formed in the result of interaction between chains of local maxima - CLM and chains of local minima - CLMin in space (a,b) "the scale of the wavelet transformation - time". We have developed the algorithms of detection for such structures, which are called "areas of convergence of extremes" - ACE. A number of computative experiments held with different types of model signals (monofriquency harmonics, the sum of several harmonic signals, amplitude modulated harmonic, "white" and "colored" noises) showed that the formation of the ACE is connected with the phenomenon of CLM and CLMin drift in frequency space. We have demonstrated a number of approaches for handling the results of a research on the example of the PEL, and determined an approach to the classification of the identified EEG phenomena.
The obtained method can be further applied for studying a wide range of signals of medico-biological character. This will significantly expand the range of detected phenomena while analysing biomedical signals, and, as a result, to raise the general informativeness of clinical-physiological studies.

1. Turovskij Ja.A. Programma PikWave 1.0. Zaregistrirovana v Rossijskom agentstve po patentam i tovarnym znakam, registracionnyj ¹ 2006613500.

2. Turovskij Ja.A., Semjonov A.G., Kiseleva E.V., Horoshih N.V. Programma Wavemax 1.0. Zaregistrirovana v Rossijskom agentstve po patentam i tovarnym znakam, registracionnyj ¹ 2012614720.

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Digital halftone image filtration based on markov chain with several states
Petrov E.P., Kharina N.L., Rzhanikova E.D., Vyatka State University, Kirov,

Keywords: digital halftone image, Markov chain, non-linear image filtration.

The requirements for volume, quality and speed of transmitted data are increasing at the moment. The most capacious data carrier is a color digital image composed of a combination of monochromatic digital halftone images described as a binary g-digit numbers set. The number of the brightness gradations in monochromatic halftone images is equal . The digital halftone image representation by binary numbers with more than eight digits allows to improve the quality of the images transmitted over communication channels. However, the higher the digit capacity of a digital halftone image is, the more time is required for its transfer. Therefore the problem of the time transfer reduction is actual and can be solved by a transition from a multigraded to a low-graded image representation of the transferring side of a communication channel and back to a multigraded image of the receiving side. For this purpose a g-digit halftone image is presented by a set of g digit binary images. Each of them is a superposition of two one-dimensional Markov chains on an orthogonal image lattice. Each of the two Markov chains is characterized by two equiprobable states and one-step transition probability matrixes for both horizontal and vertical directions. Note that digital binary images included in a digital halftone image are correlated among themselves, and the higher the digital binary images order is, the higher its correlation is. Constructing the neighboring digital binary image clusters that should be uniform in size, we get an image with a smaller number of brightness gradation. For example, clustering the digital binary images forming the 8-digit halftone image pairwise, we get low-graded images with four brightness gradations. Suppose that the clusters of neighboring binary images, as well as digital binary image, are two-dimensional Markov chains with several states. The clusters of neighboring binary images can be transmitted through a communication channel by multiposition phase-shift keyed signals. Using this kind of signals reduces the noise stability of image transfer as compared with binary signals. However, this reduction is compensated by means of non-linear filtration algorithms synthesized in this work, efficiently realizing the statistical redundance caused by the interdigit correlation of an image.
The white Gaussian noise model was used, the filtration simulation of a halftone image transmitted by means of binary and low-graded images was carried out. For the evaluation filtration test, a mean square error was calculated at the input and at the output of the nonlinear filter. As a result of the filtration, the mean square error decreased four times in both cases.
Hence, a transition from a g-digit halftone image to a low-graded image allows to use the statistical redundance of an image as much as possible and to reduce the image transfer time, i.e. "to compress" the digital image by a number of times equal to the number of digital binary images included into the low-graded image.

1. Petrov E.P., Trubin I.S., Chastikov I.A. Non-linear filtration of video sequences of digital halftone images of Markov type. // Uspekhi sovremennoi radioelektroniki (Achievements of Modern Radioelectronics) - 2007, no.11, pp. 54-87.

2. Petrov E.P., Medvedeva E.V. Non-linear filtration of statistically related video sequences based on hidden Markov chains // Radiotekhnika i elektronika (Journal of Communications Technologies and Electronics), 2010, Ò.55, ¹ 3, pp. 330-339.

3. Medvedeva E.V. Adaptive non-linear filtration of color video images // Informatsionnye tekhnologii (Information Technologies), ¹11, 2009, pp. 61 - 64.

Image compression based on block decomposition in the wavelet-packets domain
Prof. Dr. Sergei V. Umnyashkin, National Research University of Electronic Technology, e-mail:
PhD student Ruslan R. Gizyatullin, National Research University of Electronic Technology, e-mail:

Keywords: adaptive basis selection, block decomposition, discrete wavelet transform, wavelet packets, image compression.

An algorithm of still image compression is proposed, which is based on wavelet packet transform. The compression algorithm uses a limited number of wavelet packet bases which are adjusted to the local spatial properties of the image processed.
First, 4-level wavelet decomposition is applied to an image to be compressed. Then the 6 subbands of the 2 highest frequency levels of the wavelet spectrum are split into adjacent square blocks, three 16×16 blocks and three 32×32 blocks of wavelet coefficients from 6 different subbands. All sets of those 6 blocks in the wavelet domain correspond to 64×64 pixel blocks mapping the original image.
The sets of 6 wavelet decomposition blocks are processed independently. We selected some 27 different templates from all possible wavelet-packet bases which our algorithm tests then as an alternative for each set of 6 wavelet blocks, the same filter banks are applied. Entropy of the bases is used as a decision rule for the basis selection.
When the wavelet packet bases are selected for all block sets then scalar quantization is applied to the decomposition coefficients. The quantized coefficients and the keys defining the basis structure are encoded by context arithmetic coder at the final step of the proposed image compression algorithm.
Experiments prove that the basis adjustment increases the peak signal-to-noise ratio (PSNR) up to 1 dB. The final performance of the proposed codec never gives the rate-distortion characteristics less than JPEG2000 standard shows, an average improvement of 0,3-0,5 dB is observed.

Methods of selection of personnel sync pulse input in uncompressed video stream from a unidirectional single-bit digital lines and their implementation on FPGA
Aminev D., ZAO "MNITI" research associate,
Fokin A., ZAO "MNITI" engineer,

Keywords: selection, data transmission, implementation on FPGA, video streams.

Òhe article investigates the problem of personnel selection in the transmission of video streams data inter-module connections is studied. When modules are located from a few meters and more often used unidirectional single-digit digital line that transmits an electrical signal to LVDS or LVTTL standards that use personnel selection. Derived formulas for calculating the ratios of receiving and transmitting frequencies and other selector settings. A generalized structure of the video stream and the selector circuit, built on the FPGA. The methods of selection of personnel sync options and their implementation on FPGA. Discussed in detail the four methods of personnel selection and describe their advantages and disadvantages:

In method 1, the frequency corresponds to the frequency selection CLKd Fin bitstream. When this bit shift register is M×2n.

In method 2, the frequency selection in CLKd 2n (n = 2) times larger than the flow rate and compared with a standard is carried out at each cycle. When this bit shift register is M×2n.

In method 3 CLKd selection frequency so as to 2n n (n = 2) times the frequency of the stream, but the comparison of each bit stream is carried on a reference corresponding to the second and third bits of the shift register word length M×2n, the first and fourth bits are ignored.

In method 4 the frequency of selection in the same CLKd 2n (n = 2) times larger than the flow rate, however, the comparison with the benchmark performed based transient personnel signal (bits 7, 8, 15, 16, 23, 24 and 31).

Selected method 4 eliminating flaws other methods, which tracks transients in sync and provides the highest probability of selection. For the proposed methods presented are timing charts personnel selection processes.

The article presents fragments selector description language Verilog, where the selection of the frame at a frequency lower frequency 2n flow with flexible reference to the standard deviation has the highest frequency. The principle of selection frame frequency flow is simple to implement, but despite the high has a greater probability of failure at mismatch, both the frequency and phase of the signal. Such personnel selector copes with problems of the frame and line selections in the transmission of uncompressed video format 512×512.

1. Aminev D.A, Uvaisov S.U, analysis protocols for high-speed data transmission in the inter-module network connections / / In.: Information and communication technologies in education, science and industry. Proceedings of the VI International Scientific and Practical Conference. In two parts. Charles II. Protvino, 2012. pp. 198-201.

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4. Aminev D.A, Soroka E.Z. Universal input device and unipolar differential digital signals / / RF Patent number 2440666, 20.01.2012g., Priority of invention from 05.07.2010

5. Aminev D.A. Uvaisov S.U, Kondrashov A.V. Analysis of technical achievements in addressing registration information flows. / / Proceedings of the International Conference "Problems of protection of intellectual property in a variety of industries, science, education and medicine in terms of Russia's accession to the WTO." Togliatti. 2012.

6. Aminev D.A. Kondrashov A.V. Analysis and classification methods for converting digital data streams for high-speed processing and recording systems / / Systems and communication and broadcasting. ¹ 1, 2. 2012. p. 37-41 .

7. Aminev D.A. Kondrashov A.V. Harmonisation Russian standards for the transmission of high-speed information flows / / Digital Signal Processing. 2013. ¹ 2. Pp. 64-65.

8. Aminev D.A. Implementing embedding additional information when encoding MPEG-2 video stream using FPGA / / Technique means. Series: Tech TV. 2011. ¹ 1. p. 98-103.

Calculation of uncertainty function for passive radar by means of FPGA and GPU
Pankratov V.G.,
Karih A.A.,
Panfilov V.N.,
Gyrov A.D.,

ambiguity function, correlation function, Doppler filtering, correlator, assess hardware costs, Fourier transformation.

Algorithm for real-time calculating uncertainty function of the received signal on a delay-frequency plane is discussed. The algorithm consists of three main stages: calculation of correlation function and forming correlation matrix, forming Doppler frequencies matrix, multiplication of the obtained matrixes and obtaining uncertainty function matrix. Thus the scalar product of the vector row of the correlation matrix on a vector is a column matrix of twiddle factor gives the matrix element function uncertainty. To reduce the number of operations the calculation of the correlation function is made using the standard FFT kernel via the spectral representation of the input signals. The scope of the algorithm applicability is defined, limitation in Doppler frequencies and delays ranges are marked.

Comparative evaluation of computation expenses when calculating uncertainty function by different methods has show that the proposed algorithm requires 500 times less operations than the direct method. The choice of element base for algorithm realization is carried out. Best of all FPGA and GPU is suitable for these tasks. The algorithm was implemented as a devices for obtaining uncertainty function for several types of signals average performance FPGA and GPU. The experiment has confirmed the gain in signal-to-noise ratio as compared with the simple correlator.

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