Digital Signal Processing

Russian
Scientific & Technical
Journal


“Digital Signal Processing” No. 2-2018

20 International Scientific Research Conference “Digital Signal Processing and its Application - DSPA-2018”

In the issue:

- hyperphase modulation

- OFDM modulation
- broadcasting technology RAVIS
- radar image synthesis
- diagnostic of the cyclic systems
- numerical integration of functions
- FPGA based implementation of FIR filters


Hyperphase Modulation - the optimal method of message transmission (Part 2)
N.A. Bykhovskiy
PhD, Professor at MTUSI, e
-mail: bykhmark@gmail.com

Keywords: energy efficienc

Abstract
The article presents an optimal HPM signal demodulator as well as its functional diagram. The author develops an algorithm for decoding of received messages and the algorithm complexity is linearly increasing when there is an increase in the HPM signals’ n – dimensionality of the space. Analysis of noise immunity was also conducted and the dependencies of error probability when receiving signals Pest0, FT) on normalized signal duration (FT) were determined. It is shown that HPM, as a method of message transmission in the communication channels with limited frequency band, has a number of significant advantages as compared with the modern methods of signal transmission by using two-dimensional signals such as, for example, QAM, APM, trellis coded modulation, etc

It is noted that operations of signal formation by using HPM in a modulator at transmission and demodulation at reception, as well as algorithms of message coding and decoding, could be rather simply implemented using modern digital signal processing equipment. The results of the conducted research show that application in the modern communication systems of HPM signals is rather promising. The article review example of technical processing of a coder and a modulator for the signals with HPM in three-dimensional space. These examples illustrate application of the results received in Part I of this article for the solution of practical problems.

References

1. Byhovskiy M.A. Giperfazovaya modulyaciya – optimalnyy metod peredachi cifrovyh soobscheniy (Chast 1) // Cifrovaya obrabotka signalov. ¹1, 2018, pp. 8-17.

2. Van Trees H.L. Detection Estimation and Modulation Theory. N.-Y.: Wiley, 2013. - 1176p.

3. Byhovskiy M.A. Pomekhoustoychivost priema optimalnyh signalov, raspolozhennyh na poverhnosti N-mernogo shara // Elektrosvyaz ¹ 3, 2016.

4. Byhovskiy M.A. Teoreticheskie osnovy proektirovaniya sistem svyazi s vysokoy energeticheskoy effektivnost'yu // Cifrovaya obrabotka signalov, ¹2, 2017.

5. A. G. Zyuko, A. I. Fal’ko, I. P. Panfilov, et al., Interference Immunity and Efficiency of the Information Transmission Systems, Ed. by A. G. Zyuko // Radio i Svyaz, Moscow, 1985

6. John Proakis. Digital Communications// McGraw-Hill Education, 2000

7. Peterson W., Weldon E. J. Jr. Error-correcting codes, Moscow, Mir, 1976, 593 p.

8. Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital Communications. New York: Plenum Press, 1981

9. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHB-Peterburg, 2013, p. 352.


Hyperphase Modulation - the optimal method of message transmission (Part 3)
N.A. Bykhovskiy
PhD, Professor at MTUSI, e
-mail: bykhmark@gmail.com

Keywords: : energy efficiency of telecommunication systems, multidimensional signal ensemble, noise immunity code, telecommunication systems’ design

Abstract

The work contains calculations of dependencies of energy losses Δρs. for telecommunication systems which use optimal signal ensembles (“SEs”) for message transmission and also can use noise-immunity codes with various codes’ speed. The performed analysis defined the conditions that allow the reduction in telecommunication systems’ energy losses to the maximum extent possible as compared to the “ideal” Shannon system. It is shown that the usage of noise-immunity codes in telecommunication systems while applying the optimal SEs is not worthwhile as it materially increases telecommunication systems’ energy losses. The author provides a comparison of characteristics of a number of modern telecommunication systems with those characteristics that could be achieved when applying the optimal SEs (optimal methods of digital modulation).

References
1. Shannon C. Probability of error for optimal codes in Gaussian channel. Bell System Techn. J., May, 1959.

2. Byhovskiy M.A. Propusknaya sposobnost' kanala svyazi pri peredache signalov ogranichennoy dlitelnosti // Elektrosvyaz ¹ 8, 2016.

3. Byhovskiy M.A. Teoreticheskie osnovy proektirovaniya sistem svyazi s vysokoy energeticheskoy effektivnost'yu // Cifrovaya obrabotka signalov, ¹2, 2017.

4. Fink L.M. The theory of transmission of discrete messages, Moscow, Sovetskoe radio, 1970, 728 p.

5. John Proakis. Digital Communications// McGraw-Hill Education, 2000

6. Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital Communications. New York: Plenum Press, 1981

7. Byhovskiy M.A. Giperfazovaya modulyaciya – optimalnyy metod peredachi cifrovyh soobscheniy (Chast 1) // Cifrovaya obrabotka signalov. ¹1, 2018, pp. 8-17.

8. Byhovskiy M.A. Giperfazovaya modulyaciya – optimanyy metod peredachi cifrovyh soobscheniy (Chast 2) // Cifrovaya obrabotka signalov. ¹ 2, 2018, pp. 3-10.

9. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHB-Peterburg, 2013, p. 352.


Development of the hybrid scheme using tone reservation and clipping-and-filtering methods for peak-to-average power ratio reduction of OFDM signals
V.N. Tran, e-mail: nghiamosmipt@gmail.com
Moscow Institute of Physics and Technology, Moscow, Russia


Keywords: Peak-to-Average Power Ratio (PAPR), OFDM modulation, Tone Reservation (TR), clipping-and-filtering (CAF), hybrid scheme, DVB-T2 modulator, FPGA.

Abstract
This paper analyzes the modified tone reservation (TR) and clipping-and-filtering (CAF) methods to reduce Peak-to-Average Power Ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals and introduces the hybrid algorithm of these modified methods on FPGA. The simulation results of the proposed method and experimental results on FPGA in the DVB-T2 context for 64-QAM symbols are presented. These results show that the PAPR of OFDM signals is significantly reduced (about 7 dB).

The modified TR method is proposed based on an discrete Fourier transform (DFT)/ inverse DFT (IDFT) pair to suppress simultaneously all peaks, as hardware scheme of the CAF methods, while in the gradient-based TR methods, the largest peak is reduced. Therefore, it improves the efficiency of reducing PAPR and possesses relatively simple hardware implementation. The modified TR method extracts clipping noise on reserved subcarriers to generate an “anti-peak” signal instead of using the impulse-like kernel.

In the modified CAF method, the clipping noise is generated and used to design a correction signal, as in TR methods. It keeps the clipping noise on the reserved subcarriers, resets to zero the frequency samples of the clipping noise associated with the pilot subcarriers and sets bounds to the in-band distortion and the out-of-band radiation to satisfy an error rate below the specified level and a given spectral mask. The clipping noise is used in analysis instead of using the clipped OFDM signal to transform the original CAF algorithm into an equivalent form.

Modifications of the original TR and CAF methods are very important to introduce a novel low complexity high efficiency hybrid algorithm which can be implemented in a common hardware architecture. The proposed hybrid algorithm has a low computational complexity because its hardware architecture is almost similar to that of the constrained clipping method and does not require a modification in the demodulation of the OFDM signal. The simulation results show that the proposed method offers a high performance in term of PAPR reduction capability. Its FPGA implementation has been tested and evaluated in the DVB-T2 modulator.

References
1. V.P. Dvorkovich, A.V. Dvorkovich. Digital video information systems (theory and practice) // Moscow: Technosphere, 2012, 1008p.

2. ESTI EN 302 755 V1.4.1. Digital video broadcasting (DVB); Frame structure channel coding and modulation for a second generation digital terrestrial television broadcasting system // European Standard, July 2015.

3. ETSI TS 102 831 V1.2.1. Digital Video Broadcasting (DVB); Implementation guidelines for a second generation digital terrestrial television broadcasting system (DVB-T2) // European Standard, Aug. 2012.

4. Han S.H. and Lee J.H. An overview of peak-to-average power ratio reduction techniques for multicarrier transmission // IEEE Wireless Communications, vol. 12, no. 2, pp. 56–65, April 2005.

5. Jiang T. and Wu Y. An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals // IEEE Transactions on Broadcasting, vol. 54, no. 2, pp. 257–268, June 2008.

6. Anoh K., Tanriover C. and Adebisi B. On the Optimization of Iterative Clipping and Filtering for PAPR Reduction in OFDM Systems // IEEE Access, vol. 5, pp. 12004–12013, June 2017.

7. Baxley R.J., Zhao C., and Zhou G.T. Constrained clipping for crest factor reduction in OFDM // IEEE Transactions on Broadcasting, vol. 52, no. 4, pp. 570–575, Dec. 2006.

8. Tellado J. Peak to average power reduction for multicarrier modulation // Ph.D. dissertation, Stanford Univ., Stanford, CA, 2000.

9. Wang Y., Xie S., and Xie Z. FISTA-Based PAPR Reduction Method For Tone Reservation’s OFDM System // IEEE Wireless Communications Letters, vol. PP, no. 99, pp. 1–1, Nov. 2017.

10. Tran V.N. and Le H.N. Reconfigurable Complex Filtering Methods for PAPR Reduction of OFDM Signals with Low Computational Complexity // 2017 IVth International Conference on Engineering and Telecommunication (EnT), Moscow, Russia, pp. 59–63, Dec. 2017.

11. Pg109. Fast Fourier Transform v9.0 // Xilinx LogiCORE IP Product Guide, Nov. 2015.


The accuracy of clutter parameters estimation

D.I. Popov, e-mail: adop@mail.ru
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: variance estimation, Doppler phase shifts, correlation matrix, correlation coefficients, training sample, clutter, estimation accuracy.

Abstract
An analysis is made of the accuracy of the estimation of the parameters of the correlation matrix of multifrequency passive interference represented in each frequency channel of a coherent-pulsed multifrequency radar by a sequence of samples of complex envelopes of the initial data following a repetition period and forming a vector-column of samples of the learning sample in each element of the range resolution. A likelihood function is introduced that describes the statistical properties of a Gaussian multifrequency passive noise.

Taking into account the asymptotic efficiency and asymptotic normality of the maximum likelihood estimations of the unknown interference parameters, the accuracy of the estimation is characterized by the variance of the estimate determined by the Cramer-Rao expression indicating the lower bound of the variance of the estimate.

On the basis of the Cramer-Rao expression, formulas are obtained for the variance of estimates of the coefficients of interperiod correlation and the Doppler shift of the phase of the interference, taking into account the volume of the training sample and the spectral parameters of the interference. The presence of uncorrelated noise leads to a noticeable decrease in accuracy at a relatively high level. The main factors determining the accuracy of the estimation are the volume of the training sample and the spectral parameters of the interference. It is shown that the use of interchannel and interperiod averaging leads to a corresponding increase in the accuracy of estimating the coefficients of interperiod correlation and the Doppler phase shift of the interference.

The resulted results of calculations and simulation statistical modeling of estimation algorithms have confirmed the asymptotic efficiency of the obtained estimates, the accuracy of which approaches the limit with a relatively small volume of the training sample.

References
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 Prin-ciples. New York: SciTech Publishing, IET, Edison. 2010. – 924 p.

3. Popov D.I. Statisticheskaja teorija radiotehnicheskih system: ucheb. posobie (Statistical theory of radio engineering systems: Textbook. allowance). Ryazan': RGRTU, 2011. 80 p. (in Rus-sian).

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

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

6. Richards M.A. Fundamentals of Radar Signal Processing, Second Edition. New York: McGraw–Hill Education, 2014. – 618 p.

7. Cifrovaja obrabotka signalov v mnogofunkcional'nyh radiolokatorah. Metody. Algoritmy. Apparatura: monografija / pod red. G. V. Zajceva (Digital signal processing in multifunctional radars. Methods. Algorithms. Equipment: monograph / ed. G. V. Zaitseva). Moscow, Radiotehnika, 2015. 376 p. (in Russian).

8. Lozovskij I.F. Cifrovaja obrabotka signalov v RLS obzora: monografija (Digital processing of signals in the radar survey: monograph). Novosibirsk, Izd-vo NGTU, 2016. 270 p. (in Russian).

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

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

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

12. Popov D.I. Adaptivnije pegektornjie filtrij kaskadnogo tipa // Cifrovaya obrabotka signa-lov. 2016. no. 2. pp. 53-56. (in Russian).

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

14. Popov D. I. Measurements of Characteristics of Clutter // Measurement Techniques. May 2017. Vol. 60. No 2. – P. 190–195.

15. Cramer G. Matematicheskie metolji statistiki (Mathematical methods of statistics) / per. s angl. pod red. A.N. Kolmogorova. Moscow: Mir, 1975. 648 p. (in Russian).


Search and Detection of Objects on Terrain Radar Images for Their Further Recognition
Brizgalov A.P., e-mail: a_bryzgalov@gosniias.ru
Kovalchuk I.V., e-mail: ilya0406@ya.ru
Hnikin A.V., e-mail: alexis_x@mail.ru

Keywords:
search, detection, radar image, sample coefficients of kurtosis and skewness, algorithm parameters, optimization, real flights.

Abstract
An algorithm of search and detection on terrain radar image (RI) of candidate for the desired object with the purpose of its further recognition is considered. The algorithm is based on calculation and comparison with threshold of sample kurtosis and skewness coefficients of RI brightness distribution inside the detection window. The algorithm analysis and its parameter optimization are developed for Rayleigh distribution of the background. Examples of the algorithm application to RIs obtained in real flights are given.

References
1. Volkov V.YU., Makarenko A.A., Rogachev V.A., Turneckiy L.S. «Obnaruzhenie i vydelenie obektov na optikoelektronnyh izobrazheniyah». Sbornik «55 let na sluzhbe otechestvu» OAO NPO «Radar - mms», Sankt-Peterburg: 2005, pp. 222 – 226.

2. Kondratenkov, G.S. and Frolov, A.Yu., (Radiovision: Radar Systems for Remote Sensing of the Earth, Moscow: Radiotekhnika, 2005.

3. Levin B.R. «Teoreticheskie osnovy statisticheskoy radiotekhniki» kniga 1-ya, izd. 2-e, M., «Sov. Radio», 1974, pp. 59 – 60.

4. Shirman, Ya. D. Theoretical foundations of radiolocation. M.: Sov.radio, 1970, 560 p.


Mismatched filter synthesis, minimizing root-mean-square sidelobe level in the two-dimensional zone for phase-coded pulse
G.V. Zaytsev, e-mail:
gennady-zaytsev@yandex.ru
N.S. Kondranina, e-mail:
kondranina.nataliya@gmail.com
D.M. Litvinov, e-mail: litvinov_dmitry@inbox.ru
PSC SIC "Almaz"

Keywords: phase-coded pulse, mismatched filtering, minimization of integrated sidelobe level, low correlation zone.

Abstract
Sidelobe suppression of a phase-coded radar pulse at the receiver filter output is a classical problem which also arises in many other technical domains. Search for an optimal solution of this problem may be often accomplished only by exhaustive search. In a special case of minimizing root-mean-square sidelobes level for a fixed modulation sequence and one-dimensional zone on the time axis the problem may be solved analytically [3]. The resulting performance for this case is investigated in [4]. Similar results for the case of two-dimensional zone in time-frequency plane are practically absent in the literature. This paper proposes a method of the optimal filter synthesis minimizing root-mean-square sidelobes level for two-dimensional zone and investigates output characteristics which may be achieved by this method.

More exactly the method minimizes the root-mean-square sidelobes level for a rectangular set of points in the suppression zone. Variation of points density allows adjusting the resulting value of sidelobes suppression.

Let s be a modulation sequence of the phase-coded pulse, expressed by row vector and x be a modulation sequence of the receiver reference. The filter output is a crosscorrelation function of the sequences s and x. It is shown in the paper that for a given s the optimal vector x, minimizing root-mean-square sidelobes level in the two-dimensional zone, is given by the formula x = sR-1, where R is a matrix (specified in the paper) which is a function of s, parameters of suppression zone, and user parameters.

The paper investigates main parameters of the filter output for the optimal solution: root-mean-square sidelobes level, maximum sidelobes level and losses in signal-to-noise ratio. It is shown that the described method allows achieving high sidelobes suppression (hundreds of dB) for the zone with relatively small area if above-mentioned points density for synthesis is set to be high. Great suppression leads to high losses in signal-to-noise ratio. For practical radar applications such a great suppression in not realizable because of other restrictions in the signal flow path. It makes it possible to set a trade-off between small suppression and large losses in signal-to-noise ratio. The paper describes necessary points density for the given suppression level.

In the paper all examples are calculated for Legendre modulation sequences [6] and 50 dB maximum sidelobe suppression level in the zone. In this case resulting losses L may be estimated by the formula L = 10S + 0.1 dB where S is the zone area. It is also shown that for the fixed losses and fixed zone configuration maximum possible area of the suppression zone is increased with increasing distance of the zone from the origin.

The proposed method is applicable for the zone with arbitrary configuration particularly for the zone containing several connected regions. The paper describes the case of two connected regions in the zone.

The resulting performance of the proposed method of filtering meets requirements of many practical problems.

References
1. N. Levanon, E. Mozeson. Radar Signals. John Wiley & Sons Inc. New Jersey. 2004. 412 p.

2. A.A. Trukhachev. Radiolokatsionnye signaly i ih primenenie (Radar signals and their applications). Ì. Voenizdat. 2005. 320 p.

3. P. Stoica, J. Li, and M. Xue. Transmit codes and receive filters for radar. IEEE Signal Processing Magazine. vol. 25. pp. 94–109. November 2008.

4. G.V. Zaytsev, N.S. Kondranina, D.M. Litvinov. Otsenka characteristic metoda nesoglasovannoy filtratsii, minimizirujuschego integral’niy uroven’ bokovih lepestkov fazokodomanipulirovannih signalov (Characterization of mismatched filtering, minimizing integrated sidelobe level for phase-coded pulse). Tsifrovaya obrabotka signalov (Digital signal processing). ¹ 1, 2017.

5. R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press. 1985. 652 p.

6. J. Jedwab. A Survey of the Merit Factor Problem for Binary Sequences. Sequences and Their Applications. Proceedings of SETA 2004. ed. T. Helleseth et al. Lecture Notes in Computer Science. vol. 3486. pp. 30–55. Springer-Verlag. Berlin Heidelberg. 2005.


Submetre resolution radar image generation algorithm for smallsized synthetic-aperture radar systems
M.V. Gnezdilov, e-mail:
mvgnezdilov@gmail.ru
I.F. Kupryashkin, e-mail:
ifk78@mail.ru
V.P. Likhachev, e-mail:
lvp_home@mail.ru
L.B. Ryazantsev, e-mail:
kernel386@mail.ru

Keywords: FMCW SAR, radar image synthesis, integrated sidelobe level, Backprojection.

Abstract
The article introduces a modified Backprojection algorithm, which ensures formation of detailed radar images of the terrain surface for small-sized synthetic aperture Frequency Modulated Continuous-Wave radars. It is shown that the high quality of generated imagery in terms of the integrated sidelobe level for a point target mark is attained in case when the specific features of the trajectory signal phase modulation stemming from the signal's discrete nature and the motion of the SAR vehicle during the time of an individual pass are properly accounted for.


References
1. Bolkunov A.A., Ryazancev L.B., Sidorenko S.V. K voprosu ocenki radiolokacionnoy zametnosti vooruzheniya, voennoy i specialnoy tekhniki s primeneniem bespilotnyh letatel'nyh apparatov // Voennaya mysl. 2017. ¹9. S. 70-73.

2. Sandia National Laboratories // URL: http://www.sandia.gov

3. ImSAR LLC [Ýëåêòðîííûé ðåñóðñ] // URL: http://www.imsar.com (äàòà îáðàùåíèÿ: 04.04.2018).

4. Shkolnyiy L.A., Radar systems aerial reconnaissance, interpretation of radar images. Moscow, VVIA im. N.E. Zhukovskogo, 2008, 531 p.

5. Duersch M. Backprojection for Synthetic Aperture Radar. Thesis for Ph.D. Brigham Young University, 2013.

6. Duersch M., Long D. Analysis of time-domain back-projection for stripmap SAR // International Journal of Remote Sensing, 2015. Vol. 36, No. 8, pp. 2010–2036.

7. Doerry À. Basics of Backprojection Algorithm for Processing Synthetic Aperture Radar Images. Sandia National Laboratories, 2016.


Diagnostic of the cyclic systems using algorithm based on Gauss-Hermite functions
D.A. Balakin, e-mail: bzzz86.balakin@yandex.ru
V.V. Shtykov
, e-mail: ShtykovVV@yandex.ru
National Research University “Moscow Power Engineering Institute”(MPEI), Russia, Moscow


Keywords: cyclic system, quasi-periodic sequence of impulse signals, Gauss-Hermite functions.

Abstract
The cyclic system is an object which response is a quasi-periodic sequence of impulse signals. Such signals, for example, take place during the operation of dynamic systems: various machines and mechanisms, living organisms and other objects. Today, the actual direction is the digital processing of signals of cyclic systems with the purpose of their diagnostics. The frequency of responses of mechanical devices, along with speed and acceleration, is one of the important kinematic parameters by which the system is tested. The determination of the rhythm of biological signals is also one of the key directions in the diagnosis of biological systems.

The article is described the basic principles of digital implementation of the algorithm for processing quasi-periodic pulse signals using the Gaussian-Hermite functions (FGH). Using this algorithm it is possible not only to detect a defect, but also to trace its dynamics throughout the process under investigation.

The algorithm is based on the basic properties of the Hermite transformation. The change in the scale of Gauss-Hermite functions is borrowed from the theory of wavelet transform. The parent function is formed as series of the Gauss-Hermite functions associated with an orthogonal filter bank. The signal detection is realized by means of cross-correlation function processing. The decision on the presence of a signal is made on the basis of the maxima of the correlation function, which corresponds to the classical theory of optimal filtration. As a result, the developed algorithm allows us to detect features of the signal, based on which the filter is constructed.

The filtering scheme can be reduced to a matrix form, where each column is characterized by a particular defect or pathology. This form of representation has a flexible structure, i.e. it is sufficient to record the matrix of the filter weights in the memory of the programmable logic integrated circuit to form the final signal analysis device. Also, there is the possibility of parallel processing, which increases the computational speed.

References

1. Kudinov, A. N., Lebedev, D. Yu., Ryzhikov, V. N., and others. Samopodobie skatterogrammi mgnovennogo serdtsa ritma (Self-likeness of the scatterogram of the instant heart of rhythm) // Vestnik TSU. Tv., 2014. no. 4. pp. 105–115.

2. Janke E., Emde F., Lesch F. Spetsialnie functsii (Special functions), M.: Nauka, 1964. 344 p.

3. Balakin, D. A., Shtykov, V. V. Postroenie ortogonalnogo banka filtrov na osnove preobrazovania Ermita dlia obrabotki signalov (The construction of orthogonal filters bank based on Hermit transform for signal processing) // Zurnal radioelectroniki (Journal of radio electronics), 2014, no. 9.

4. Gradshtein, I. S., Ryzhik, I. M. Tablitsa integralov, sum riadov i proizvedenii (Tables of integrals, sums of series and products), M.: Fizmat, 1963. 1100 p. 5. Baskakov, S., I. Radiotekhnicheskie tsepi i signali (Radio circuits and signals), M.: Vish. shkola, 2000. 450 p.


Some sampling theory applications to numerical integration of functions
Soroka E.Z., e-mail: soroka@mniti.ru

Keywords: numerical integration, sampling theory, low-pass filter, pulse response.

Abstract
The most popular numerical integration methods (rectangle rule, trapezoidal rule, parabolic rule, and 3/8 rule) have been examined by means of the sampling theory while the reconstruction of functions realized by low-pass filters with certain pulse responses. Verified that (under fixed number of samples) numerical integration gives exactly the same results on application of rectangle ruleand trapezoidal rule, as well asunder using pulse responses with some symmetry.


References

1. Samarskiy, A. A., Gulin, A. V.: Numerical Methods, Nauka, Moscow. 1989, 432 p.

2. Kahaner D., Mouler K., Nesh S.: Numerical Methods and Software. Prentice Hall, New York. 1988, 575 p.

3. Krylov, V.I. and Shul’gina, L.T., Handbook of Numerical Integration, Moscow: Nauka, 1966, 372 p.

4. Ignat'ev N.K. Discretization and its applications. Moscow: Svyaz, 1980, 284p.

5. P. A. M. Dirac The Principles of Quantum Mechanics. Snowball Publishing, 1960, 480p.

6. I.N. Bronshtein, K.A. Semendyayev, Handbook of mathematics for engineers and students of higher technical schools, Moscow: Nauka, 1986, 544 p.


FPGA based energy-efficient implementation of high-speed FIR filters
Spazhakin M.I., e-mail: spazhakinmi@rambler.ru

Keywords: FIR filter, FPGA, ACO algorithm, CSD structure.

Abstract
A comparative analysis of technical solutions based on the using of hardware multipliers, logic elements, as well as on the combined using of different type resources is carried out in the article. It is shown that application of the combined method of digital filters realization in accordance with the proposed optimization technique allows to reduce the power consumption by 4-15% compared to the implementation on logical elements and by more than 50% in relation to the implementation only on hardware multipliers

References

1. H. Samueli, “An improved search algorithm for the design of multiplierless FIR filters with powers-of-two coefficients,” IEEE Trans. Circuits and Systems, Vol.36, No.7, pp.1044-1047, 1989. DOI: 10.1109/31.31347

2. N. Takahashi and K. Suyama, Design of CSD coefficient FIR filters based on branch and bound method, Proc. of ISCIT2010, pp.575-578, 2010. DOI: 10.1109/ISCIT.2010.5665055

3. Y. Arie and K. Suyama, Evolutionary stagnation avoidance for design of CSD coefficient FIR filters using GA, Proc. of ITC-CSCC 2016, 2016.

4. R. Baudin and G. Lesthievent. Design of FIR Filters with Sum of Power-of-Two Representation Using Simulated Annealing, 2014 7th Advanced Satellite Multimedia Systems Conference and the 13th Signal Processing for Space Communications Workshop (ASMS/SPSC). DOI: 10.1109/ASMS-SPSC.2014.6934565

5. T. Sasahara and K. Suyama, An ACO approach for design of CSD coefficient FIR filters, Proc. of APSIPA ASC 2015, pp.463-468, 2015. DOI: 10.1109/APSIPA.2015.7415314

6. T. Sasahara and K. Suyama, Verification of search process in CSD coefficient FIR filter design, 2016 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS). DOI: 10.1109/ISPACS.2016.7824710

7. Alan V. Oppenheim, Ronald W. Schafer Discrete-Time Signal Processing (3rd Edition). Prentice-Hall Signal Processing Series, 2009, 1144 p.

8. M. Dorigo and G. D. Caro, Ant colony optimization: a new meta-heuristic, Proc. of Congress on Evolutionary Computation 99, Vol.2, 1999, pp.1470-1477. DOI: 10.1109/CEC.1999.782657

9. G. Rui and L. S. DeBrunner, A novel fast canonical-signed-digit conversion technique for multiplication. Proc. Of IEEE Conference pn Acoustics, Speech and Signal Processing, ICASSSP-2011, pp. 1637-1640, 2011. DOI: 10.1109/ICASSP.2011.5946812

10. T. Sasahara and K. Suyama, An Effectiveness of ACO Approach in Design of CSD Coefficient FIR Filters. Intelligent Signal Processing and Communication Systems (ISPACS), 2015 International Symposium on. DOI: 10.1109/ISPACS.2015.7432839


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