Digital Signal Processing 
Russian 
Minimumofmaximum weighted error in magnitude response approximation of analog and digital classical filters Abstract The author of this paper answered that for this it is necessary to solve the algebraic equation of the fourth degree which includes elliptic functions and that this equation is bulky. Besides, a numerical example is given. Since the answer attracted interest, and there is no definite answer on the raised question in literature, in the article more detailed generalized answer is given. It is shown that the solution is connected with finding of a minimumofmaximum weighed error for the magnitude response approximation and really for this purpose it is necessary to solve the algebraic equation of the fourth degree which in turn under certain conditions addresses in the simple approximate formula. The received expressions are suitable not only for elliptic (Zolotarev – Cauer) filters, but also for other classical analog and digital filters of Chebyshev and Butterworth with lowpass, highpass, bandpass and bandstop magnitude responses. 2. Vlcek M., Unbehauen R. Degree, ripple and transition width of elliptic filters // IEEE Trans., 1989, CAS36, no. 3, pp. 469472. 3. Calahan D.A. Modern network synthesis // New York, 1964. 4. Mingazin A.T. Extreme parameters of analog and digital filters // Elektrosvyaz, 1999, no. 1, pp. 2223. 5. Alyoshin D.V, Mingazin A.T. A program for calculation of extreme parameters of digital and analog filters and its application // Digital Signal Processing. Russian Scientific and Technical Journal, 2006, no. 1, pp. 4549.
Nonlinear distortion signals with amplitude modulation in quantization Keywords: amplitude modulation, quantization, spectral analysis, nonlinear distortion, coding, direct and complementary codes, demodulation, truncation, rounding. References 2. Bruhanov U.A., Lukashevich U.A. Nelineinye iskageniya garmonicheskih signalov pri kvantovanie // Padiotehnika, 2009, nomer 10, str. 5760. 3. Bruhanov U.A., Lukashevich U.A. Vliyanie izbytochnoy diskretizacyii na nelineynye iskageniya pri analogochifrovogo preobrazovaniya signalov . Padiotehnika, 2014, nomer 12, str. 3035. 4. Bruhanov U.A., Lukashevich U.A. Nelineinye iskageniya pri sigmadelita analogochifrovogo preobrazovaniya signalov // Padiotehnika and elektronika, 2017, tom 62, nomer 3, str. 224233. 5. Bruhanov U.A. Metidika issledovaniya nelineinyh kolebaniy v sistemah diskretnogo vremeni pri pereodicheskih vozdeystviyah // Padiotehnika and elektronika, 2006, tom 51, nomer 2, str. 196201. 6. Bruhanov U.A. Metod issledovaniya pereodicheskih prochessov v neavtonomnyh sistemah diskretnogo vremeni s kvantovaniem // Padiotehnika and elektronika, 2008, tom 53, nomer 7, str. 851857.
Comparative analysis of four IIR filter structures Abstract Dependences of the output noisesignal ratio and coefficient wordlength from a filter order for a number of magnitude response requirements are presented. The analysis of these dependences allows to note the following: It is possible to reduce significantly the coefficient wordlength and practically not to worsen or even to improve a little the noisesignal ratio by purposely increasing a filter order. For cascade structures with edge frequencies close 0.5 and for structures based on allpass networks with edge frequencies in all baseband there is not meaning to increase a filter order more than by two. For edge frequencies close 0 or 0.5 the best results on two analyzed parameters are inherent to cascade structure on links of the optimal form. For edge frequencies in the neighborhood of 0.25 the structures on links of the direct form and more  structure based on allpass networks there is the advantage on the noisesignal ratio, and cascade structures  on longwise the coefficient wordlength. The advantage of cascade structures is lost with the requirement of very small passband ripple. 2. Dehner G.F. Noise optimized IIR digital filter design  tutorial and some new aspects // Signal Processing, 2003, vol. 83, no. 8, pp. 15651582. 3. Mingazin A. Alternatives of IIR filter design // Components & Technologies, 2017, no. 6, pp.106116. 4. Gazsi L. Explicit formulas for lattice wave digital filters // IEEE Trans., 1985, CAS32, no.1, pp. 6888. 5. Mingazin A.T., Zorich A.A. Minimization of roundoff noise in cascade recursive digital filters // Elektronnaya Tekhnika, 1992, ser. 10, no. 1,2, pp. 3743. 6. Mingazin A.T. Noise, coefficient wordlenght and è order of IIR filters // 20th Int. Conf. Digital signal processing and its applications, (DSPA2018) vol.1, pp.208213. 7. Mingazin A., Gordienko S., Gureev À. IIR filter design: tolerance initial parameter space of ZoljtarevCauer filters // Components & Technologies, 2016, no. 10, pp.122126. 8. Vaidyanathan P.P. Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial // Proceedings of the IEEE, 1990, vol. 78, no. 1, pp.5693.
Abstract References 2. Preatt U. Digital image processing. M.: World, 1982, Book 2 – 480 pp. 3. Krasilynikov N.N. Digital processing 2D and 3Dimages. SPb: BHV – Peterburg. 2011 – 608 pp. 4. Polovko A.M., Butusov P.N. Interpolation. Methods and computer process engineering. SPb: BHV – Peterburg. 2004 – 320 pp. 5. Arzumanian E.P. Bilineynuy interpolyator dlya geometpicheskogo preobrazovaniy izobrageniy // Tehnika sredstv svyazi. Seriy Tehnika Televideniy. M.: 2017. – pp. 6981.
Abstract References 2. J. Tellado. Peak to average power reduction for multicarrier modulation Ph.D. dissertation, Stanford Univ., Stanford, CA, Sep. 1999. 3. X. Huang, J. Lu, J. Zheng, J. Chuang, and J. Gu. Reduction of peaktoaverage power ratio of OFDM signals with companding transform // IEE Elec. Lett., vol. 37, Apr. 2001, pp. 506 507. 4. B. S. Krongold and D. L. Jones. PAR reduction in OFDM via active constellation extension // IEEE Trans. Broadcast., vol. 49, no. 3, Sep. 2003, pp. 258 268. 5. S. H. Han, J. H. Lee. An Overview of PeaktoAverage Power Ratio Reduction Techniques for Multicarrier Transmission // IEEE Wireless Communication, April 2005, pp 56 65. 6. Le Van Ki. Issledovanie algoritmov obrabotki signalov s OFDM modulyacyite I razrabotka rekomendachii po umensheniu PIK faktora // Chifrovaya obrabotka signalov. 2016. Nom. 1, str. 2933. 7. Le Van Ki. Realizachiya sistemi kodirovaniya s umensheniem Pikfaktora OFDM signalov // Chifrovaya obrabotka signalov. 2017. Nom. 4, str. 6768.
Abstract The article studies the properties of the cyclic autocorrelation function (ACF) of multilevel complex sequences of Zadoff  Chu used in current LTE OFDM technologies of modern communication systems, depending on the number of levels of quantization of elementary signal sequences in two versions: without considering quantization noises and taking into account these noises. Simulation of the sequence is performed In MATLAB at quantization levels of the real and imaginary parts of the sequence L=2,4,8,16,32,64. The mathematical model of sequence Zadoff – Chu cyclic autocorrelation of the sequence, the linear characteristics of the quantizer and the calculation formula for calculating the ratio of the square of the maximum of the ACF of the sequence Zadoff – Chu to the average of the square of side lobes, the relationship module, the maximum value of the side lobe to the maximum of the ACF and graphs the ratio of the square of the maximum of the ACF quantized sequence Zadoff – Chu to the average of the square of side lobes, depending on the characteristics of the quantization with and without allowance for the quantization noise. The conclusions about the possibility of reducing the bit sequence Zadoff  Chu to 4 ... 6 digits. The ratio of the module of the maximum value of the side lobes to the maximum of the cyclic AKF increased from 1.33% at 64 quantization levels to 2.92% at 16 quantization levels, which opens up the possibility of using lowcost computing with lowbit data without significantly reducing the noise immunity of the generated sequences. References 2. The physical level of LTE.  Electronic components, ¹10/2010, 3641s. 3. ETSI TS 136 211 V10.0.0 (201101) . Technical Specification.  European Telecommunications Standards Institute, 2011104s. 4. Sesia S., Toufik I., Baker M. LTE – The UMTS Long Term Evolution: From Theory to Practice.  Torquay, UK: John Wiley & Sons, 2009 611s. 5. Malygin, I. V. The chipsets to build the devices Spread Spectrum. // AllRussian information resource. [Electronic resource.] – Mode of access: http://cxem.net/sprav/sprav110.php. (date accessed: 31.10.2018). 6. Hasanov M. S., Kurganov V. V. Methods for determining the coefficients of quasioptimal FIR filter of pseudorandom binary sequence convolution. // AllRussian information resource. [Electronic resource]. – Mode of access: http://www.mesconference.EN/data/year2014/pdf/D145.pdf (date accessed: 31.10.2018). 7. Digital signal processor 1892VM3T. // AllRussian information resource. [Electronic resource] – Mode of access: http://multicore.ru/index.php?id=48 (date accessed: 31.10.2018). 8. The quantization noise. // AllRussian information resource. [Electronic resource] – Mode of access: https://dic.academic.ru/dic.nsf/ruwiki/212854. (date accessed: 03.11.2018).
The soft mask algorithm is similar to other algorithms in the frequency domain, but soft mask’s gain function is a probability of speech presence in each point of the timefrequency representation of the speech signal. An improved method for soft mask estimation using a recurrent neural network and an algorithm for suppressing noise in speech signals based on it was proposed in the paper. Compared with the previous version of the algorithm using the convolutional neural network, the network structure was changed, and the learning algorithm was revised. In the proposed version, the soft mask obtained via the Rayleigh distribution of amplitude noise spectrum in each frequency band is used as the target variable for neural network training algorithm. A base of speech signals compiled from the records of the CHAINS speech corpus was used. For the training of the neural network 30 recordings were used (4 recordings per announcer), with a total duration of 1 hour 17 minutes 29 seconds. Testing was performed on the recordings of the remaining 6 speakers (34 recordings per speaker), with a total duration of 9 minutes and 12 seconds. 2. Boll, S. Suppression of acoustic noise in speech using spectral subtraction / S. Boll // IEEE Transactions on Acoustics, Speech, and Signal Processing. – 1979. – Vol. 27. – ¹ 2. – P. 113–120. 3. Scalart, P. Speech enhancement based on a priori signal to noise estimation / P. Scalart, J.V. Filho // 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings. – IEEE, 1996. – Vol. 2. – P. 629–632. 4. Ephraim, Y. Speech enhancement using a minimummean square error shorttime spectral amplitude estimator / Y. Ephraim, D. Malah // IEEE Transactions on Acoustics, Speech, and Signal Processing. – 1984. – Vol. 32. – ¹ 6. – P. 1109–1121. 5. Plapous, C. A twostep noise reduction technique / C. Plapous, C. Marro, L. Mauuary, P. Scalart // 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing. – 2004. – Vol. 1. – P. 289–92. 6. Lu, Y. A geometric approach to spectral subtraction / Y. Lu, P.C. Loizou // Speech Communication. – 2008. – Vol. 50. – ¹ 6. – P. 453–466. 7. Plapous, C. Improved SignaltoNoise Ratio Estimation for Speech Enhancement / C. Plapous, C. Marro, P. Scalart // IEEE Transactions on Audio, Speech and Language Processing. – 2006. – Vol. 14. – ¹ 6. – P. 2098–2108. 8. Lim, J. Enhancement and bandwidth compression of noisy speech / J. Lim, A. Oppenheim // Proceedings of the IEEE. – 1979. – Vol. 67. – ¹ 12. – P. 1586–1604. 9. Azarov I.S., Vashkevich M.I., Lihachev D.S., Petrovskiy A.A/ Algoritmy ochistki rechevogo signala ot slognyh pomeh putem filtrachii v modulyachionnoy oblasti // Chifrovaya obrabotka signalov. 2013.  nom. 1, str. 2531. 10. Wang, D. On Ideal Binary Mask As the Computational Goal of Auditory Scene Analysis / D. Wang // Speech Separation by Humans and Machines. – Boston: Kluwer Academic Publishers, 2005. – P. 181–197. 11. Lu, Y. Estimators of the MagnitudeSquared Spectrum and Methods for Incorporating SNR Uncertainty / Y. Lu, P.C. Loizou // IEEE Transactions on Audio, Speech, and Language Processing. – 2011. – Vol. 19. – ¹ 5. – P. 1123–1137. 12. Tupitsin, G. Twostep noise reduction based on soft mask for robust speaker identification / G. Tupitsin, A. Topnikov, A. Priorov // 2016 18th Conference of Open Innovations Association and Seminar on Information Security and Protection of Information Technology (FRUCTISPIT). – IEEE, 2016. – P. 351–356. 13. Xu, Y. A Regression Approach to Speech Enhancement Based on Deep Neural Networks / Y. Xu, J. Du, L. Dai, C. Lee // IEEE/ACM Transactions on Audio, Speech, and Language Processing. – 2015. – Vol. 23. – ¹ 1. – P. 7–19. 14. Zhao, H. ConvolutionalRecurrent Neural Networks for Speech Enhancement / H. Zhao, S.Zarar, I. Tashev, C. Lee // 2018 IEEE International Conference on Acoustics, Speech and Signal Processing.  2018. P. 24012405. 15. Kolbak, M. Monaural Speech Enhancement using Deep Neural Networks by Maximizing a ShortTime Objective Intelligibility Measure / M. Kolbak, Z. Tan, J. Jensen. – 2018. 16. Hou, J. AudioVisual Speech Enhancement Based on Multimodal Deep Convolutional Neural Network [Ýëåêòðîííûé ðåñóðñ] / J. Hou, S. Wang, Y. Lai, Y. Tsao, H. Chang, H. Wang. – Ðåæèì äîñòóïà: https://arxiv.org/abs/1703.10893. 17. Cohen, I. Noise Reduction in Speech Processing: Springer Topics in Signal Processing. Vol. 2 / I. Cohen, Y. Huang, J. Chen, J. Benesty. – Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. 18. Wang, D. TimeFrequency Masking for Speech Separation and Its Potential for Hearing Aid Design / D. Wang // Trends in Amplification. – 2008. – Vol. 12. – ¹ 4. – P. 332–353. 19. Hu, Y. Techniques for estimating the ideal binary mask / Y. Hu, P. Loizou // Proc. 11th Int. Workshop Acoust. Echo Noise Control. – 2008. – P. 154–157. 20. Jensen, J. Spectral Magnitude Minimum MeanSquare Error Estimation Using Binary and Continuous Gain Functions / J. Jensen, R.C. Hendriks // IEEE Transactions on Audio, Speech, and Language Processing. – 2012. – Vol. 20. – ¹ 1. – P. 92–102. 21. McAulay, R. Speech enhancement using a softdecision noise suppression filter / R. McAulay, M. Malpass // IEEE Transactions on Acoustics, Speech, and Signal Processing. – 1980. 22. Cho, K. Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation / K. Cho, B. van Merrienboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, Y. Bengio // Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). – Stroudsburg, PA, USA: Association for Computational Linguistics, 2014. – P. 1724–1734. 23. Clevert, D.A. Fast and Accurate Deep Network Learning by Exponential Linear Units [Ýëåêòðîííûé ðåñóðñ] / D.A. Clevert, T. Unterthiner, S. Hochreiter. – Ðåæèì äîñòóïà: https://arxiv.org/abs/1511.07289. 24. Varga, A. Assessment for automatic speech recognition: II. NOISEX92: A database and an experiment to study the effect of additive noise on speech recognition systems / A. Varga, H.J.M. Steeneken // Speech Communication. – 1993. – Vol. 12. – ¹ 3. – P. 247–251. 25. Jones, E. SciPy: Open source scientific tools for Python [Ýëåêòðîííûé ðåñóðñ] / E. Jones, T. Oliphant, P. Peterson, others. – Ðåæèì äîñòóïà: http://www.scipy.org. 26. Chollet, F. Keras [Ýëåêòðîííûé ðåñóðñ] / F. Chollet, others. – Ðåæèì äîñòóïà: https://keras.io. 27. Cummins, F. The CHAINS Speech Corpus: CHAracterizing INdividual Speakers / F. Cummins, M. Grimaldi, T. Leonard, J. Simko // Proc of SPECOM. – 2006. – P. 1–6. 28. International Telecommunication Union. 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Abstract 2. Buzzi S., Lops M., Venturino L. Trackbeforedetect procedures for early detection of moving target from airborne radars // IEEE Transaction on aerospace and electronic system. Vol. 41. No. 3. July 2005. PP. 937954. 3. Shulin L., Xinliang Chen New analytical approach to detection threshold of a dynamic programming trackbeforedetect algorithm // IET Radar, Sonar and Navigation. Vol. 7. PP. 773779. 4. Johnston A. Performance Analysis of a Dynamic Programming Track Before Detect Algorithm // IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002. PP. 228242.
Abstract Algorithm to improve spectral estimation
Through K we denote the coefficient of improvement of the spectrum evaluation, by which we will understand the increase in K times the sampling frequency of the continuous Fourier transformers. The improvement factor K can be any natural number, large or equal to two The DFT formula for fixed K looks like The latter ratio is represented as a combination of K Npoint DFT whereabouts For each L=0,...K1, the DFT is implemented on the basis of the FFT algorithm with the corresponding coefficients. The article concludes that the value of the analysis points shift on the frequency axis can be an arbitrary real number from the halfinterval from [0;1), i.e. the following transformation is true The last transformation allows for the sequence of fixed length data at different values r ∈ [0;1) to perform the sampling of continuous Fourier transformers with as small a sampling step as possible. Conclusion
2. Ifeachor, Emmanual C., Jervis, Barrie W. Digital Signal Processing. A Practical Approach. 2nd ed. Translation from English. – M.: Publishing House «Williams», 2004, 992 p. 3. Tuyakov S.V. Development of the methods and algorithms for the subband modeling of the empirical data: dissertation of the candidate of physical and mathematical sciences. Belgorod National Research University, Belgorod, 2011.
The advantages of antenna selection in MIMO systems versus conventional MIMO systems without antenna selection Abstract MIMO technology allow to significantly increase data transmission rates in wireless communications system without expanding of bandwidth of using communication system or increasing of transmitter power. Using MIMO technology with a spatial multiplexing the high rate data symbol stream divides to many low rate substreams, which are transmitting in same time with different antennas. General MIMO system has the number of transmit/receive chains equal to the number of transmission/receiving antennas respectively. Receiving and transmitting of carried signal carried out in same time at all transmitting and receiving antennas simultaneously on the same frequency. In case of adding to MIMO system of one more antenna in pair with the additional path, we have increasing of noise immunity. However, this action increases the cost and complexity of the implementation of the communication system. The radio chains make general contribution to the cost and complexity of the communication system. Therefore, it is desirable to reduce their number. So, it is very promising to use Antenna Selection algorithms, that allow to select a subset of transmit / receive antennas (depends on number of chains) among the available in communication system transmit / receive antennas. Statistical simulation results given in this article show, that MIMO systems with Antenna Selection provide a significant power gain in comparison to conventional MIMO systems without Antenna Selection. Assessment of this power gain is given for various conditions and Antenna Selection criteria. 2. Shital Shegokar Jangid. Antenna Selection with Spatial Multiplexing MIMO Systems. International Journal on Recent and Innovation Trends in Computing and Communication, February 2015, pp. 97100. 3. Kreindelin V.B., Hazov M.L. Algoritmyi pereklucheniya antenn v sistemah MIMO // Jelektrosvyaz. 2017. – nom. 10, str. 5964. 4. G. Huang, C.B.Papadias and S.Venkatesan. MIMO Communication for Cellular Networks. USA, Springer Science+Busyness Media LLC, 2012, 314 p. 5. Andreas F. Molisch. Wireless Communications. Second Edition, UK, Wiley, 2011. 827 p. 6. Bakulin M.G., Kreindelin V.B., Hazov M.L. Kruterii avovybora antenn v sistemah MIMO // Jelektrosvyaz. 2018. – nom. 10, str. 7881. 7. Kreindelin V.B.,Pankratov D.U. Analiz propusknoy sposobnosti radiokanala sistemy MIMO v usloviyah prostranstvennokorrelirovannyh zamiraniy // Informachionnye prochessy. – 2017. – nom. 3. str. 188198. 8. Oesges C., Clerckx B. MIMO Wireless Communications. Channels, Techniques and Standards for MultiAntenna, MultiUser and MultiCell Systems.  U.K.: Academic Press, 2013. — 733 p. 9. Huang G., Papadias C.B., Venkatesan S. MIMO Communication for Cellular Networks. USA, Springer Science+Busyness Media LLC, 2012.  314 p. 10. MIMO System Technology for Wireless Communications./ Edited by George Tsoulos. USA, FL, Boca Raton, CRC Press, 2006, 378 p. 11. http://www.datasheetlib.com/datasheet/386306/hws408_hexawave.html 12. http://datasheet.elcodis.com/pdf2/105/36/1053632/njg1535hd3.pdf 13. https://www.infineon.com/dgdl?fileId=db3a30433f1b26e8013f2db58bc03856
Abstract 2. W.G. Carrara, R.S. Goodman, and R.M. Majewski, Spotlight Synthetic Aperture Radar. Signal Processing Algorithms, Artech House, Boston, London, 1995. 3. Ch. V. Jakowatz, D.E. Wahl, P.H. Eichel, D.C. Ghiglia, P.A. Thompson. Spotlightmode synthetic aperture radar: a signal processing approach. Springer. 1996. 4. R.L. Morrison Jr., M.N. Do, and D.C. Munson, “SAR Image Autofocus By Sharpness Optimization: A Theoretical Study,” IEEE Journal, 2003, pp. 113. 5. K.H. Liu, A. Wiesel, and D.C. Munson, “Synthetic Aperture Radar Autofocus via Semidefinite Relaxation,” IEEE Transactions on Image Processing, vol. 22, is. 6, 2013, pp. 23172326. 6. K.H. Liu, A. Wiesel, and D.C. Munson, “Synthetic Aperture Radar Autofocus Based on a Bilinear Model,” IEEE Transactions on Image Processing,” vol. 21, is. 5, 2012, pp. 27352746. 7. J. Torgrimsson, P. Dammert, H. Hellsten, L. Ulander, “An Efficient Solution to the Factorized Geometrical Autofocus Problem,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, num. 8, 2016, pp. 47324748. 8. P. Eichel, D. Ghiglia, and C. Jakowatz Jr., "Speckle processing method for syntheticapertureradar phase correction," Optics Letters, vol. 14, pp. 13, 1989. 9. D.E. Wahl, P.H. Eichel, D.C. Ghiglia, C.V. Jakowatz Jr.,“Phase gradient autofocus – a robust tool for high resolution SAR phase correction,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 30, is. 3, pp. 827 – 835, 1994. 10. Vityazev S.V., Androsov B.B., Vityazev V.V., Shershnev E.D. Algoritmy avtofokusirovki radioizobrageniy v usloviyah dinamichnyh traektornyh nestabilynostey // Cuifrovaya obrabotka signalov. Nom. 1, 2012, str. 6470. 11. Vityazev S.V., Androsov B.B., Vityazev V.V. Modelirovanie i issledovanie effektivnosti algoritma sintezirovaniya radioizobrageniy v regime “doplerovskogo obugeniya lucha” s avtofukosirovkoey po gradient fazi // Chifrovaya obrabotka signalov i ee primenenie: Trudi 17 megnunarodnoy nauch.tehnich. konf. – Tom 1  M., 2015. – str. 315318. 12. Vityazev S.V., Androsov B.B., Vityazev V.V., Nikishkin P.B. Razrabotka programmnoalgoritmicheskogo obespecheniya obrabotki traektornogo signala v regime “doplerovskogo obugeniya lucha” // Chifrovaya obrabotka signalov i ee primenenie: Trudi 19 megnunarodnoy nauch.tehnich. konf. – Tom 1  M., 2017. – str. 543547. 13. V. Androsov, S. Vityazev, A. Kharin, V. Vityazev, “An Approach to Autofocus in Carborne Radar Imaging Systems,” 16th IEEE EastWest Design and Test Symposium (EWDTS2018), 2018. P. 847850.
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