Digital Signal Processing |
Russian |
Peculiarities of RLS adaptive filtering algorithms application in fractionally spaced equalizers
Abstract 2. Djigan V.I. Recursive least squares an idea whose time has come // Proceedings of the 7-th International Workshop on Spectral Methods and Multirate Signal Processing Moscow, 2007. P. 255260. 3. Farhang-Boroujeny B. Adaptive filters theory and applications, 2-nd ed. John Willey & Sons, 2013. 778 p. 4. Djigan V.I. Adaptivnaya fil'traciya signalov. Teoriya i algoritmy (Adaptive filtering: theory and algorithms). Moscow: Tekhnosfera, 2013. 528 p. (in Russian) 5. Haykin S. Adaptive filter theory, 5-th ed. Pearson Education Inc., 2014. 889 p. 6. Benesty J., HuangY., Eds. Adaptive signal processing: applications to real-workd problems. Sprringer-Verlag., 2003. 356 p. 7. Djigan V.I. Adaptivnye fil'try i ih prilozheniya v radiotekhnike i svyazi (Adaptive filters and its applications in radio and communication engineering). Part 1 // Sovremennaya elektronika (Modern Electronics). 2009. Ή9. P. 5663. (in Russian) 8. Djigan V.I. Adaptivnye fil'try i ih prilozheniya v radiotekhnike i svyazi (Adaptive filters and its applications in radio and communication engineering). Part 2 // Sovremennaya elektronika (Modern Electronics). 2010. Ή1. P. 7277. (in Russian) 9. Djigan V.I. Adaptivnye fil'try i ih prilozheniya v radiotekhnike i svyazi (Adaptive filters and its applications in radio and communication engineering). Part 3 // Sovremennaya elektronika (Modern Electronics). 2010. Ή2. P. 7077. (in Russian) 10. Monzingo R.A., Haupt R.L., Miller T.W. Introduction to adaptive arrays, 2nd ed. SciTech Publishing, 2011. 510 p. 11. Kuo S.M., Morgan D.S. Active noise control // Proceedings of the IEEE. 1999. Vol. 87. Ή 6. P. 943973. 12. Messerschmitt D. Echo cancellation in speech and data transmission // IEEE Journal on Selected Areas in Communications. 1984. Vol. 2. Ή2. P. 283297. 13. Nezami M.K. Fundamentals of power amplifier linearization using digital pre-distortion // High Frequency Electronics, 2004. V. 3. Ή 8. P. 5459. 14. Qureshi S. Adaptive equalization // IEEE Communications Magazine. 1982. Vol. 20. Ή2. P. 916. 15. Proakis J.G., Salehi M. Digital communications, 5-th ed. McGraw Hill, 2007. 1170 p. 16. Lucky R.W. Automatic equalization for digital communication // Bell System Technical Journal. 1965. Vol. 44. Ή 2. P. 547588. 17. Becker F.K., Holzman L.N., Lucky R.W., Port E. Automatic equalization for digital communication // Proceedings of the IEEE. 1965. Vol. 52. Ή 1. P. 9697. 18. Qureshi S. Adaptive equalization // Proceedings of the IEEE. 1985. Vol. 73. Ή 9. P. 13491387. 19. Lucky R.W. The adaptive equalizer // IEEE Signal Processing Magazine. 2006. Vol. 23. Ή 3. P. 104107. 20. Belfiore C.A., Park J.H. Decision feedback equalization // Proceedings of the IEEE. 1979. Vol. 67. Ή 8. P. 11431156. 21. George D., Bowen R., Storey J. An adaptive decision feedback equalizer // IEEE Transactions on Communications. 1971. Vol. 19. Ή 3. P. 282293. 22. Gitlin R.D., Weinstein S.B. Fractionally-spaced equalization: an improoved digital transwersal equalizer // The Bell System Technical Journal. 1981. Vol. 60. Ή 2. P. 275296. 23. Treichler J.R. Fijalkow I., Johnson C.R. Fractionally spaced equalizers // IEEE Signal Processing Magazine. 1996. Vol. 13. Ή 3. P. 6581. 24. Bayoumi M.A. VLSI design methodologies for digital signal processing architectures. Springer, 1994. 399 p. 25. Kuo S.M., Gan W.-S. S. Digital signal processors: architectures, implementations and applications. Prentice Hal, 2004. 624 p. 26. Welch T.B., Wright H.G.,Morrow M.G. Real-time digital signal processing from MATLAB to C with the TMS320C6x DSPs, 3rd ed. CRC Press, 2017. 480 p. 27. Woods R., McAllister J., Lightbody G., Ying Yi. FPGA-based implementation of signal processing systems, 2nd ed. Willey, 2017. 360 p. 28. Giordano A.A., Hsu F.M. Least square estimation with application to digital signal processing. Canada, Toronto: John Wiley and Sons, Inc., 1985. 412 p.
Comparison of time-frequency transforms: Fourier analysis, wavelets and allpass transformed filter banks
Keywords: time-frequency transform, filter bank, allpass transform, constant Q analysis. Based on the obtained results, it can be concluded that the STFT and the corresponding DFT-modulated filter bank should be used when it is required to decompose the signal into "atoms" uniformly covering the time-frequency plane. The wavelet filter bank as well as the allpass transformed DFT filter bank are well suited for constant Q analysis. Such analysis is especially important in applications where it is necessary to model the auditory perception. However, the allpass transformed DFT filter bank has some advantage over the wavelet-based filter bank in that it allows better frequency localization in the low-pass region. In addition, it should be noted the flexibility of the approach based on the allpass transform. The degree of deformation of the frequency axis depends on one parameter, changing which time-frequency tilling can be smoothly controlled. References 2. Mallat, S. A wavelet tour of signal processing. New Yourk: Academic Press, 1999. 637 p. 3. Vary, P. Digital filter banks with unequal resolution // Short Communication Digest of European Signal Processing Conference (EUSIPCO), 1980. pp. 4142. 4. Vary, P. "Ein Beitrag zur Kurzzeitspektralanalyse mit digitalen Systemen" (PhD thesis), [Electronic resource]. 1978. Mode of access: https://www.tib.eu/de/suchen/id/TIBKAT%3A020659989. 5. Quatieri, T.F. Discretetime speech signal processing: principles and practice / Prentice Hall Signal Processing Series. Prentice Hall PTR, 2002. P. 781. 6. Goodwin, M.M. The STFT, sinusoidal models, and speech modification // Springer Handbook of Speech Processing. Springer, 2008. pp. 229258. 7. Shensa, M. J. The discrete wavelet transform: wedding the a trous and mallat algorithms // IEEE Transactions on signal processing. 1992. vol. 40, no. 10. pp. 24642482. 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. 9. R. Blahut, Fast Algorithms for Digital Signal Processing. Massachusetts: Addison-Wesley, 1985. 450 p. 10. Broome, P. W. Discrete orthonormal sequences / P. W. Broome // Journal of the Association for Computing Machinery. 1965. vol. 12, no. 2. pp. 151168. 11. Evangelista, G. Frequencywarped filter banks and wavelet transforms: a discretetime approach via laguerre expansion / G. Evangelista, S. Cavaliere // IEEE Transactions on Signal Processing. 1998. vol. 46, no. 10. pp. 26382650. 12. Oppenheim, A. Computation of spectra with unequal resolution using the fast Fourier transform, / A. Oppenheim, D. Johnson, K. Steiglitz // Proceedings of the IEEE, 1971. vol. 59, no. 2, pp. 299-301. 13. Oppenheim, A. Discrete representation of signals / A. Oppenheim, D. Johnson, K. Steiglitz // Proceedings of the IEEE. 1972. vol. 60. pp. 681691. 14. Gulzow, T. Comparison of a discrete wavelet transformation and a nonuniform polyphase filterbank applied to spectralsubtraction speech enhancement / T. Gulzow, A. Engelsberg, U. Heute // Signal processing. 1998. Vol. 64, no. 1. pp. 519. 15. Nielsen, M. On the construction and frequency localization of finite orthogonal quadrature filters / M. Nielsen // Journal of Approximation Theory. 2001. vol. 108. pp. 3652.
Effective signal transmission methods in satellite communications systems
Abstract It was noted that SSSE systems are simpler in technical implementation compared to SCS of the DVB-S2 standard. The use of multidimensional SSSE also simplifies the implementation of different operating modes, allowing you to adapt the transmission of messages with high reliability to possible changes in the propagation conditions of radio waves in the satellite communication channel. This is due to the fact that in systems with SSSE there is no need to use noise-resistant codes of large length and very complex decoders. It is shown that in systems with SSSE the length of transmitted signals is significantly less than the length of code combinations in SCS standard DVB-S2. Therefore, the use of communication systems with SSSE is especially attractive in cases where it is necessary to transmit short informational messages and the transmission time should be minimally possible. 2. European standard. ETSI EN 302 307-1 V1.4.1. Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications; Part 1: DVB-S2. // ETSI. 2014. 80 p. 3. Peterson, W. W. & Weldon, E. J. Error Correcting Codes, Revised 2nd Edition. // MIT Press. 1972. 549 p. 4. Shannon C. Probability of error for optimal codes in Gaussian channel. Bell System Techn. J., May, 1959. pp. 611-656 5. Bykhovskiy M.A. Giperfazovaya modulyatsiya optimal'nyy metod peredachi tsifrovykh soobshcheniy (Chast' 1). Tsifrovaya obrabotka signalov. (Bykhovskiy M.A. Hyperphase modulation is the optimal method for transmitting digital messages (Part 1). Digital signal processing. M., 2018. no. 1. pp. 8-11. 6. Bykhovskiy M.A. Giperfazovaya modulyatsiya optimal'nyy metod peredachi tsifrovykh soobshcheniy (Chast' 2). Tsifrovaya obrabotka signalov. (Bykhovskiy M.A. Hyperphase modulation is the optimal method for transmitting digital messages (Part 21). Digital signal processing. M., 2018. no. 1. pp. 3-10. 7. Bykhovskiy M.A. Giperfazovaya modulyatsiya optimal'nyy metod peredachi tsifrovykh soobshcheniy (Chast' 3). Tsifrovaya obrabotka signalov. (Bykhovskiy M.A. Hyperphase modulation is the optimal method for transmitting digital messages (Part 3). Digital signal processing. M., 2018. no. 1. pp. 11-17. 8. Bykhovskiy M.A. Giperfazovaya modulyatsiya optimal'nyy metod peredachi soobshcheniy v gaussovskikh kanalakh svyazi. M.: Tekhnosfera, (Bykhovskiy M.A. Hyperphase modulation is the optimal method for transmitting messages in Gaussian communication channels. //Moscow, Technosphere.) 2018. p. 310. 9. Proakis J. G. Digital Communications. 3rd Edition. // McGraw Hill. 1995. 608 p.
Abstract To form PSS, we use sequences with Good correlation characteristics ZC(u, n), where u is the indices (roots) of the sequences (u= 25, 29 ,34), and n=62 is the number of elements. The LTE standard regulates OFDM technology, and 62 Central subcarriers are allocated for the distribution of sequence elements that form synchro signals to accommodate elements of the corresponding sequences. The article defines the conditions for forming a normalized threshold for analyzing the peaks of PSS correlation functions, and develops a mathematical model of the transmitted multi frequency OFDM symbol of the primary PSS sync signal formed on the basis of the ZCi(u,n) sequence, according to the LTE technology standard. The results of modeling all combinations of normalized correlation functions are summarized in a table. The structure of the classical version of the algorithm for processing received OFDM symbols is given, and the algorithm for processing PSS correlation functions in the time domain, without switching to the frequency domain, is described. An approximate calculation of the reduction of calculations when using the algorithm in the time domain of PSS processing is performed. Based on the results of simulation in the MATLAB operating environment, a 3D software model of the correlation function of the PSS synchro signal was developed based on the ZC(25,62) set sequence, in coordinates (time x frequency x normalized amplitude). The 3D model graph is based on a resource matrix (256x20) of elements; the time grid step 0,52*10-6s, frequency grid step 50 Hz. One of the main tasks of designing mobile user systems is to reduce the hardware and software resources of the systems. In terms of this problem, the PSS correlation function is modeled for a quantized sequence ZC(25.62) with a quantization step Q=1/32. The analysis of the obtained data for a quantized sequence with a step of Q = 1/32 and a non-quantized sequence ZC(25.62) allows us to conclude that synchronization along the correlation curve of the primary multi-frequency synchro signal (PSS) in the time domain is possible without passing into the frequency compensation region of the Doppler shift. The synchronization accuracy on the correlation function of the PSS, in case of constructing a multifrequency PSS symbol as unquantized and quantized with quantization step Q = 1/32 sequence ZC(of 25.62) equal to ± 0,52*10-6, and for correlation of the curve of the ZC sequence(of 25.62), obtained by the classical treatment of a received PSS symbol, i.e. the transition in the frequency region processed with FFT and frequency equalization by the equalizer. In this case, the accuracy of frequency synchronization for PSS based on non quantized ZC(25.62) is about ±50 Hz; for PSS based on quantized ZC(25.62) about ±100 Hz, which is quite acceptable for carrier frequency values with f0 = 100 MHz and higher based on the permissible carrier frequency detuning of 0.1 ppm. References 2. Gelgor A. L., Popov E. A. LTE technology for mobile data transmission: a textbook. SPb.: Polytechnic University press, 2011 - 204 pages 3. 3GPP, "3GPP TS 36.104 VII. 8.2. 3rd Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) radio transmission and reception ( Release 11)", 3rd Generation Partnership Project, Tech. Rep., April, 2014. 4. Kiseleva T. P. Investigation of the properties of the cyclic autocorrelation function of the Zadov Chu sequence depending on the quantization characteristics of the sequence elements. Moscow: Digital Signal Processing, no. 4, 2018, 40-44C 5. The error function .[Electronic resource] Mode of access: https://abakbot.ru/online-16/451-erf (date accessed: 10.02.2020). 6. Gonorovsky I. S.-Radio engineering circuits and signals. - Moscow: Radio and communications, 1986, 386-390s. 7. Choosing a number system for computer use - [Electronic resource] - access Mode: http://scask.ru/p_book_pta.php?id=13 (accessed 29.09.2019)
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Abstract In this paper, another effort is made in order to improve VIP analysis, namely, it is proposed to plotting the dependence of the controlled parameter of the magnitude response of optimal FIR filters not from one as earlier, but immediately from two selected initial parameters. This involves MATLAB three-dimensional graphics. After description of controlled and initial parameters some examples of analysis of presented dependencies for optimal halfband FIR filter of direct structure with one and three quantization steps of its coefficients are given. It is shown that the use of three quantization steps, instead of one-step, makes it possible to significantly simplify multipliers in the filter when it is implemented on VLSI. It saves the chip area and power consumption. 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