Differential algorithms of digital signal processing
DOI:
https://doi.org/10.3103/S073527271007006XKeywords:
DSP, time frequency transform, сonvolutionAbstract
A general approach to constructing differential algorithms of digital signal processing (DSP) which contain the corresponding transformation functions is provided. As an example the discrete Fourier transform algorithms, implemented using this approach, and some derivative algorithms—Hartley transform, short-time Fourier transform and lapped transform, cosine transform, and Mellin, Hilbert and wavelet transforms are presented. The use of these algorithms allows increasing efficiency and processing power of DSP.
References
G. Korn and Т. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968; Nauka, Moscow, 1974).
R. Steele, Delta Modulation Systems (John Wiley & Sons Inc., New York, 1975; Svyaz’, Moscow, 1979).
М. D. Venediktov, B. P. Zhenevskii, V. V. Markov, and G. S. Eidus, Delta-Modulation. Theory and Application (Svyaz’, Moscow, 1976) [in Russian].
W. A. Pogribny, Delta-Modulation in Digital Signal Processing (Radio i Svyaz’, Moscow, 1990) [in Russian].
D. G. Zrilic, Circuits and Systems Based on Delta Modulation (Springer-Verlag, Berlin, 2005).
N. S. Jayant, “On the Power Spectrum of the Staircase Function in Linear Delta Modulation,” IEEE Trans. Acoust., Speech, Signal Process. 23, No. 2, 162 (1975).
B. Liu and L. Goldstein, “Power Spectra of ADPCM,” IEEE Trans. Acoust., Speech, Signal Process. 25, No. 1, 56 (1977).
W. A. Pogribny, “Application of delta-modulation in discrete Fourier transform,” DAN USSR. Ser. А: Fiziko-matem. i techn. Nauki, No. 8, 64 (1985).
W. Pogribny and M. Drzycimski, “Fuzzy Extreme Analysis for Signal Compression,” in Proc. IEEE ICSES 2008 Int. Conf. on Signals and Electronic Systems, Krakow, Poland, 2008 (Krakow, 2008), pp. 31–34.
W. Pogribny and D. Surma, “Sliding Discrete Fourier Transform in Differential Format,” Information Extraction and Processing, No. 28 (104), 48 (2008).
W. Pogribny and M. Drechny, “Speech processing with the usage of cosine transform on the basis of synthetic DPCM,” in Proc. 48th Int. Symp. IEEE–ELMAR focused on Multimedia Signal Processing and Communications, Zadar, Croatia, 2006 (Zadar, 2006), pp. 119–122.
W. Pogribny, B. Marciniak, and T. Marciniak, “Digital Filtration with Use of Synthetic DPCM,” in Proc. 4th IEEE Int. Symp. on Image and Signal Processing and Analysis, Zagreb, Croatia, 2005 (Zagreb, 2005), pp. 430–433.
W. Pogribny and M. Drechny, “Fast Operations with the Use of Differential Codes,” in Proc. IEEE EUROCON 2007 Int. Conf. ‘Computer as a Tool,’ Session TPC–3 ‘Computer Engineering’, Warsaw, Poland, 2007 (Warsaw, 2007), pp. 525–529.
А.А. Samarskii, Differential Circuits Theory (Nauka, Moscow, 1989) [in Russian].
N. E. Huang and S. P. Shen (eds.), Hilbert–Huang Transform and Its Applications (World Scientific Publishing Co. Pte. Ltd., Singapore, 2005).
K. Sayood, Introduction to Data Compression (Morgan Kaufmann Publishers, San Francisco, 2002).
A. D. Poularikas (ed.), The Transforms and Applications Handbook, 2nd ed. (CRC Press LLC, Boca Raton, 2000).
J. Y. Stein, Digital Signal Processing: A Computer Science Perspective (John Wiley & Sons Inc., New York, 2000).
I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, “The Dual–Tree Complex Wavelet Transform,” IEEE SP Magazine (Signal Processing) 22, No. 6, 123 (2005).
W. Pogribny and M. Drechny, “Parallel Computations in Mixed Formats,” in Proc. IASTED Int. Conf. on Advances in Computer Science and Technology (ACST 2007), Phuket, Thailand, 2007 (Phuket, 2007), pp. 287–292.
W. А. Pogribny, I. V. Rozhankovskii, and V. I. Lozinskii, “Matched Filtration in Combined Formats for Digital Location,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 46(12), 3 (2003); Radioelectron. Commun. Syst. 46(12), 1 (2003).
