此页面上的内容需要较新版本的 Adobe Flash Player。

获取 Adobe Flash Player

Kravchenko atomic transforms in digital signal processing

V. F. Kravchenko, D. V. Churikov

 

(Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia)

 

Abstract:The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L1 and L2 on the basis of the theory of atomic functions (AF) are presented. The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.

 

Key words:atomic functions(AF); Fourier series; space-time transforms; digital signal processing (DSP)

 

CLD number: TN911.7 Document code: A

 

Article ID: 1674-8042(2012)03-0228-07  doi: 10.3969/j.issn.1674-8042.2012.03.006

 

References

 

[1] Kravchenko V F. Lectures on the theory of atomic functions and their some applications. Radiotechnika, Moscow, 2003.
[2] Kravchenko V F, Rvachev V L. boolean algebra, atomic functions and wavelets in physical applications. Fizmatlit, Moscow, 2006.
[3] Kravchenko V F. Digital signal and image processing in radio physical applications. Fizmatlit, Moscow, 2007.
[4] Kravchenko V F, Perez-Meana H M, Ponomaryov V I. Adaptive digital processing of multidimentional signals with applications. Fizmatlit, Moscow, 2009.
[5] Kravchenko V F, Churikov D V. New analytical WA-systems of Kravchenko functions. Proc. of the International Conference “Days on Diffraction”, St. Petersburg, Russia, 2010: 93-98.
[6]  Kravchenko V F, Churikov D V. Correlation radar signal processing on basis of probability Kravchenko weight functions. Proc. of IEEE 10th International Conference on Signal Processing (ICSP’10), Beijing, 2010: 1906-1909.
[7] Kravchenko V F, Churikov D V. Analytical Kravchenko-Kotelnikov and Kravchenko-Levitan wavelets in the digital UWB signal processing. Telecommunications and Radio Engineering, 2011,70(9): 759-786.
[8] Titchmarsh E C. Introduction to the theory of Fourier's integrals. Oxford University Press, 1937.
[9] Harkevich A A. Spectrums and the analysis. Publishing House LKI, Moscow, 2007.

 


[full text view]