The parallel circuit of fourier discrete and fast transformations on the basis of the base elements polynomial representation
Matematičeskoe modelirovanie, Tome 18 (2006) no. 11, pp. 3-13.

Voir la notice de l'article provenant de la source Math-Net.Ru

Circuits of the parallel evaluation of the functions, approximated by the orthogonal trigonometrical polynoms, including summation of Fourier series, performance of Diskret Fourier Transformation (DFT), Fast Fourier Transformation (FFT) are stated. The any number of basis' elements of the given decomposition is in parallel calculated with the minimal time complexity at dynamic change of counting, thus circuits combine calculation of basis' elements with performance of orthogonal transformations.
@article{MM_2006_18_11_a0,
     author = {Ya. E. Romm and S. A. Firsova},
     title = {The parallel circuit of fourier discrete and fast transformations on the basis of the base elements polynomial representation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {18},
     number = {11},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_11_a0/}
}
TY  - JOUR
AU  - Ya. E. Romm
AU  - S. A. Firsova
TI  - The parallel circuit of fourier discrete and fast transformations on the basis of the base elements polynomial representation
JO  - Matematičeskoe modelirovanie
PY  - 2006
SP  - 3
EP  - 13
VL  - 18
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2006_18_11_a0/
LA  - ru
ID  - MM_2006_18_11_a0
ER  - 
%0 Journal Article
%A Ya. E. Romm
%A S. A. Firsova
%T The parallel circuit of fourier discrete and fast transformations on the basis of the base elements polynomial representation
%J Matematičeskoe modelirovanie
%D 2006
%P 3-13
%V 18
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2006_18_11_a0/
%G ru
%F MM_2006_18_11_a0
Ya. E. Romm; S. A. Firsova. The parallel circuit of fourier discrete and fast transformations on the basis of the base elements polynomial representation. Matematičeskoe modelirovanie, Tome 18 (2006) no. 11, pp. 3-13. http://geodesic.mathdoc.fr/item/MM_2006_18_11_a0/

[1] Lyuk Yu., Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980

[2] Berezin I. S., Zhidkov N. G., Metody vychislenii, T. 1, Nauka, M., 1970

[3] Romm Ya. E., “Parallelnye iteratsionnye skhemy lineinoi algebry s prilozheniem k analizu ustoichivosti reshenii sistem lineinykh differentsialnykh uravnenii”, Kibernetika i sistemnyi analiz, 2004, no. 4, 119–142 | MR | Zbl

[4] Stone H. S., “Problems of parallel computation”, Complexity of Sequent. Paral Numer. Algor, ed. T. F. Traub, Acad. Press, NY, 1973, 1–16

[5] Faddeeva V. N., Faddeev D. K., “Parallelnye vychisleniya v lineinoi algebre”, Kibernetika, 1977, no. 6, 28–40 | MR | Zbl

[6] Solodovnikov V. I., “Verkhnie otsenki slozhnosti resheniya sistem lineinykh uravnenii”, Teoriya slozhnosti vychislenii. I, Zapiski nauchnykh seminarov LOMI, 118, L., 1982, 159–187 | MR | Zbl

[7] Kappelini V., Konstantinidis A. Dzh., Emiliani P., Tsifrovye filtry i ikh primenenie, Energoatomizdat, M., 1983

[8] Leus V. A., “O vremennoi slozhnosti parallelnoi realizatsii chislennogo preobrazovaniya Fure”, Matem. modelirovanie, 7:10 (1995), 99–110 | MR | Zbl

[9] Cooley J. W., Tukey J. W., Math. Comp., 19 (1965), 297–301 | DOI | MR | Zbl

[10] Rodrig G. (red.), Parallelnye vychisleniya, Nauka, M., 1986 | MR

[11] Oppengeim A. V., Shafer R. V., Tsifrovaya obrabotka signalov, ed. S. Ya. Shats, Svyaz, M., 1979 | Zbl

[12] Turulin I. I. Pod obschei red. L.K. Samoilova, Raschet i primenenie bystrodeistvuyuschikh tsifrovykh rekursivnykh filtrov s konechnoi impulsnoi kharakteristikoi: Monografiya, Izd-vo TRTU, Taganrog, 1999

[13] Petrovskii A. A., Kachinskii M. V., Shkredov S. A., “Formalizatsiya opisaniya i sinteza protsessorov DPF mnogomernykh signalov”, Avtomat. i vychisl. tekhn., 2002, no. 3, 48–56

[14] Klimova O. V., “Kompleksnyi teoretiko-gruppovoi podkhod k postroeniyu sovremennykh algoritmov DPF i svertki. Novye informatsionnye tekhnologii v issledovanii diskretnykh struktur”, Doklady 3 Vseross. konferentsii (Tomsk, 12–14 sentyabrya, 2000), Izd-vo TNTs SO RAN, Tomsk, 27–33

[15] Firsova S. A., Algoritmy optimizatsii vremennoi slozhnosti kusochno-polinomialnoi approksimatsii funktsii v primenenii k bystromu preobrazovaniyu Fure na osnove parallelnogo vychisleniya elementov bazisa, avtoreferat dissertatsii na soiskanie uchenoi stepeni kand. tekhn. nauk, TRTU, Taganrog, 2004

[16] Zalmanzon L. A., Preobrazovanie Fure, Uolsha, Khaara i ikh primenenie v upravlenii, svyazi i drugikh oblastyakh, Nauka, M., 1989 | MR | Zbl