Таблица F4.A-1.5. Свертка 2-х векторов в (A-1)-арифметике

Таблица F4.A-1.5 Свертка 2-х векторов (r)X[t] и (r)H[t] длины T= 8
в поле Галуа

GF( 1 + 224 ) = GF( 1 + 216 ) = GF( F4 )

в (A-1)-арифметике, T–1 = 1/T = 0'224. 0 = 57345
Результаты в (A-1)-арифметике в виде 17-битовых слов = ПСНВ+ mod F4, т.е. в диапазоне [ 0..+65536]

t (r)X[t]
вх.Сигнал
(r)X[f]=
ЧПФ((r)X[t])
(r)H[t]
вх.Сигнал
(r)H[f]=
ЧПФ((r)H[t])
(r)E[f]=
(r)X[f]·(r)H[f]
(r)E[t]=
оЧПФ((r)E[f])
(r)G[t]=
(r)E[t]/T mod F2
0 0' 0. 1 = 2 0' 0. 17 = 18 0' 0. 0 = 1 0' 0. 2 = 3 0' 0. 53 = 54 0' 0. 15 = 16 0' 0. 1 = 2
1 0' 0. 14 = 15 0' 1.241 = 498 0' 0. 1 = 2 0' 0. 32 = 33 0' 64. 49 = 16434 0' 0.151 = 152 0' 0. 18 = 19
2 0' 0. 0 = 1 0' 15. 0 = 3841 1' 0. 0 = 0 0' 2. 0 = 513 0' 16.226 = 4323 0' 0.247 = 248 0' 0. 30 = 31
3 1' 0. 0 = 0 0'239. 1 = 61186 1' 0. 0 = 0 0' 32. 0 = 8193 0' 17. 32 = 4385 0' 0. 15 = 16 0' 0. 1 = 2
4 1' 0. 0 = 0 0'255.244 = 65525 1' 0. 0 = 0 0'255.255 = 2^16 0' 0. 11 = 12 1' 0. 0 = 0 1' 0. 0 = 0
5 1' 0. 0 = 0 0' 0. 17 = 18 1' 0. 0 = 0 0'255.225 = 65506 0'253.210 = 64979 1' 0. 0 = 0 1' 0. 0 = 0
6 1' 0. 0 = 0 0'241. 1 = 61698 1' 0. 0 = 0 0'254. 1 = 65026 0'238.227 = 61156 1' 0. 0 = 0 1' 0. 0 = 0
7 1' 0. 0 = 0 0' 15. 2 = 3843 1' 0. 0 = 0 0'224. 1 = 57346 0'176.227 = 45284 1' 0. 0 = 0 1' 0. 0 = 0




© 2006 г., Александр Тимофеев, г.Харьков, Украина. E-mail: atimopheyev@yahoo.com