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. 31 = 32 0' 0. 63 = 64 0' 0. 0 = 1 0' 0. 2 = 3 0' 0.191 = 192 0' 0.255 = 256 0' 0. 31 = 32
1 0' 0. 63 = 64 0'228. 32 = 58401 0' 0. 1 = 2 0' 0. 32 = 33 0'104. 35 = 26660 0' 3.255 = 1024 0' 0.127 = 128
2 0'255.224 = 65505 0' 64. 63 = 16448 1' 0. 0 = 0 0' 2. 0 = 513 0'191.191 = 49088 0' 2.255 = 768 0' 0. 95 = 96
3 1' 0. 0 = 0 0' 32. 27 = 8220 1' 0. 0 = 0 0' 32. 0 = 8193 0'156. 24 = 39961 0'254. 0 = 65025 0'255.192 = 65473
4 1' 0. 0 = 0 0'255.192 = 65473 1' 0. 0 = 0 0'255.255 = 2^16 0' 0. 63 = 64 1' 0. 0 = 0 1' 0. 0 = 0
5 1' 0. 0 = 0 0'220. 32 = 56353 1' 0. 0 = 0 0'255.225 = 65506 0' 88. 27 = 22556 1' 0. 0 = 0 1' 0. 0 = 0
6 1' 0. 0 = 0 0'192. 64 = 49217 1' 0. 0 = 0 0'254. 1 = 65026 0' 63.192 = 16321 1' 0. 0 = 0 1' 0. 0 = 0
7 1' 0. 0 = 0 0' 32. 35 = 8228 1' 0. 0 = 0 0'224. 1 = 57346 0'164. 40 = 42025 1' 0. 0 = 0 1' 0. 0 = 0




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