Таблица F3.A-1.6. Свертка 2-х векторов в (A-1)-арифметике

Таблица F3.A-1.6 Свертка 2-х векторов (r)X[t] и (r)H[t] длины T= 8
в поле Галуа

GF( 1 + 223 ) = GF( 1 + 28 ) = GF( F3 )

в (A-1)-арифметике, T^–1 = 1/T = 0'11100000B = -32
Результаты в (A-1)-арифметике в виде 9-битовых слов = ПСАНВ± mod F3, т.е. в диапазоне [–128..+128]

(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     0'00011111 =  32        0'00111111 =  64        0'00000000 =   1        0'00000010 =   3        0'10111111 = -65        0'11111111 =  -1        0'00011111 =  32
   1     0'00111111 =  64        0'00100000 =  33        0'00000001 =   2        0'00001000 =   9        0'00100111 =  40        0'11111100 =  -4        0'01111111 = 128
   2     0'11100000 = -32        0'00111011 =  60        1'00000000 =   0        0'00100000 =  33        0'10110100 = -76        0'11111101 =  -3        0'01011111 =  96
   3     1'00000000 =   0        0'00001101 =  14        1'00000000 =   0        0'10000000 =-128        0'00000110 =   7        0'00000001 =   2        0'11000000 = -64
   4     1'00000000 =   0        0'11000000 = -64        1'00000000 =   0        0'11111111 =  -1        0'00111111 =  64        1'00000000 =   0        1'00000000 =   0
   5     1'00000000 =   0        0'00100010 =  35        1'00000000 =   0        0'11111001 =  -7        0'00001011 =  12        1'00000000 =   0        1'00000000 =   0
   6     1'00000000 =   0        0'01000011 =  68        1'00000000 =   0        0'11100001 = -31        0'11001100 = -52        1'00000000 =   0        1'00000000 =   0
   7     1'00000000 =   0        0'00101101 =  46        1'00000000 =   0        0'10000001 =-127        0'01000100 =  69        1'00000000 =   0        1'00000000 =   0