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=16
в поле Галуа

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

в (A-1)-арифметике, T^–1 = 1/T = 0'11110000B = -16
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     0'10111111 = -65        0'11000010 = -62        0'00000000 =   1        0'00000010 =   3        0'01000110 =  71        0'11110100 = -12        0'10111111 = -65
   1     0'01111111 = 128        0'11001100 = -52        0'00000001 =   2        0'00000100 =   5        0'11111101 =  -3        0'11100000 = -32        0'11111110 =  -2
   2     0'10000011 =-125        0'11110101 = -11        1'00000000 =   0        0'00001000 =   9        0'10011101 = -99        0'00100111 =  40        0'10000010 =-126
   3     1'00000000 =   0        0'10011010 =-102        1'00000000 =   0        0'00010000 =  17        0'01000000 =  65        0'01101111 = 112        0'00000110 =   7
   4     1'00000000 =   0        0'00110011 =  52        1'00000000 =   0        0'00100000 =  33        0'10101101 = -83        1'00000000 =   0        1'00000000 =   0
   5     1'00000000 =   0        0'10100001 = -95        1'00000000 =   0        0'01000000 =  65        0'11111001 =  -7        1'00000000 =   0        1'00000000 =   0
   6     1'00000000 =   0        0'01100111 = 104        1'00000000 =   0        0'10000000 =-128        0'00110011 =  52        1'00000000 =   0        1'00000000 =   0
   7     1'00000000 =   0        0'10100000 = -96        1'00000000 =   0        1'00000000 =   0        1'00000000 =   0        1'00000000 =   0        1'00000000 =   0
   8     1'00000000 =   0        0'11000011 = -61        1'00000000 =   0        0'11111111 =  -1        0'00111100 =  61        1'00000000 =   0        1'00000000 =   0
   9     1'00000000 =   0        0'11001110 = -50        1'00000000 =   0        0'11111101 =  -3        0'10010101 =-107        1'00000000 =   0        1'00000000 =   0
  10     1'00000000 =   0        0'11111001 =  -7        1'00000000 =   0        0'11111001 =  -7        0'00110000 =  49        1'00000000 =   0        1'00000000 =   0
  11     1'00000000 =   0        0'10100010 = -94        1'00000000 =   0        0'11110001 = -15        0'01111100 = 125        1'00000000 =   0        1'00000000 =   0
  12     1'00000000 =   0        0'01000011 =  68        1'00000000 =   0        0'11100001 = -31        0'11001100 = -52        1'00000000 =   0        1'00000000 =   0
  13     1'00000000 =   0        0'11000001 = -63        1'00000000 =   0        0'11000001 = -63        0'01110001 = 114        1'00000000 =   0        1'00000000 =   0
  14     1'00000000 =   0        0'10100111 = -89        1'00000000 =   0        0'10000001 =-127        0'11111011 =  -5        1'00000000 =   0        1'00000000 =   0
  15     1'00000000 =   0        0'00011111 =  32        1'00000000 =   0        0'00000001 =   2        0'00111111 =  64        1'00000000 =   0        1'00000000 =   0