Abstract

Based on the mixed negative binary number system, we propose an inner-product algorithm for digital complex-valued matrix–vector multiplication. The features are no carries, no signs, no indications for decimal points, and simple preprocessing and postprocessing. Correspondingly, an optical architecture of incoherent optical correlation with spatial digital coding of data is suggested. Negative binary complex matrix–vector multiplication can be realized optically in parallel with a high accuracy. The experimental result is also given.

© 1994 Optical Society of America

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References

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1989 (1)

1986 (4)

1985 (1)

1984 (1)

R. P. Bocker, Opt. Eng. 23, 26 (1984).

1983 (1)

1980 (1)

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

1979 (1)

1967 (1)

M. P. de Regt, Comput. Design 6, 53 (1967).

Athale, R. A.

Baranoski, E.

Bocker, R.

B. Drake, R. Bocker, M. Lasher, R. Patterson, W. Miceli, Opt. Eng. 25, 38 (1986).

Bocker, R. P.

Bromley, K.

Carlotto, M.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Casasent, D.

Clayton, S. K.

de Regt, M. P.

M. P. de Regt, Comput. Design 6, 53 (1967).

Drake, B.

B. Drake, R. Bocker, M. Lasher, R. Patterson, W. Miceli, Opt. Eng. 25, 38 (1986).

Goodman, J. W.

Grinberg, J.

Huang, A.

Ishihara, S.

Lasher, M.

B. Drake, R. Bocker, M. Lasher, R. Patterson, W. Miceli, Opt. Eng. 25, 38 (1986).

Maron, E.

Miceli, W.

B. Drake, R. Bocker, M. Lasher, R. Patterson, W. Miceli, Opt. Eng. 25, 38 (1986).

Neft, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Owechko, Y.

Patterson, R.

B. Drake, R. Bocker, M. Lasher, R. Patterson, W. Miceli, Opt. Eng. 25, 38 (1986).

Perlee, C.

Psaltis, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Soffer, B. H.

Taylor, B. K.

Tsunoda, Y.

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Figures (5)

Fig. 1
Fig. 1

Optical incoherent correlation architecture for negabinary complex matrix-vector multiplication. A and B denote masks.

Fig. 2
Fig. 2

Pattern of the coded mask for the matrix.

Fig. 3
Fig. 3

Pattern of the coded mask for the vector.

Fig. 4
Fig. 4

(a) Light source array, (b) the possible output distribution.

Fig. 5
Fig. 5

Photograph of the result.

Equations (10)

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a = n = - L P a n ( - 2 ) n             ( a n 0 ) ,
a = { a K , a K - 1 , , a 1 , a 0 , a - 1 , , a - L + 1 , a - L } , b n = { b n - K , b n - K + 1 , , b n - 1 , b n , b n + 1 , , b n + L - 1 , b n + L } .
c n = a · b n .
c n R = a R · b n R - a I · b n I , c n I = a R · b n I - a I · b n R .
- a I · b n I ( - 2 ) n = { + 2 a I · b n I ( - 2 ) n - 1 + 1 2 a I · b n I ( - 2 ) n + 1 .
c n R ( i ) = j a R ( i , j ) · b n R ( j ) + 1 2 a I ( i , j ) · b n + 1 I ( j )             [ or 2 a I ( i , j ) · b n - 1 I ( j ) ] , c n I ( i ) = j a R ( i , j ) · b n I ( j ) + a I ( i , j ) · b n R ( j ) .
[ 2 - 5 5 j 2 - j 5 j 5 2 + j 2 2 - j 5 5 + j 5 ] [ 3 - j 3 1 - j ] = [ 11 + j 10 - 10 + j 11 1 ] .
[ 0110 : 0000 1111 : 0000 0101 : 0000 0000 : 0110 0000 : 1111 0000 : 0101 0110 : 0110 0110 : 1111 0101 : 0101 ] × [ 0111 : 0000 0000 : 1101 0001 : 0011 ] = [ 00012311 : 1224322 1 2 112 3 2 110 : 0012311 1 2 113 7 2 421 : 0134532 ] ,
I ( - f 2 f 1 x i , - f 2 f 1 y i ) = [ A R ( α , β ) B I ( α - x i L f 1 , β - y i L f 1 ) + A I ( α , β ) B R ( α - x i L f 1 , β - y i L f i ) ] d α d β ,             x i > 0 ; I ( - f 2 f 1 x i , - f 2 f 1 y i ) = [ A R ( α , β ) B R ( α - x i L f 1 , β - y i L f 1 ) + A I ( α , β ) B I / 2 ( α - x i L f 1 , β - y i L f i ) ] d α d β ,             x i < 0.
2 , 2 , 3 , 4 , 2 , 2 , 1 1 , 1 , 3 , 2 , 1 , 0 , 0 , 0 1 , 1 , 3 , 2 , 1 , 0 , 0 0 , 1 , 1 , 1.5 , 2 , 1 , 1 , 0.5 2 , 3 , 5 , 4 , 3 , 1 , 0 1 , 2 , 4 , 3.5 , 3 , 1 , 1 , 0.5.

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