Abstract

The results of a feasibility study of an optical adaptive filter are presented. The processor is a time-domain implementation using correlation cancellation loops. Included is a theoretical verification of the correlation cancellation loop approach for linear prediction. The processor architecture and performance are described in detail. The results are encouraging although limited by laboratory equipment.

© 1983 Optical Society of America

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References

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  1. D. R. Morgan, S. E. Craig, IEEE Trans. Acoust. Speech Signal Processing ASSP-24, 494 (1976).
    [CrossRef]
  2. J. Makhoul, Proc. IEEE 63, 561 (1975).
    [CrossRef]
  3. J. Makhoul, IEEE Trans. Acoust. Speech Signal Processing ASSP-23, 283 (1975).
    [CrossRef]
  4. R. W. Lucky, Bell Syst. Tech. J. 47, 549 (1968).
  5. A. Korpel, Proc. IEEE 69, 48 (1981).
    [CrossRef]
  6. W. T. Rhodes, Proc. IEEE 69, 65 (1981).
    [CrossRef]

1981

A. Korpel, Proc. IEEE 69, 48 (1981).
[CrossRef]

W. T. Rhodes, Proc. IEEE 69, 65 (1981).
[CrossRef]

1976

D. R. Morgan, S. E. Craig, IEEE Trans. Acoust. Speech Signal Processing ASSP-24, 494 (1976).
[CrossRef]

1975

J. Makhoul, Proc. IEEE 63, 561 (1975).
[CrossRef]

J. Makhoul, IEEE Trans. Acoust. Speech Signal Processing ASSP-23, 283 (1975).
[CrossRef]

1968

R. W. Lucky, Bell Syst. Tech. J. 47, 549 (1968).

Craig, S. E.

D. R. Morgan, S. E. Craig, IEEE Trans. Acoust. Speech Signal Processing ASSP-24, 494 (1976).
[CrossRef]

Korpel, A.

A. Korpel, Proc. IEEE 69, 48 (1981).
[CrossRef]

Lucky, R. W.

R. W. Lucky, Bell Syst. Tech. J. 47, 549 (1968).

Makhoul, J.

J. Makhoul, Proc. IEEE 63, 561 (1975).
[CrossRef]

J. Makhoul, IEEE Trans. Acoust. Speech Signal Processing ASSP-23, 283 (1975).
[CrossRef]

Morgan, D. R.

D. R. Morgan, S. E. Craig, IEEE Trans. Acoust. Speech Signal Processing ASSP-24, 494 (1976).
[CrossRef]

Rhodes, W. T.

W. T. Rhodes, Proc. IEEE 69, 65 (1981).
[CrossRef]

Bell Syst. Tech. J.

R. W. Lucky, Bell Syst. Tech. J. 47, 549 (1968).

IEEE Trans. Acoust. Speech Signal Processing

D. R. Morgan, S. E. Craig, IEEE Trans. Acoust. Speech Signal Processing ASSP-24, 494 (1976).
[CrossRef]

J. Makhoul, IEEE Trans. Acoust. Speech Signal Processing ASSP-23, 283 (1975).
[CrossRef]

Proc. IEEE

J. Makhoul, Proc. IEEE 63, 561 (1975).
[CrossRef]

A. Korpel, Proc. IEEE 69, 48 (1981).
[CrossRef]

W. T. Rhodes, Proc. IEEE 69, 65 (1981).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Adaptive linear predictor constructed with correlation cancellation loops.

Fig. 2
Fig. 2

Modulation of input light intensity by electrically driven Bragg cell with a time aperture of D/υ sec.

Fig. 3
Fig. 3

Modulation of input light intensity by both an electrooptic modulator and a Bragg cell, resulting in a total light modulation proportional to the product of the two separate modulations.

Fig. 4
Fig. 4

Block diagram of the optical adaptive filter.

Fig. 5
Fig. 5

Schematic of the optical portion of the optical adaptive filter: f, focal length; C, cylindrical lens; S; spherical lens, POL, polarizer; COL; collimator; BC, Bragg cell; EO, electrooptic modulator; PMT, photomultiplier tube; LCLV, liquid crystal light valve.

Fig. 6
Fig. 6

Diagram of the modified correlation cancellation loop circuit.

Fig. 7
Fig. 7

Diagram of relative polarizations of read beam incident light, read beam reflected light, and analyzer.

Fig. 8
Fig. 8

Error signal transient response for a 3.6-MHz sinusoidal input x(t). Vertical scale, 100 mV/div; horizontal scale, 500 μsec/div; relative gain values, (a) A, (b) (5/2)A, (c) 5A, and (d) 10A.

Fig. 9
Fig. 9

Error signal spectrum for 3.6-MHz sinusoidal input x(t). Vertical scale, 10 dB/div; horizontal scale, 2 MHz/div; relative gain values, (a) open loop, (b) A, (c) (5/2)A, (d) 5A, and (e) 10A.

Fig. 10
Fig. 10

Top trace, x(t); bottom trace, x ˆ ( t ) for an impulse train input x(t); top vertical scale, 0.2 V/div; bottom vertical scale, 0.1 V/div; horizontal scale, 0.5 μsec/div; relative gain values, (a) B, (b) 2B, (c) 5B, (d) 10B, and (e) 20B.

Fig. 11
Fig. 11

Error signal spectrum for an impulse train input x(t). Vertical scale, 10 dB/div; horizontal scale, 2 MHz/div; relative gain values, (a) open loop, (b) B, (c) 2B, (d) 5B, and (e) 10B.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

x ˆ ( t ) = n = 1 N a n x ( t n T ) .
a p ( E { [ x ( t ) x ˆ ( t ) ] 2 } ) = E { a p [ x ( t ) x ˆ ( t ) ] 2 } = 0.
E { a p [ x 2 ( t ) 2 x ˆ ( t ) x ( t ) + x ˆ 2 ( t ) ] } = E [ 2 x ( t ) x ˆ ( t ) a p + 2 x ˆ ( t ) x ˆ ( t ) a p ] = 0.
E { [ x ( t ) x ˆ ( t ) ] x ˆ ( t ) a p } = 0 ,
x ˆ ( t ) a p = x ( t p T ) .
E { [ x ( t ) n = 1 N a n x ( t n T ) ] x ( t p T ) } = 0 ,
E [ x ( t ) x ( t p T ) ] = E [ n = 1 N a n x ( t n T ) x ( t p T ) ] .
E [ x ( t ) x ( t p T ) ] = n = 1 N a n E [ x ( t n T ) x ( t p T ) ] .
a ˙ p ( t ) = μ x ( t p T ) [ x ( t ) n = 1 N a n ( t ) x ( t n T ) ] ,
x ( t ) n = 1 N a n ( t ) x ( t n T ) = e ( t ) ,
lim t E { μ x ( t p T ) [ x ( t ) n = 1 N a n ( t ) x ( t n T ) ] } = 0.
lim t E [ x ( t ) x ( t p T ) ] n = 1 N E [ a n ( t ) x ( t n T ) x ( t p T ) ] = 0.
lim t E [ a n ( t ) x ( t n T ) x ( t p T ) ] = lim t E [ a n ( t ) ] E [ x ( t n T ) x ( t p T ) ] ,
E [ x ( t ) x ( t p T ) ] = n = 1 N a n E [ x ( t n T ) x ( t p T ) ]

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