Abstract

A new class of optimum spatial filters is developed. This class is optimum for filters with a magnitude constraint on the filter transfer function. Some special cases of this class are found to be similar to the Wiener filter, matched filter, and probability-weighted spatial filter. The derivation of the probability-weighted spatial filter is extended to include complex-valued signals.

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  1. A. B. Vander Lugt, IEEE Trans. IT-10, 2 (1964).
  2. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 219.
  3. H. L. VanTrees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), p. 226.
  4. I. Selin, Detection Theory (Princeton U. P., Princeton, N. J., 1965), p. 46.
  5. W. T. Cathey, Jr., J. Opt. Soc. Am. 61, 478 (1971).
  6. L. Franks, Signal Theory (Prentice–Hall, Englewood Cliffs, N. J., 1969), p. 247.
  7. J. B. Thomas, An Introduction to Statistical Communication Theory (Wiley, New York, 1969).
  8. B. Liu and N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).
  9. M. Severcan, Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Ranges, Stanford University Information Systems Laboratory Technical Report No. 6415-6, Dec. 1973, p. 13, p. 28, and Ch. 3.
  10. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw–Hill, New York, 1968), p. 287.
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), p. 178.
  12. H. Cramer and M. R. Leadbetter, Stationary and Related Stochastic Processes (Wiley, New York, 1967), p. 96.

Severcan, M.

M. Severcan, Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Ranges, Stanford University Information Systems Laboratory Technical Report No. 6415-6, Dec. 1973, p. 13, p. 28, and Ch. 3.

Vander Lugt, A. B.

A. B. Vander Lugt, IEEE Trans. IT-10, 2 (1964).

Cathey, Jr., W. T.

W. T. Cathey, Jr., J. Opt. Soc. Am. 61, 478 (1971).

Cramer, H.

H. Cramer and M. R. Leadbetter, Stationary and Related Stochastic Processes (Wiley, New York, 1967), p. 96.

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 219.

Franks, L.

L. Franks, Signal Theory (Prentice–Hall, Englewood Cliffs, N. J., 1969), p. 247.

Gallagher, N. C.

B. Liu and N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), p. 178.

Leadbetter, M. R.

H. Cramer and M. R. Leadbetter, Stationary and Related Stochastic Processes (Wiley, New York, 1967), p. 96.

Liu, B.

B. Liu and N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw–Hill, New York, 1968), p. 287.

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 219.

Selin, I.

I. Selin, Detection Theory (Princeton U. P., Princeton, N. J., 1965), p. 46.

Thomas, J. B.

J. B. Thomas, An Introduction to Statistical Communication Theory (Wiley, New York, 1969).

VanTrees, H. L.

H. L. VanTrees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), p. 226.

Other (12)

A. B. Vander Lugt, IEEE Trans. IT-10, 2 (1964).

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 219.

H. L. VanTrees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), p. 226.

I. Selin, Detection Theory (Princeton U. P., Princeton, N. J., 1965), p. 46.

W. T. Cathey, Jr., J. Opt. Soc. Am. 61, 478 (1971).

L. Franks, Signal Theory (Prentice–Hall, Englewood Cliffs, N. J., 1969), p. 247.

J. B. Thomas, An Introduction to Statistical Communication Theory (Wiley, New York, 1969).

B. Liu and N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).

M. Severcan, Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Ranges, Stanford University Information Systems Laboratory Technical Report No. 6415-6, Dec. 1973, p. 13, p. 28, and Ch. 3.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw–Hill, New York, 1968), p. 287.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), p. 178.

H. Cramer and M. R. Leadbetter, Stationary and Related Stochastic Processes (Wiley, New York, 1967), p. 96.

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