By Henry Stark

ISBN-10: 0126632200

ISBN-13: 9780126632200

ISBN-10: 0323145930

ISBN-13: 9780323145930

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8, 2165-2172. [16] C. W. Barnes (1966). J. Opt. Soc. Am. 56, 575-578. [17] R. W. Gerchberg (1974). Opt. Acta 21, 709-720. [18] A. Papoulis (1975). IEEE Trans. Circuits Syst. CAS-22, 735-742. [19] J. A. Cadzow (1979). IEEE Trans. , Speech, Signal Process. ASS-27, 4-11. [20] M. S. Sabri and W. Steenaart (1978). IEEE Trans. Circuits Syst. CAS-25, 74-78. [21] D. C. Youla (1978). IEEE Trans. Circuits Syst. CAS-25, 694-701. [22] H. Stark and G. Shao (1977). Appl. Opt. 10, 1670-1674. APPLICATIONS OF OPTICAL FOURIER TRANSFORMS Chapter 2 Pattern Recognition via Complex Spatial Filtering SILVERIO P.

7-9) for L large. Hence we see that, without smoothing, the noise power is as much as the signal power. This is the same result we observed in Eq. 5-1). This means that, if we wish to extract a stable estimate of S(u) from 5^(w), we must perform a smoothing operation on £f(u). 7-10) where &>(u) = S(M)[1 + W(M)]. 7-11) We impose the following conditions on W(u): W(u) = 0, |M| > c/2, \W(u)\2 du = X, W(u)du = 1. 7-12a) reflects our insistence that our filter has finite bandwidth c. 7-12b) is a constraint on the energy in the window and also amounts to constraining the variance of the smoothed sample spectrum.

Higher Transcendental Functions," Vol. 2. McGraw-Hill, New York. [5] A. Papoulis (1968). " McGraw-Hill, New York. [6] H. Stark (1968). Tech. Rep. T-l/006-1-00. Riverside Res. , New York. [7] M. G. Jenkins and D. G. Watts (1968). " HoldenDay, San Francisco, California. [8] N. I. Achieser (1956). " Ungar, New York. [9] A. Papoulis (1973). IEEE Trans. Inf. Theory IT-19, 9-12. [10] H. Stark and B. Dimitriadis (1975). J. Opt. Soc. Am. 65, 425-431. [11] A. Papoulis (1972). J. Opt. Soc. Am. 62, 1423-1429.

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