R. N. Bracewell and J. A. Roberts, Australian J. Phys. 7, 615 (1954).
See for example J. D. Kraus, Radio Astronomy (McGraw-Hill Book Co., New York, 1966), p. 69.
See Ref. 1, p. 627.
D. S. Jones, Generalized Functions (McGraw-Hill Book Co., New York, 1966), p. 354.
H. Wolter, in Progress in Optics I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), Ch. V, Sec. 4.6.
D. Slepian and H. O. Pollak, Bell System Tech. J. 40, 43 (1961).
G. J. Buck and J. J. Gustinic, IEEE Trans. Antennas Propagation AP-15, 376 (1967).
B. R. Frieden, J. Opt. Soc. Am. 57, 1013 (1967).
C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).
N. Wiener, The Extrapolation, Interpolation and Smoothing of Stationary Time Series (John Wiley & Sons, Inc., New York, 1949), Ch. III, p. 81.
C. W. Helstrom. J. Opt. Soc. Am. 57, 297 (1967).
D. Slepian, J. Opt. Soc. Am. 57, 918 (1967).
See for example W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill Book Co., New York, 1958), p. 224.
A. V. Balakrishnan, Trans. IRE IT-3, 143 (1957).
Expectation should be interpreted as the statistical average over the ensemble of process realizations.
Note that Slepian and Pollak6 define the frequency interval (—Ω, Ω) rather than (-Ω/2, Ω/2) as in this paper. Hence in their formulas Ω should be replaced by Ω/2. With this slight change their definitions are used directly.
This is derived in Ref. (8), Eq. (2.7).
See Ref. 11, Eq. (2.5).
See Ref. 1, Eq. (2.6).
This follows from Ref. (6), Eqs. (27), (28), and (29).
The expression [x] means the smallest integer larger than x.
D. Slepian, J. Math. Phys. 44, No. 2, 107 (1965). Note that Flammer’s normalization is used in this reference.
J. A. Stratton, P. M. Morre, L. J. Chu, J. D. C. Little, F. J. Corbato, Spheroidal Wave Functions (M.I.T. Press, Cambridge, Mass., 1956), pp. 203ndash;229.
D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).
See Ref. 11, Sec. 2.
See Ref. 11, Eq. (2.13).
See Ref. 6, Sec. 4.1.
H. J. Landau and H. O. Pollak, Bell System Tech. J. 41, 1295 (1962).
E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publ. Co., Reading, Mass., 1963), p. 77.
R. Courant and D. Helbert, Methods of Mathematical Physics (Interscience Publ., John Wiley & Sons, Inc., New York, 1966), p. 427.
D. Slepian, Trans. IRE P GIT-3, 68 (1954).