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A Lower Bound and Other Properties of the Mean‐Square Error of Linear Measurement Systems
1.H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
2.C. W. McCombie, Repts. Progr. in Phys. 16, 266 (1953).
3.R. C. Jones, Advances in Electronics 5, 1 (1953).
4.J. J. Freemen, Principles of Noise (John Wiley & Sons, Inc., New York, 1958).
5.D. Middleton, Introduction to Statistical Communication Theory (McGraw‐Hill, Book Company, Inc., New York, 1960).
6.L. Brillouin, Science and Information Theory (Academic Press Inc., New York, 1956).
7.Unbiased is used here in the mathematical sense. An unbiased estimate r of μ is an estimate such that where the operator E denotes the operation of taking an average value in the ensemble sense.
8.J. L. Hammond, Jr., Proc. IRE 49, 1701 (1961).
9.To be strictly correct, P() is the conditional probability of the event specified subject to the hypothesis that the mean value of is γ. Interpreted physically, this assumption implies that the quantity to be measured γ is fixed although it is unknown.
10.Reference 1, Eq. (4.8), p. 37.
11.Equation (22) is a good approximation at room temperature up to frequencies on the order of cps.
12.Reference 5, Chap. 3, Eq. (3.106), p. 173.
13.S. Goldman, Transformation Calculus and Electrical Transients (Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 1949), Chap. 7, p. 238.
14.E. W. Hobson, The Theory of Functions of a Real Variable and the Theory of Fourier’s Series (Dover Publications, Inc., New York, 1926), 2nd ed., Vol. 1, Chap. 7, p. 617.
15.Reference 14, Vol. 2, Chap. 9, p. 747.
16.I. P. Natanson, Theory of Functions of a Real Variable (Frederick Ungar Publishing Company, New York, 1955), Chap. 7, p. 165.
17.G. P. Harnwell, Principles of Electricity and Electromagnetism (McGraw‐Hill Book Company, Inc., New York, 1938), Chap. 10, p. 329.
18.Reference 2, p. 270.
19.Reference 2, p. 307.
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