The rectification of non-Gaussian noise
Authors:
James A. Mullen and David Middleton
Journal:
Quart. Appl. Math. 15 (1958), 395-419
MSC:
Primary 60.0X
DOI:
https://doi.org/10.1090/qam/90936
MathSciNet review:
90936
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Additional Information
F. Y. Edgeworth, The law of error, Trans. Cambridge Phil. Soc. 20, 36-65, 113-141 (1905)
K. Pearson, Mathematical theory of migration, Drapers Co. Research Memoirs Biometric Series No. 3 (1906)
G. R. Arthur, Approach of noise after a nonlinear device to a normal density, J. Appl. Phys. 23, 1143-1146 (1952)
G. R. Arthur, The statistical properties of the output of a frequency sensitive device, J. Appl. Phys. 25, 1185-1196 (1954)
G. C. Sponsler and F. L. Shader, PPI light spot brightness probability distributions, J. Appl. Phys. 25, 1271-1277 (1954)
T. A. Magness, Spectral response of a quadratic detector to non-gaussian noise, J. Appl. Phys. 25, 1357-1365 (1954)
B. Gold and G. O. Young, The response of linear systems to nongaussian noise, Trans. Inst. Rad. Eng. PGIT-3, March 1954
- H. Hurwitz Jr. and M. Kac, Statistical analysis of certain types of random functions, Ann. Math. Statistics 15 (1944), 173–181. MR 10933, DOI https://doi.org/10.1214/aoms/1177731282
D. Middleton, On the theory of random noise. Phenomenological Models I and II, and erratum, J. Appl. Phys. 22, 1143-1152, 1153-1163, 1326 (1951)
- A. Blanc-Lapierre and Robert Fortet, Théorie des fonctions aléatoires. Applications à divers phénomènes de fluctuation, Masson et Cie, Paris, 1953 (French). Avec un chapitre sur la mécanique des fluides par J. Kampé de Fériet. MR 0061780
J. A. Mullen and D. Middleton, The rectification of low-density noise, Tech. Rept. 219, 1955, Cruft Laboratory, Harvard University
M. Slack, Probability distributions of sinusoidal oscillations combined in random phase, J. Inst. Elec. Eng. 93, Pt. 3, 76-87 (1946)
- Julian Keilson and James E. Storer, On Brownian motion, Boltzmann’s equation, and the Fokker-Planck equation, Quart. Appl. Math. 10 (1952), 243–253. MR 50216, DOI https://doi.org/10.1090/S0033-569X-1952-50216-0
- David Middleton, Some general results in the theory of noise through non-linear devices, Quart. Appl. Math. 5 (1948), 445–498. MR 23484, DOI https://doi.org/10.1090/S0033-569X-1948-23484-1
- Mark Kac and A. J. F. Siegert, On the theory of noise in radio receivers with square law detectors, J. Appl. Phys. 18 (1947), 383–397. MR 20229
- M. A. Meyer and David Middleton, On the distributions of signals and noise after rectification and filtering, J. Appl. Phys. 25 (1954), 1037–1052. MR 62374
Am. Math. Soc., Second symposium in applied mathematics, McGraw-Hill, New York, 1950, p. 91
- S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 24 (1945), 46–156. MR 11918, DOI https://doi.org/10.1002/j.1538-7305.1945.tb00453.x
D. Middleton, op. cit., App. 3
Bateman Project Staff, Higher transcendental functions, McGraw-Hill, New York, 1953, Sec. 6.13
G. N. Watson, Theory of Bessel functions, Cambridge Univ., 1952, Sec. 13.24
J. A. Mullen and D. Middleton, The rectification of nearly gaussian noise, Tech. Rept. 189, 1954, Cruft Laboratory, Harvard University
D. Gabor, Theory of communication, J. Inst. Elec. Eng. 93, 111, 429 (1946)
F. Y. Edgeworth, The law of error, Trans. Cambridge Phil. Soc. 20, 36-65, 113-141 (1905)
K. Pearson, Mathematical theory of migration, Drapers Co. Research Memoirs Biometric Series No. 3 (1906)
G. R. Arthur, Approach of noise after a nonlinear device to a normal density, J. Appl. Phys. 23, 1143-1146 (1952)
G. R. Arthur, The statistical properties of the output of a frequency sensitive device, J. Appl. Phys. 25, 1185-1196 (1954)
G. C. Sponsler and F. L. Shader, PPI light spot brightness probability distributions, J. Appl. Phys. 25, 1271-1277 (1954)
T. A. Magness, Spectral response of a quadratic detector to non-gaussian noise, J. Appl. Phys. 25, 1357-1365 (1954)
B. Gold and G. O. Young, The response of linear systems to nongaussian noise, Trans. Inst. Rad. Eng. PGIT-3, March 1954
H. Hurwitz and M. Kac, Statistical analysis of a certain type of random function, Ann. Math. Stat. 15, 173-182 (1944)
D. Middleton, On the theory of random noise. Phenomenological Models I and II, and erratum, J. Appl. Phys. 22, 1143-1152, 1153-1163, 1326 (1951)
A. Blanc-Lapierre and R. Fortet, Théorie des fonctions aléatoires, Masson et Cie, Paris, 1953, Sec. 4.7
J. A. Mullen and D. Middleton, The rectification of low-density noise, Tech. Rept. 219, 1955, Cruft Laboratory, Harvard University
M. Slack, Probability distributions of sinusoidal oscillations combined in random phase, J. Inst. Elec. Eng. 93, Pt. 3, 76-87 (1946)
J. Keilson and J. E. Storer, On Brownian motion, Boltzmann’s equation, and the Fokker-Planck equation, Quart. Appl. Math. 10, 243-253 (1952)
D. Middleton, Some general results in the theory of noise through non-linear devices, Quart. Appl. Math. 5, 445-498, Sec. 3, (1948)
M. Kac and A. J. F. Siegert, On the theory of noise in radio receivers with square law detectors, J. Appl. Phys. 18, 383-397 (1947)
M. A. Meyer and D. Middleton, On the distributions of signals and noise after rectification and filtering, J. Appl. Phys. 25, 1037-1052 (1954)
Am. Math. Soc., Second symposium in applied mathematics, McGraw-Hill, New York, 1950, p. 91
S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 23, 24 (1944, 1945)
D. Middleton, op. cit., App. 3
Bateman Project Staff, Higher transcendental functions, McGraw-Hill, New York, 1953, Sec. 6.13
G. N. Watson, Theory of Bessel functions, Cambridge Univ., 1952, Sec. 13.24
J. A. Mullen and D. Middleton, The rectification of nearly gaussian noise, Tech. Rept. 189, 1954, Cruft Laboratory, Harvard University
D. Gabor, Theory of communication, J. Inst. Elec. Eng. 93, 111, 429 (1946)
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© Copyright 1958
American Mathematical Society
