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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References | Similar Articles | Additional Information

**[1]**F. Y. Edgeworth,*The law of error*, Trans. Cambridge Phil. Soc.**20**, 36-65, 113-141 (1905)**[2]**K. Pearson,*Mathematical theory of migration*, Drapers Co. Research Memoirs Biometric Series No. 3 (1906)**[3]**G. R. Arthur,*Approach of noise after a nonlinear device to a normal density*, J. Appl. Phys.**23**, 1143-1146 (1952)**[4]**G. R. Arthur,*The statistical properties of the output of a frequency sensitive device*, J. Appl. Phys.**25**, 1185-1196 (1954)**[5]**G. C. Sponsler and F. L. Shader,*PPI light spot brightness probability distributions*, J. Appl. Phys.**25**, 1271-1277 (1954)**[6]**T. A. Magness,*Spectral response of a quadratic detector to non-gaussian noise*, J. Appl. Phys.**25**, 1357-1365 (1954)**[7]**B. Gold and G. O. Young,*The response of linear systems to nongaussian noise*, Trans. Inst. Rad. Eng. PGIT-3, March 1954**[8]**H. Hurwitz and M. Kac,*Statistical analysis of a certain type of random function*, Ann. Math. Stat.**15**, 173-182 (1944) MR**0010933****[9]**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)**[10]**A. Blanc-Lapierre and R. Fortet,*Théorie des fonctions aléatoires*, Masson et Cie, Paris, 1953, Sec. 4.7 MR**0061780****[11]**J. A. Mullen and D. Middleton,*The rectification of low-density noise*, Tech. Rept. 219, 1955, Cruft Laboratory, Harvard University**[12]**M. Slack,*Probability distributions of sinusoidal oscillations combined in random phase*, J. Inst. Elec. Eng.**93**, Pt. 3, 76-87 (1946)**[13]**J. Keilson and J. E. Storer,*On Brownian motion, Boltzmann's equation, and the Fokker-Planck equation*, Quart. Appl. Math.**10**, 243-253 (1952) MR**0050216****[14]**D. Middleton,*Some general results in the theory of noise through non-linear devices*, Quart. Appl. Math.**5**, 445-498, Sec. 3, (1948) MR**0023484****[15]**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) MR**0020229****[16]**M. A. Meyer and D. Middleton,*On the distributions of signals and noise after rectification and filtering*, J. Appl. Phys.**25**, 1037-1052 (1954) MR**0062374****[17]**Am. Math. Soc.,*Second symposium in applied mathematics*, McGraw-Hill, New York, 1950, p. 91**[18]**S. O. Rice,*Mathematical analysis of random noise*, Bell System Tech. J.**23, 24**(1944, 1945) MR**0011918****[19]**D. Middleton,*op. cit*., App. 3**[20]**Bateman Project Staff,*Higher transcendental functions*, McGraw-Hill, New York, 1953, Sec. 6.13**[21]**G. N. Watson,*Theory of Bessel functions*, Cambridge Univ., 1952, Sec. 13.24**[22]**J. A. Mullen and D. Middleton,*The rectification of nearly gaussian noise*, Tech. Rept. 189, 1954, Cruft Laboratory, Harvard University**[23]**D. Gabor,*Theory of communication*, J. Inst. Elec. Eng.**93**, 111, 429 (1946)

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Additional Information

DOI:
https://doi.org/10.1090/qam/90936

Article copyright:
© Copyright 1958
American Mathematical Society