## Nelson M. Blachman

33 Linda Avenue, Suite 2208

Oakland, California 94611-4819

Phone: 510-653-8769

Born in Cleveland, Ohio, in 1923, Nelson Blachman received the B.S. degree in physics from Case School of Applied Science (now a part of Case Western Reserve University) in 1943 and the A.M. degree in physics and the Ph.D. degree in engineering sciences and applied physics from Harvard University in 1947.

From 1943 to 1945 he was a member of the Theory Group and of the Transducer Group at the Underwater Sound Laboratory of Harvard University, where he was involved with the design and measurement of electroacoustic transducers and with the analysis of sonar-system designs. From 1945 to 1946 he worked at Harvard's Cruft Laboratory on the effect of noise upon radio communication, particularly FM. As a member of the Theory Group of the Accelerator Project at the Brookhaven National Laboratory, Upton, L.I., N.Y., from 1947 to 1951 he was concerned with the theory and the design of the Cosmotron, Brookhaven's 3-GeV proton synchrotron. From 1951 to 1954 he worked in the Mathematical Sciences Division of the Office of Naval Research, Washington, D.C., in the administration of its program of research support in the fields of computers and mathematics. In 1954 he joined the Electronic Defense Organization of the GTE Government Systems Corporation in Mountain View, Calif., where he was, until his retirement in 1993, a consulting scientist on statistical communication theory and related topics.

From 1958 to 1960 and from 1976 to 1978 he took leaves of absence to do scientific-liaison work in the field of electronics as a member of the staff of the London Branch of the U.S. Office of Naval Research. In 1964-1965 he taught communication theory, in Spanish, at the Escuela Técnica Superior de Ingenieros de Telecomunicación, Madrid, and in the Facultad de Ciencias of the University of Madrid under the Fulbright Program while on sabbatical leave from GTE. He has also taught at Stanford University and in the off-campus programs of the University of Maryland and the University of California. In 1985 he took a leave of absence from GTE to spend a sabbatical year in the Computer Science and Systems Branch of the Naval Research Laboratory, Washington, D.C.

He is a fellow of the Institute of Electrical and Electronic Engineers, the American Association for the Advancement of Science, and the Institution of Electrical Engineers (London).

``The System of Microstresses in Cold-Worked Metal,'' * Physical
Review* **70** (9, 10), 698-704 (November 1 and 15, 1946)
(baccalaureate
dissertation).

``A Theoretical Study of the Demodulation of a Frequency-Modulated Carrier and Random Noise by an F-M Receiver,'' Cruft Laboratory, Harvard University, Technical Report No. 31 (March 5, 1948) (doctoral dissertation).

``The Scattering of Particles by the Gas in a Synchrotron'' (with
E. D. Courant), * Physical Review* **74** (1), 140-144 (July 15,
1948);
and 75 (2), 315 (January 15, 1949).

``The Demodulation of an F-M Carrier and Random Noise by a Limiter
and Discriminator,'' * Journal of Applied Physics* **20** (1), 38-47
(January 1949).

``The Counting Volume of a Cylindrical Ionization Chamber,''
* Review of Scientific Instruments* **20** (7), 477-479 (July 1949).

``The Dynamnics of a Synchrotron with Straight Section'' (with E.
D. Courant), * Review of Scientific Instruments* **20** (8), 596-601
(August 1949).

``The Demodulation of an F-M Carrier and Random Noise by a
Discriminator,'' * Journal of Applied Physics* **20** (10), 976-983
(Oct 1949); abstract in * Proceedings of the I.R.E.* **37** (8), 895
(August 1949).

``Synchrotron-Oscillation Resonance,'' * Review of Scientific
Instruments* **21** (11), 908-911 (November 1950).

``Forced Betatron Oscillation in a Synchrotron with Straight
Sections,'' * Review of Scientific Instruments* **22** (8), 569-571
(August 1951).

``Synchrotron-Oscillation Resonance,'' * Review of Scientific
Instruments* **23** (5), 250 (May 1952).

``A Comparison of the Informational Capacities of Amplitude- and
Phase-Modulation Communication Systems,'' * Proceedings of the I.R.E.*
**41** (6), 748-759 (June 1953).

``The Output Signal-to-Noise Ratio of a Power-Law Device,''
* Journal of Applied Physics* **24** (6), 783-785 (June 1953).

``Bounds on Entropy,'' * Journal of Applied Physics*
**24** (10), 1340 (October 1953).

``Minimum-Cost Encoding of Information,'' * Transactions of the
I.R.E. Professional Group on Information Theory* ** PGIT-3** 139-149
(March
1954).

``On Wiring of Two-Dimensional Multiple-Coincidence Magnetic
Memories,'' * I.R.E. Transactions on Electronic Computers* ** EC-5**
(1),
19-21 (March 1956).

``-ACs'' (on automatic digital computers), * American
Scientist* **44** (2), 198-203 (April 1956).

``Communication as a Game,'' * I.R.E. WESCON Convention
Record* Part 2, 61-66 (August 1957).

``Limiting Frequency-Modulation Spectra,'' * American
Scientist* **1** (1), 26-37 (September 1957).

``On Fourier Series for Gaussian Noise,'' * Information and
Control* **1** (1), 56-63 (September 1957).

``Loss of Signal Detectability in Band-Pass Limiters,'' *
I.R.E. Transactions on Information Theory* ** IT-44** 174 (December
1958).

``Optimum Search for Objects Having Unknown Arrival Times'' (with
Frank Proschan), * Operations Research* **7** (5), 625-638
(September-October 1959).

``Prolegomena to Optimum Discrete Search Procedures,'' * Naval
Research Logistics Quarterly* **6** (4), 273-281 (December 1959).

``The Effect of a Limiter Upon Signals in the Presence of Noise,''
* I.R.E. Transactions on Information Theory* ** IT-4** (1) 52 (March
1960).

``On the Effect of Noise in a Nonlinear Control System,''
* Automatic and Remote Control* the Proceedings of the First Congress
of
the International Federation for Automatic Control, Moscow, 1960;
J. F. Coales et al., eds., Butterworths, London, 1961, vol. 2, pp. 770-773.

``On the Integration and Summation of Trigonometric and Exponential
Functions,'' * Proceedings of the I.R.E.* **49** (6), 1088 (June
1961).

``Enquête sur la Technologie des Calculatrices
Numériques en Europe,'' * Bulletin du Centre International
Provisoire
de Calcul* (Rome), **14** 18-38 (July 1961).

``A Generalization of Mutual Information,'' * Proceedings of the
I.R.E.* **49** (8), 1331-1332 (August 1961).

``Some Properties of a Large Set of Random Signals'' (abstract),
* Annals of Mathematical Statistics* **32** (3), 916 (September
1961).

``On the Capacity of a Band-Limited Channel Perturbed by
Statistically Dependent Interference,'' * I.R.E. Transactions on
Information Theory* ** IT-8** (1), 48-55 (January 1962).

``A Generalization of Woodward's Theorem on FM Spectra,''
* Information and Control* **5** (1), 55-63 (March 1962).

``Prevarication vs. Redundancy,'' * Proceedings of the
I.R.E.* **50** (7), 1711-1712 (July 1962).

``The Effect of Statistically Dependent Interference upon Channel
Capacity,'' * I.R.E. Transactions on Information Theory* ** IT-8**
(5),
S53-S57 (September 1962).

``Costo Minimo di Codificazione dell'Informazione,'' * La Scuola
in Azione* (Scuola Enrico Mattei di Studi Superiori sugli Idrocarburi,
San
Donato Milanese), 26-41 (November 1962).

``The Information Content of a Work of Art,'' * The Scientist
Speculates* I.J. Good, ed., Heinemann, London, 1962, and Basic Books, New
York, 1963, 63-65.

``On FSK Parity Checking,'' * IEEE Transactions on Information
Theory* ** IT-9** 121-123 (April 1963).

``The Closest Packing of Equal Spheres in a Larger Sphere,''
* American Mathematical Monthly* **70** 526-529 (May 1963).

``On the Pessimum Interference with Random Signals'' (abstract),
* Annals of Mathematical Statistics* **34** (2), 678 (June 1963).

``Multiple Packing of Spherical Caps'' (with L. Few), *
Mathematika* **10** 84-88 (June 1963).

``Band-Pass Nonlinearities,'' * IEEE Transactions on Information
Theory* ** IT-10** 162-164 (April 1964).

``The Correlation Function of Gaussian Noise After Error-Function
Limiting,'' * Journal of Electronics and Control* **16** 509-511
(May 1964).

``FM Reception and the Zeros of Narrow-Band Gaussian Noise,'' *
IEEE Transactions on Information Theory* ** IT-10** 235-241 (July
1964).

``Minimum-Cost Transmission of Information,'' * Journal of
Electronics and Control* **7** 508-511 (December 1964).

``The Information Rate of a Continued Fraction,'' * IEEE
Transactions on Information Theory* ** IT-11** 150-151 (January 1965).

``The Convolution Inequality for Entropy Powers,'' * IEEE
Transactions on Information Theory* ** IT-11** 267-271 (April 1965).

* Noise and Its Effect on Communication* McGraw-Hill Book
Company, New York, 1966.

``Two-Signal Interaction in a Logarithmic IF Amplifier,''
* IEEE Transactions on Communication Technology* ** COM-15** (2),
305-307 (April 1967).

``The Signal x Signal, Noise x Noise, and Signal x Noise Output of
a
Nonlinearity,'' * IEEE Transactions on Information Theory* **
IT-14**
(1), 21-27 (January 1968).

``The Amount of Information that *y* Gives about *X*,''
*
IEEE Transactions on Information Theory* ** IT-14** (1), 27-31
(January
1968).

``The Uncorrelated Output Components of a Nonlinearity,'' * IEEE
Transactions on Information Theory* ** IT-14** (2), 250-255 (March
1968).

``The Reception of Pulsed Signals by a Detuned Receiver,''
* IEEE Transactions on Aerospace and Electronic Systems* ** AES-4**
(3), 486-489 (May 1968).

``The Output Signal-to-Noise Ratio of a Bandpass Limiter,''
* IEEE Transactions on Aerospace and Electronics Systems* **
AES-4** (4), 635 (July 1968).

``The Spectrum of a High-Index FM Waveform: Woodward's Theorem
Revisited" (with G. A. McAlpine), * IEEE Transactions on Communication
Technology* ** COM-17** (2), 201-208 (April 1969).

``Position Determination from Radio Bearings,'' * IEEE
Transactions on Aerospace and Electronic Systems* ** AES-5** (3),
558-560
(May 1969).

``On the Moments and Tails of the Spectrum of an FM Wave,''
* Radio Science* **4** (5), 437-439 (May 1969).

``Geometry of Optimum Incoherent Detection,'' * IEEE Transactions
on Information Theory* ** IT-16** (2), 202-205 (March 1970).

``Detectors, Bandpass Nonlinearities, and Their Optimization:
Inversion of the Chebyshev Transform,'' * IEEE Transactions on Information
Theory* ** IT-17** (4), 398-404 (July 1971).

``Signal/Noise-Ratio Performance of Optimum Nonlinearities,''
* Electronics Letters* **7** (14), 393-395 (July 15, 1971).

``Spectral Analysis with Sinusoids and Walsh Functions,'' * IEEE
Transactions on Aerospace and Electronic Systems* ** AES-7** (5),
900-905
(September 1971).

``The Effect of Noise on Bearings Obtained by Amplitude
Comparison,'' * IEEE Transactions on Aerospace and Electronic
Systems* ** AES-7** (5), 1007-1009 (September 1971).

``Some Comments Concerning Walsh Functions,'' * IEEE Transactions
on Information Theory* ** IT-18** (3), 427-428 (May 1972).

``The Effect of Nonlinearity upon Signals in the Presence of
Noise,'' * IEEE Transactions on Communications* ** COM-21** (2),
152-154 (February 1973).

``Detection of a PSK Signal Transmitted through a Hard-Limited
Channel'' (with P. C. Jain), * IEEE Transactions on Information
Theory* ** IT-19** (5), 623-630 (September 1973).

``Sinusoids versus Walsh Functions,'' * Proceedings of the
IEEE* **62** (3), 346-354 (March 1974).

``The Power Spectrum of a Digital Signal,'' * IEEE Transactions
on Communications* ** COM-22** (3), 349-350 (March 1974).

``Dynamic FM Discriminator Distortion,'' * Electronics
Letters* **10** (10), 185-186 (16 May 1974).

``The Spectrum of a TDM PPM Signal,'' * IEEE Transactions on
Communications* ** COM-11** (6), 864-866 (June 1974).

``Reducing Ohmmeter Error,'' * Proceedings of the IEEE*
**62** (7), 1038 (July 1974).

``F.M. Click Rates: A Simple Derivation'' (with J. H. Roberts),
* Electronics Letters* **10** (15), 305-307 (25 July 1974).

``The SNR Threshold in PPM Reception,'' * IEEE Transactions on
Communications* ** COM-22** (8), 1094-1098 (August 1974).

``New Bound for the Spectrum of an F.M. Wave,'' * Proceedings of
the IEE* (London), **121** (9), 920-922 (September 1974).

``An Astonishing Reduction in the Bandwidth of Noise'' (with Simon
Mayerhofer), * Proceedings of the IEEE* **63** (7), 1077-1078 (July
1975).

``Zero-Crossing Rate for the Sum of Two Sinusoids or a Signal plus
Noise,'' * IEEE Transactions on Information Theory* ** IT-21** (6),
671-675 (November 1975).

``The Effect of Noise upon Polar-Display Instantaneous Frequency
Measurement,'' * IEEE Transactions on Instrumentation and Measurement*
** IM-25** (3), 214-221 (September 1976).

``Narrowband Gaussian Noise: Variance of the Number of Zero
Crossings,'' * Electronics Letters* **14** (3), 75-76 (2 February
1978).

``The Output Signals and Noise from a Nonlinearity with
Amplitude-Dependent Phase Shift,'' * IEEE Transactions on Information
Theory* ** IT-25** (1), 77-79 (January 1979).

``Four-Dimensional Geometry,'' * IEEE Communications
Magazine* **17** (6), 20-25 (November 1979).

``The Effect of a Large Signal upon a Small Signal in a Memoryless
Nonlinear Bandpass Amplifier,'' * IEEE Transactions on
Communications* ** COM-29** (1), 72-73 (January 1981).

``The Effect of Phase Error on DPSK Error Probability,'' *
IEEE Transactions on Communications* ** COM-29** (9), 364-365 (March
1981).

``Third-Order Intermodulation due to Quantization,'' * IEEE
Transactions on Communications* ** COM-29** (9), 1386-1389 (September
1981).

``Intermodulation in Terms of the Harmonic Output of a
Nonlinearity,'' * IEEE Transactions on Acoustics, Speech, and Signal
Processing* ** ASSP-29** (6), 1202-1205 (December 1981).

``Output Correlation Functions of Power-Law Nonlinearities Fed by
Gaussian Noise,'' * Electronics Letters* **18** (8), 347-348 (15
April
1982).

* Noise and Its Effect on Communication* second edition,
Krieger Publishing Company, Malabar, Florida, 1982.

``Carrier-Tracking-Loop Performance for Quaternary and Binary PSK
Signals'' (with S. H. Mousavinezhad), * IEEE Transactions on Aerospace and
Electronic Systems* ** AES-19** (2), 162-167 (March 1983).

``The Continued Fraction as an Information Source,'' * IEEE
Transactions on Information Theory* ** IT-30** (4), 671-674 (July
1984).

``The Intermodulation and Distortion due to Quantization of
Sinusoids,'' * IEEE Transactions on Acoustics, Speech, and Signal
Processing* ** ASSP-33** (6), 1417-1426 (December 1985).

``Trigonometric Approximations to Bessel Functions'' (with
S. H. Mousavinezhad), * IEEE Transactions on Aerospace and Electronic
Systems* ** AES-22** (1), 2-7 (January 1986).

``Confidence Intervals based on One or More Observations'' (with
R. E. Machol), * IEEE Transactions on Information Theory* ** IT-33**
(3), 373-382 (May 1987).

``Phase and Logarithm of Amplitude of a Signal plus Noise,'' *
Electronics Letters* ** 24** (8), 482-483 (14 April 1988).

``Reception of Pulsed Signals by Detuned Receiver: Addenda and
Corrections,'' * IEEE Transactions on Aerospace and Electronic Systems*
** AES-24** (4), 457-459 (July 1988).

``Gaussian Noise--Part I: The Shape of Large Excursions,'' *
IEEE
Transactions on Information Theory* ** IT-34** (6), 1396-1400
(November 1988).

``Gaussian Noise--Part II: Distribution of Phase Change of
Narrowband
Noise plus Sinusoid,'' * IEEE Transactions on Information Theory* **
IT-34** (6), 1401-1405 (November 1988).

``On Combining Target-Location Ellipses,'' * IEEE Transactions on
Aerospace and Electronic Systems* ** AES-25** (2), 284-287 (March
1989).

``Extensions and Critique of Minimum-Relative-Entropy Spectral
Estimation,'' * IEEE Transactions on Aerospace and Electronic Systems*
**
25** (5), 650-659 (September 1989).

``Transform Related to Spherical Distributions and Its Inversion,''
* Electronics Letters* ** 25** (22), 1492-1493 (26 October 1989).

``The Spectrum of the Square of a Synchronous Random Pulse Train''
(with S. H. Mousavinezhad), * IEEE Transactions on Communications* **
38**
(1), 13-17 (January 1990).

``Projection of a Spherical Distribution and Its Inversion,'' *
IEEE Transactions on Acoustics, Speech, and Signal Processing* ** 39**
(11),
2544-2547 (November 1991).

``Gaussian Noise: Prediction Based on Its Value and *N*
Derivatives,'' * IEE Proceeings--F: Radar and Signal Processing*
** 140** (2), 98-1 02 (April 1993).

``There Are * Nine* Regular Polyhedra, Not Just Five,''
* The Mathematica Journal* **3** (2), 76-78 + electronic supplement
(spring 1993).

``Optimum Memoryless Bandpass Nonlinearities,'' * IEE
Proceedings--I: Communications, Speech and Vision* **140** (6),
436-444
(December 1993).

``Beneficial Effects of Spectral Correlation on Synchronization,''
pp. 362-390 of * Cyclostationarity in Communications and Signal
Processing* W. A. Gardner, Ed. New York: IEEE Press, 1994.

``A Maximum Volume,'' * SIAM Review* **36** (2), 278-281
(June
1994).

``Interference Suppression by Biased Nonlinearities'' (with P. C.
Jain and P. M. Chapell), * IEEE Transactions on Information Theory*
**41** (2), 496-507 (March 1995).

``Random Exploration of the Three Regular Polytopes,'' * IEEE
Transactions on Information Theory* **41** (6), Part II, 2081-2087
(November
1995).

``Comment on `Bayesian Resolution of the Exchange Paradox','' (with
R. Christensen and J. M. Utts), * The American Statistician* **50**
(1),
98-99 (February 1996).

``The Shape of Low Minima of the Envelope of Narrowband Gaussian
Noise,'' * IEEE Transactions on Information Theory* **42** (3),
1007-1009
(May 1996).

``The Shape of Low Minima of the Envelope of a Signal plus Noise,''
* IEEE Transactions on Information Theory*, **44** (2), 882-886
(March 1998).

``The Distributions of the Local Extrema of Gaussian Noise and of
Its Envelope,'' * IEEE Transactions on Information
Theory* **45** (6), 2115-2121 (September 1999).

``Elusive Optimality in the Box Problem'' (with D. M. Kilgour),
* Mathematics Magazine*, **74** (3), 171-181 (June 2001).

``Geometric Properties of a Large Set of Random Signals,''
* IEEE Transactions on Information Theory* **48** (3), 748-752
(March 2002).

``Real-World Solution of the Two-Envelope Problem with a
Heavy-Tailed Distribution,'' * The Mathematical Scientist* **28**.1,
43-48 (June 2003).

``Optimal Sequential Selection from Among *n* Boxes,'' * The
Mathematical Scientist* **28**.2, 115-120 (December 2003).

``A Chain of Curlicues,'' * The Mathematical Scientist*
**32**.1, 6-12 (June 2007).

``Repeated Subdivision of Triangles by their Medians,'' * The
Mathematical Scientist* **34**.1, 15-19 (June 2009).

``Some Surprising Rationalities of Tangent Circles,'' * The
Mathematical Scientist* **37**.1, 80-82 (June 2012).

``Three Tangent Circles' Incircle,'' *The Mathematical
Scientist* **37**.2, 151-153 (December 2012).