Detectors, Bandpass Nonlinearities, and Their Optimization: Inversion of the Chebyshev Transform

IEEE Transactions on Information Theory

Volumn 17, Issue 4, 1971, Pages 398-404

  Blachman, Nelson M ^a  

^a OSRAM SYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DESCRIBING FUNCTIONS; MATHEMATICAL TRANSFORMS; NONLINEARITIES; SIGNAL DETECTION;

INFORMATION THEORY;

EID: 0015094971     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1971.1054647     Document Type: Article

References (8)

1. N. M. Blachman, “Bandpass nonlinearities,” IEEE Trans. Inform. Theory (Corresp.), vol. IT-IO, Apr. 1964, pp. 162–164.
2. N. M. Blachman, Noise and Its Effect on Communication. New York: McGraw-Hill, 1966, p. 78, problem 5-2; p. 133; pp. 57, 58.
3. M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions (Applied Mathematics Series 55). Washington, D.C.: NBS, 1964, p. 255; p. 258, sec. 6.2.
4. This solution can be traced back to 0. Schlomilch in 1857. See E. T. Whittaker and G. N. Watson, Modern Analysis, 4th ed. Cambridge: Cambridge Univ. Press, 1927, p. 229.
5. This inversion formula was found in 1962 by J. E. Gibson and E. S. di Tada, “On the inverse describing-function problem,” in 1963 Proc. IFAC. London: Butterworth, 1964, pp. 29–34.
6. Bateman Manuscript Project, Tables of Integral Transforms, vol. 1, A. ErdBlyi, Ed. New York: McGraw-Hill, 1954, pp. 305, 341 ff.
7. L. Schmideg, “Note on the evaluation of Fourier coefficients of power-law devices,” Proc. IEEE (Lett.), vol. 56, Aug. 1968, pp. 1383–1384. The author is grateful to F. M. Clayton of the G.E.C. Hirst Research Centre for bringing to his attention this work, which served as the key to the higher order inverse transforms.
8. N. M. Blachman, “The signal x signal, noise x noise, and signal x noise output of a nonlinearity,” IEEE Trans. Inform. Theory, vol. IT-14, Jan. 1968, pp. 21–27.