On transfer functions and transients

Author:
Armen H. Zemanian

Journal:
Quart. Appl. Math. **16** (1958), 273-294

MSC:
Primary 78.00

DOI:
https://doi.org/10.1090/qam/102342

Correction:
Quart. Appl. Math. **17** (1959), 320-320.

MathSciNet review:
102342

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Abstract | References | Similar Articles | Additional Information

Abstract: In the first part of this paper the concept of the positive real function is generalized so that it is applicable to transfer functions and the functions, satisfying this generalized concept, are arranged into classes. Some tests are then developed which may be used to determine whether a transfer function belongs to a particular class. It is also shown that if transfer functions have certain general forms then they will automatically be members of one of the classes. Finally, several properties of the phase functions for such system functions are developed.

**[1]**A. H. Zemanian,*Bounds existing on the time and frequency responses of various types of networks*, Proc. IRE**42**, 835-839 (May 1954)**[2]**A. H. Zemanian,*Further bounds existing on the transient responses of various types of networks*, Proc. IRE**43**, 322-326 (March 1955) MR**0067754****[3]**A. H. Zemanian,*Restrictions on the shape factors of the step response of positive real system functions*, Proc. IRE,**44**, 1160-1165 (Sept. 1956) MR**0081750****[4]**I. A. Ovseyevich,*Certain bounds on the time functions of a linear system given by its frequency characteristic*, Izvestia Akad. Nauk, Otdel. Tekh. Nauk, S.S.S.R., pp. 59-68 (Feb. 1956)**[5]**O.P.D. Cutteridge,*Transient response of two-terminal networks*, Inst. Elec. Eng., Monograph No.**212R**(Dec. 1956)**[6]**E. W. Tschudi,*Admittance and transfer function for an n-mesh R C filter network*, Proc. I.R.E.**38**, 309-310 (March 1950)**[7]**R. R. Kenyon,*Response characteristics of resistance-reactance ladder networks*, Proc. I.R.E.**39**, 557-559 (May 1951)**[8]**L. Storch,*The multisection RC filter network problem*, Proc. I.R.E.**39**, 1456-1458 (Nov. 1951)**[9]**B. K. Bhattacharya,*Admittance and transfer function of a multimesh resistance-capacitance filter network*, Indian J. Phys.**26**, 563-574 (Nov. 1952)**[10]**E. Green,*Amplitude-frequency characteristics of ladder networks*, Marconi's Wireless Telegraph Co., Chelmsford, Essex, 1954, pp. 6-11**[11]**E. A. Guillemin,*The mathematics of circuit analysis*, John Wiley and Sons, New York, 1949, p. 400 MR**0044595****[12]***Ibid*., p. 395**[13]**L. Weisner,*Introduction to the theory of equations*, The Macmillan Co., 1938, Chap. 5**[14]**A. Hurwitz,*Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt*, Math. Ann.**46**, 273-284 (1895) MR**1510884****[15]**A. H. Zemanian,*Some inequalities for Fourier transforms*, Proc. Am. Math. Soc.**8**, No. 3, (June 1957) MR**0086934****[16]**A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi,*Higher transcendental functions*, vol. I, McGraw-Hill Book Co., 1953, Eq. 2.8 (46) and 1.2 (8)**[17]**H. T. Davis,*Tables of the higher mathematical functions*, vol. I, Principia Press, Bloomington, Ind., 1933**[18]**R. C. Palmer and L. Mautner,*A new figure of merit for the transient response of video amplifiers*, Proc. IRE**37**, 1073-1077 (Sept. 1949)

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Additional Information

DOI:
https://doi.org/10.1090/qam/102342

Article copyright:
© Copyright 1958
American Mathematical Society