IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 35, NO. 4, NOVEMBER 1993 485

Correspondence

Comment on “On the Use of Hilbert Transform for Processing Measured CW Data”

Vitta1 P. Pyati

In the above titled paper’ appearing in this TRANSACTIONS, the author Tesche (by failing to emphasize the underlying principle of cuusuZity) seems to convey the impression (first paragraph of the Introduction) that Cauchy residue theorem when applied to a function of a complex variable somehow leads to Hilbert transform relationship between the real and imaginary parts. To clarify matters, if a function f ( t ) = 0, for t < 0, then its Fourier transform F ( w ) will be regular in the upper half-plane. By integrating over a path consisting of the real axis and a semi-circle at infinity one obtains the desired principal value (misspelled as principle value) integral relationships. It is perhaps appropriate to cite other notable events in the history of Hilbert transforms. Kramers and Kronig [ 11 showed that the real and imaginary parts of the complex permittivity of a dielectric material are connected by Hilbert transforms. James and Andrasic [2] have made an interesting use of this result. Gabor’s [3] analytic signal, which is commonplace in communication theory, owes its origin to Hilbert transforms. Furthermore, time-limited signals have their own version of Hilbert transforms [4], [5] which find application in the solution of integral equations.

REFERENCES

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media. New York Addison-Wesley, 1960, pp. 25&262. J. R. James and G. Andrasic, “Assessing the accuracy of wideband electrical data using Hilbert transforms,” Proc. Inst. Elec. Eng., vol. 177, no. 3, pp. 184188, June 1990. D. Gabor, “Theory of communications,” J. Inst. Elec. Eng. (London), vol. 93, pt. 111, pp. 429457, 1946. F. B. Hildebrand, Methods of Applied Mathematics. Englewood Cliffs, NJ: Prentice-Hall, 1952, pp. 325-326. L. I. Volkovyskii et al., A Collection of Problems on Complex Analysis. Reading, MA: Addison Wesley, 1965, p. 174, para. 5.

Manuscript received June 18, 1993. The author is with the Department of Electrical and Computer Engineering,

Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433.

IEEE Log Number 9212205. ‘P. M. Tesche, IEEE Trans. Electromagn. Compat., vol. 34, no. 3, pp.

259-266, Aug. 1992.

Letter to the Editor Responding to a Recent Paper by P. D. Fisher

D. W. MacPherson

I have read with interest the article by Dr. P. David Fisher’. There are two major scientific errors in this paper which make the analysis and conclusions insupportable by the information presented.

The first is an experimental design error. In stating that 5000 measurements were taken the author has ignored his selection bias. In actual fact, the author measured radiation from thirty models of radar guns, with multiple measurements (thousands) being taken from certain models and very few measurements being taken from others (see Table 111). From this design, all that he should have calculated is the reproducibility, variability, and the standard deviation or confidence intervals about the mean radiation of 10 radar guns from manufacturer number 1, 5 radar guns from manufacturer number 2, 12 radar guns from manufacturer number 3, etc. In short, all that could be concluded from these measurements is the precision of the instruments used for measurement of microwave radiation. The accuracy of measurement cannot be assessed with this experimental design.

The second error is related to his research question: “What are the microwave exposure levels encountered by police radar operators.. .?” To which he then “conclude[s] with a high degree of certainty that there is no evidence to support the allegation that police traffic radar operators are at risk due to prolonged exposure to microwave emissions from their radar guns.”

By not posing questions such as the following: what is the point microwave radiation dose, what is the cumulative dose over the short- and long-term exposure, what are the cumulative effects of microwave irradiation plus other forms of nonionizing radiation, what are the incremental effects of this source of microwave radiation over and above other sources of nonionizing radiation exposure, etc., the author cannot begin to address any questions related to health or safety. Then, without actually measuring some human health outcomes; for example “cancer, neurological disorders, or reproductive problems,” which may take years or decades to be detectable, or any other health status parameter the author has stepped over the line of credible scientific interpretation and is making statements of conclusion for which he has no scientific data.

As implied by the author, health and safety related to microwave exposure are significant concerns to certain working groups. These are also of concern to the general public. The inadequacy in which these concerns can be addressed by the methods of engineers and physicists is evident in this paper. Health is a human outcome. Epidemiology, biometrics, and medical scientific methods are the tools to be used to answer these questions.

Manuscript received March 26, 1993. The author is with the Department of Pathology, McMaster University,

Hamilton, Ont., L8N 325, Canada. IEEE Log Number 921 1287. P. D. Fisher, “Microwave exposure levels encountered by police traffic

radar operators,” IEEE Trans. Electromagn. Compat., vol. 35, pp. 3645, Feb. 1993.

0018-9375/93$03.00 0 1993 IEEE