X. Processing and Transmission of Information

00 00 u(t-T/2) u (t + T/2) exp(-jwt) dt was introduced by Ville (1), and its significance with respect to the quality of radar measurements was suggested by Woodward (2), and enlarged upon by Siebert (3). For some time we have been studying the mathematical properties of this function-with the hope of ultimately devising the necessary and sufficient conditions that a function of two variables be representable as in Eq. 1. Such conditions might prove useful in evolving a theory of radar synthesis. The results obtained thus far are summarized below. Proofs are presented only when the method of proof is not obvious. Definitions 1. We assume that u(t) is a reasonably well-behaved, complex-valued function of the real variable, t. In particular, any integrals involving u(t) are assumed to exist. 2. We define 00 * 1 U (w) = 0-oo so that 00u(t) uo 3. We shall call a complex function O(T,W) of two real variables, T and w, a 0-function if and only if there exists a function u(t) which is such that O(T,) may be represented as in Eq. 1. 4. We shall call a real positive function 4(T,W) of two real variables, T and w, a u(t) exp(-jwt) dt U' (w) exp(jot) de