In comparing a signalf(t)with its amplitude-distorted formg(f(t)), whereg(\cdot)is a monotonically increasing function of its argument, one is led to consider the correlation function \begin{equation} R(s) \triangleq \int_{-\infty}^{\infty} dtg (f(t))f(t-s). \end{equation} A rigorous proof is given of the inequalityR(s) \leq R(O). Generalizations are presented for the cases of finite domains and of signals defined in two-dimensional space.

The expertise of systems and control engineering is potentially relevant to the problems of contemporary urban society. But to realize this potential, a paradigm which represents urban problems as problems of design and control must be developed. A possible structure for such a paradigm is suggested by Simon's conception of an " artificial science" which emphasizes the problem of designing inner environments whose object is to attain goals and to function adaptively in outer environments [11]. This paper proposes an organization-environment model, combining the Urban Dynamics and hierarchical multilevel systems approaches as one possible basis for such a science. A descriptive formal model of an urban government using the multiechelon approach is developed, and the consistency postulate for the system is defined. This definition illustrates a commonly encountered problem in political systems, namely, the imperfect relationship between electoral and administrative processes and "the general welfare." But this problem cannot be examined systematically until an operational overall system goal for a specific system is defined. Modifications of the Forrester Urban Dynamics model to include a coefficient of "satisfaction" are described to illustrate a potentially useful definition of such a goal. Preliminary results indicate that the values of this coefficient are consistent with the implicit normative assumptions of the Forrester model.