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Networks are frequently designed on the basis of minimizing a meas- ure of error to a given specification. The physical limitations of prac- tical circuit elements can often be introduced into such problems by means of constraints placed on the form of the solution. The paper presents_anew way of introducing such constraints and reviews some examples in which constraints have been successfully employed. The constraints discussed may be divided into two groups; namely, those depending on some isolated feature of the frequency character- istic of the solution, such as the dc gain or the parasitic-capacitance high-frequency asymptote, and those depending on the complete frequency characteristic, such as the power-handling capacity of an output stage. It is suggested that the introduction of constraints may require a change in the basis of error assessment. In this con- nection an example is given based on a time-weighted criterion. A review of the statistical method of analysis of signals is included, with a critical discussion of the definition of the spectral density function, which forms the basis of the statistical methods of circuit design.