Synthesizing a controller frequency response is a common requirement in feedback system design. A method is described for synthesizing a continuous-timeminimum-phase frequency response specification. For a discrete set of frequencies, the designer may specify linear inequalities that bound the magnitude and phase of the frequency response. A linear programming problem is formulated using these bounding inequalities, together with constraints that force the frequency response to be minimum-phase and sufficiently smooth so that it can be approximated with a low-order transfer function. The objective for the linear programming problem is to minimize the frequency weighted gain of the controller. The problem solution prescribes both the magnitude and phase of the frequency response specification. A controller that approximates the specification can then be readily designed using existing continuous-timer filter approximation methods. A design example is presented to demonstrate the application of the proposed method.