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In certain situations, a single transmission system must be designed to function satisfactorily when used for any source from a class of sources. In this situation, the rate-distortion function is the minimum capacity required by any transmission system that can transmit each source from with average distortion . One of the most interesting classes of sources is a class of random processes. Here we consider a weighted-square error-distortion measure and the class of all stationary random processes that satisfy a certain strong mixing property, that have zero mean, known power, and a bounded fourth moment, and that satisfy one of the following alternative specifications on the spectrum: 1) the spectrum is known exactly; 2) the amount of power within the band is known for frequencies ; or 3) the fraction of power outside some frequency is . For the class of sources determined by each of the above three cases and for an arbitrary error-weighting function we evaluate the rate-distortion function.