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The optimum signal processing to follow a given radiometer front-end is derived when it is desired to estimate, with smallest rms error, the temperature of a radio source. We find, for the important special case of small sources, that the optimum radiometer is implemented by the use of a compensating filter followed by square-law detection and integration. We consider two examples of receiver front-end gain characteristics, the Lorentzian and Gaussian shapes. Improvement over conventional radiometer performance is shown to be possible.