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The effective weighting function for weather radar is defined. This weighting function considers the effects of both the transmitted signal and the receiver filter. It is used to assign effective ranges to samples taken at prescribed times. For uniformly distributed targets it is shown that "signal"-to-noise ratio depends on the receiver filter, transmitted signal envelope, and receiver noise spectral density. Maximization of this signal-to-noise ratio when range resolution constraints are imposed is discussed, and a receiver design approach specifically adapted for Doppler weather radars is developed.