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The energy spectrum [X2(f)] of a ??windowed sample?? of an unmodulated RF carrier will generally exhibit a peak value at or near the carrier frequency. The location of this peak is frequently used in signal analysis as an estimate of the true carrier frequency. This paper investigates the error in such estimates in cases where the signal arrives in the presence of ??broad-band?? additive noise and shows that the error is due to both the added noise and spectral ??leakage?? effects. Both these error mechanisms are affected by window duration and window shape. This paper proceeds further to pose two optimization criteria for the selection of a ??best window?? shape for the minimization of estimation error. The two criteria are related to two differing views of prior un-certainty about the actual carrier frequency. These criteria accordingly provide different, but similar forms for the optimum window. Moreover, in worsening signal-to-noise conditions, both forms of optimum window tend to a rectangular shape.