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Presented here are general limits on bandpass filter performance as a denoising step for parameter estimation. Monocomponent analytic FM signals in white Gaussian noise are assumed. Analytic and numerical evidence is presented to support the argument that the Gaussian filter can be used as a canonical bandpass filter for the purpose of such an analysis. Simple, approximate Cramer-Rao bound formulas for amplitude, phase and IF estimates are presented for limiting cases.