Effect of filter frequency response on the uncertainty in measuring statistical estimators of input noise

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Abstract
It is shown that in a system consisting of a bandpass filter followed by an ideal linear detector and then an integrator, with white noise as the system input, the statistical uncertainty of the output of the integrator depends on the shape of the bandpass filter power transfer function. That is, for a constant integration time and a constant equivalent noise bandwidth (defined in the usual sense), the statistical uncertainty of the integrator output is a function of the shape of the bandpass filter power transfer function. A new equivalent noise bandwidth is proposed to account for this variation with filter shape so that the relations derived by Rice for rectangular cutoff bandpass filters can be used.

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