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The output noise spectrum and the group delay of active filters are related. For any state-space realization of any transfer function without finite transmission zeros, there is a combination of noise transfer functions that is equal to the group delay. For any transfer function without transmission zeros, it is possible to generate a filter for which the output noise spectrum is an exact multiple of the group delay. This relationship allows for quick noise estimates, and gives insight into the noise behavior of filters.
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G. Groenewold (2007) studied this question.
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