Minimum Sensitive Hessenberg Representations with Connections to Model Reduction
The signal processing community has long considered the problem of sensitivity in respect of the design of analog and digital filters. In analog filters, it is the component (i.e. R, L or C) tolerances and amplifier sensitivities (i.e. internal amplifier noise levels) which are significant whereas in digital filtering the corresponding considerations are in respect of the coefficient (i.e. choice of wordlength) and arithmetic sensitivities (numerically roundoff noise). In both cases, the nett effect of these inaccuracies on the filter response is critically dependent on the internal (state-space) structure of the filter. If one optimizes the filter structure with respect to the internal noise (amplifier or arithmetic) then the resulting so-called minimum noise gain structures have been shown to exhibit low sensitivity with respect to component or coefficient sensitivity. This is not a proven mathematical result but one which has been observed through numerous design studies.
KeywordsModel Reduction Internal Noise Continuous Time System Minimum Sensitivity Model Reduction Technique
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