Roundoff noise in floating point state space digital filters

The roundoff noise properties of floating-point state-space digital filters are examined. It is shown that the roundoff noise behavior of these filters is related to their coefficient sensitivity. Expressions for the variance of the output roundoff noise are derived when the input to the filter is a zero-mean, wide-sense stationary random process. These expressions, as expected, depend on the input signal statistics along with the filter parameters, in particular the controllability and observability grammians.<
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