In more general cases there are an abundance of extensions to the central limit theorem for specific relaxations of the constraints on independence and identical distribution. Malized integrator (transfer function H( z) = lim n − 1(1 − z −n) /(1 − z − 1) )Īnd the input is made up of a stream of independent identically distributed (iid) random variables, the Gaussian approximation will clearly hold no matter what the input distribution, by the central limit theorem. In the most extreme example, where the LTI system under investigation approaches a nor. Often the largest deviation from the Gaussian model is likely to be at the primary inputs to the system, since the internal nodes are formed by a weighted sum of present and past input values. The assumption is that such a deviation will be small enough for practical cases and for the purposes to which this model will be put. Will cause the intermediate signals in the modelled system to deviate to some extent from their idealized Gaussian form. In reality, however, inputs may follow a large variety of distributions which A saturation computation graph G S (V, S, C ) is an annotated form of a computation graph G (V, S ). The formal representation of a saturation system is as a saturation computation graph G S ( V, S, C), as defined below.ĭefinition 5.4. The Linear Time Invariant system from which the saturation system is constructed is referred to as the underlying LTI system. At least one of these nonlinearities must have a cut-o less than the 1 peak value at that output. A saturation system is a system constructed from a Linear Time Invariant system by introducing at least one saturation nonlinearity at an output of an operation. The nonlinearity is more general as the cut-o used to model a two’s complement saturator will be an integral power of two, however there is no such restriction on saturation nonlinearity cut-o. 6.4.6 Combined Binding and Word-Length SelectionĪ saturation nonlinearity can be considered as a generalized model for a two’s complement saturator.6.4.5 Scheduling with Incomplete Word-Length Information.6.3.1 Resources, Instances and Control Steps.5.4.2 The Saturated Gaussian Distribution.5.4.1 Conditioning an Annotated Computation Graph.4.6.3 Limit-cycles in Multiple Word-Length Implementations.4.5 Optimization Strategy 2: Optimum Solutions.4.4 Optimization Strategy 1: Heuristic Search.4.1.1 Word-Length Propagation and Conditioning.2.1.2 The Field-Programmable Gate Array.
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