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Fixed Point Refinement: A systems approach

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Taking any signal processing algorithm to implementation requires a good choice of fixed-point representation. The trade off between accuracy of computation and the cost of implementation tends to minimize the costs while compromising the accuracy of computation to an acceptable level. This word-length optimization problem is combinatorial and NP-Hard. The presentation focuses on two aspects of the word-length optimization problem. One, the problem of quickly evaluating the accuracy degradation of a fixed-point system and two, a divide and conquer approach to address large word-length optimization problems.

Three contributions over the existing state of the art will be discussed in the presentation. One, the characterization of quantization noise power with a stochastic model that mimics the behavior of total output quantization noise characteristics of any computational system. Application of this quantization noise model helps to divide and aggregate the quantization noise power in a hierarchical fashion. Two, a semi-analytical approach to accelerate the process of fixed-point simulation in the presence of un-smooth operators. Three, using quantization noise power instead of assigned word-lengths to in a divide and conquer approach to word-length optimization.

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