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A Tutorial on Performance Metrics and Noise Propagation in Digital IIR Filters

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This paper addresses issues of digital IIR filter performance, namely the likelihood of fixed-point overflow and the propagation of quantization error. Measuring these quantities requires a method of determining a transfer function between arbitrary nodes of a filter structure. Norm functions are defined for application to these transfer functions which address overflow and error propagation issues depending on the signals employed. In addition, functions of the state matrix of an IIR filter are defined that measure the potential for limit cycles.

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