Abstract
Input-output or poles sensitivity is widely used to evaluate the resilience of a filter realization to coefficients quantization in an FWL implementation process. However, these measures do not exactly consider the various implementation schemes and are not accurate in general case. This paper generalizes the classical transfer function sensitivity and pole sensitivity measure, by taking into consideration the exact fixed-point representation of the coefficients. Working in the general framework of the specialized implicit descriptor representation, it shows how a statistical quantization error model may be used in order to define stochastic sensitivity measures that are definitely pertinent and normalized. The general framework of MIMO filters and controllers is considered. All the results are illustrated through an example.
Highlights
The majority of control or signal processing systems is implemented in digital general purpose processors, DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate-Array), and so forth
It is well known that these Finite Word Length (FWL) effects depend on the structure of the realization
In [6] where the transfer function error appears for the first time, the coefficients are supposed to have the same fixed-point representation, so their second-order moments are all equal and denoted σ02
Summary
The majority of control or signal processing systems is implemented in digital general purpose processors, DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate-Array), and so forth Since these devices cannot compute with infinite precision and approximate real-number parameters with a finite binary representation, the numerical implementation of controllers (filters) leads to deterioration in characteristics and performance. This has two separate origins, corresponding to the quantization of the embedded coefficients and the round-off errors occurring during the computations. In state-space form, the realization depends on the choice of the basis of the state vector This motivates us to investigate the coefficient sensitivity minimization problem. A∗ will denote the conjugate, A the transpose, AH the transpose-conjugate, tr(A) the trace operator, E{A} the mean operator, Re(A) the real part, and A × B the Schur product of A and B, respectively
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