Optimal State Space Descriptions
This chapter describes the next step towards the implementation of wavelet filters. Departing from the transfer functions defined in Chapter 4, we derive a state space description of the wavelet filter. Since state space descriptions are not unique representations of a dynamical system, they allow the designer to find an implementation that fits best to the requirements imposed, e.g. coefficients that are readily implemented, a prescribed circuit topology, or maximum dynamic range. The description is transformed into the desired form by state space transforms or similarity transforms. In the context of low-power, low-voltage analogue integrated circuits, the most important requirements are dynamic range, sensitivity, and sparsity, all of which are treated in Chapter 5.
KeywordsTransfer Function State Space Canonical Form Continue Fraction Expansion State Space Representation
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