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- W610142042 abstract "In this chapter, we will apply the observer-based perspective to the problem of digital filtering and design a filter structure that has good properties under finite precision conditions. As of date, there are several digital filter structures that provide good behavior under these conditions [Pec89, PM93, MR76, Fet86, GM75, DD80, DvdV19, RK84, VM84, JLK79, BF77]. A common feature of several of these filter structures is that they fall under the category of “orthogonal” digital filters [Fet88]. Here, the word “orthogonal” is used in the following context: the transfer functions from the input to the states of the filter are orthonormal, or in other words, the Controllability Grammian of the filter is the identity matrix (these structures are also called input-normal form); additionally, if the filter structure realizes an allpass transfer function, the transfer functions from the filter states to its output are also orthonormal (the Observability Grammian is also the identity matrix) (structures with an identity Observability Grammian are also called output-normal form). In earlier literature, the term “orthogonal” has also been used in a different context: to characterize filters that are realized as terminated two-ports, with the two-port having a unitary transfer matrix [DD80, DvdV19, RK84]. In the following text, ‘orthogonal2’ will be used when referring to this type of orthogonality1." @default.
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- W610142042 date "1996-01-01" @default.
- W610142042 modified "2023-09-26" @default.
- W610142042 title "The Feedback-Based Orthogonal Filter Structure" @default.
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- W610142042 doi "https://doi.org/10.1007/978-1-4613-1305-2_2" @default.
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