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First-Order Complex Resonators

For distinct poles, the recursive terms in the complete partial fraction expansion of Eq.(9.2) can be realized as a parallel sum of complex one-pole filter sections, thereby producing a parallel complex resonator filter bank. Complex resonators are efficient for processing complex input signals, and they are especially easy to work with. Note that a complex resonator bank is similarly obtained by implementing a diagonalized state-space model [Eq.(G.22)].


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2023-09-17 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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