principe_gamma_1993 - IEEE TRANSACTIONS ON SIGNAL...

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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 2, FEBRUARY 1993 649 The Gamma Filter-A New Class of Adaptive IIR Filters with Restricted Feedback Jose C. Principe, Senior Member, IEEE, Bert de Vries, Member, IEEE, and Pedro G. de Oliveira, Member, IEEE Abstract-In this paper we introduce the generalized feedfor- ward filter, a new class of adaptive filters that combines at- tractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters. A particular case, the gamma filter, generalizes Widrow’s adap- tive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and least mean square (LMS) adaptation is of the same com- putational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. We extend the Wiener-Hopf equation to the gamma filter and develop some analysis tools. I. INTRODUCTION FINITE impulse response (IIR) filters are more effi- T”. cient than finite impulse response (FIR) filters, but in adaptive signal processing, FIR systems are used almost exclusively [5], [ 121. This is largely due to the difficulty of ensuring stability during adaptation of IIR systems. Moreover, gradient descent adaptive procedures are not guaranteed to find global optima in the nonconvex error surfaces of IIR systems [ 101. Yet IIR systems have an important advantage over FIR systems. For a Kth order FIR system, both the region of support of the impulse response and the number of adap- tive parameters equal K. For an IIR system, the length of the impulse response is uncoupled from the order (and number of parameters) of the system. Since the length of the impulse response of a filter is closely related to the depth of memory of the system, IIR systems are preferred over FIR systems for modeling of systems and signals characterized by a deep memory and a small number of free parameters. These features are typical for low-pass frequency signals, as is the case for most biological and other real-world signals. In this paper we introduce the generalized feedforward filter, an IIR filter with restricted feedback architecture. The gamma filter, a particular instance of the generalized feedforward filter, is analyzed in detail. The gamma filter borrows desirable features from both IIR and FIR system: Manuscript received June 17, 1991; revised January 6, 1992. This work was supported in part by NSF Grants ECS-8915218 and DDM-8914084. The work of P. Guedes de Oliveira at the University of Florida was shp- ported in part by JNICT. J. C. Principe and B. de Vries are with the Computational Neuro-engi- neering Laboratory, Department of Electrical Engineering, University of Florida, Gainesville, FL 3261 1.
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This note was uploaded on 06/05/2011 for the course EEL 6502 taught by Professor Principe during the Spring '08 term at University of Florida.

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principe_gamma_1993 - IEEE TRANSACTIONS ON SIGNAL...

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