Orthonormal adaptive IIR filter with polyphase realization

In this work, a particular realization for adaptive IIR filtering and a related special interpretation of the Steiglitz-McBride method are presented. The proposed realization is based on an orthonormal family of functions. The intrinsic unstable behavior of adaptive IIR filters when modeling highly underdamped poles is avoided by visualizing the orthogonal filter as a particular polyphase realization. A stationary point analysis of the resulting adaptive filter shows that it maintains a one-to-one coefficient mapping with the direct-form realization. In this manner, many known properties of the SM algorithm related to the direct-form realization can be extended to the proposed realization. Computer simulations are given illustrating the good performance of the proposed adaptive IIR filter with respect to computational complexity, modeling capability, and reduced order performance. The main application emphasis is oriented to echo cancellation, but other areas of adaptive signal processing can also be considered