Adaptive infinite inpulse-response (IIR) notch filters have been widely studied for many years. However, further efforts are still to be made to pursue new algorithms which work better than the conventional plain gradient algorithm but have little increase in complexity. In this paper, we employ the gradient linearization, Taylor series expansion, and calculus of variations to derive a novel memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter, which improves the estimation performance considerably. Approximate closed-form expressions for the stability bounds on the step size parameter and the steady-state coefficient variance are also derived. Extensive simulations indicate the significant improvement that may be achieved using the new algorithm, and verify the validity of the analytical results.Index Terms-Frequency estimation, gradient algorithm, infinite impulse-response notch filtering, performance analysis.

In this paper, we present a novel lattice structure of M -channel paraunitary filter banks. M -channel paraunitary filter banks without imposing the linear phase constraint outperform the linear phase paraunitary filter banks in image coding. Removing the redundancy of the lattice structure in filter banks, the comple and minimul structure is derived. Based on this structure, the pairwise mirror-image filter banks are also derived by restricting the rotation angles. Finnaly we show some examples to validate the proposed method.

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SUMMARYThis paper proposes a new lattice structure for the M-channel paraunitary filterbank. When a filterbank is realized by using a lattice structure, there is an advantage that properties such as phase linearity and the paraunitarity can be retained if the coefficients are quantized. A large number of lattice structures have been proposed, but there remains the problem that the proposed structures contain redundancy. This paper first eliminates the redundancy from the lattice structure and presents a new lattice structure for the generalized filterbank without restrictions such as phase linearity. Based on the proposed structure and restricting the parameters, a pairwise mirror image filterbank structure is presented. Finally, the usefulness of the approach is demonstrated by simulation.