A general representation of the quaternion gradients presented in the literature is proposed, and an universal update equation for QLMS-like algorithms is obtained. The general update law is used to study the convergence of widely linear (WL) algorithms. It is proved that techniques obtained with a gradient similar to the i-gradient are the fastest-converging in two situations: 1) When the corr...

Two-dimensional (2D) adaptive filtering is a technique that can be applied to many image and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to 2D structure and the novel 2D adaptive filters are established. Based on this extension, the 2D variable step-size normalized least mean squares (2D-VSSNLMS), the 2D-VSS affine projection algorithms (2D-...

In this paper Boolean filters and a variation of these, FIR-Boolean hybrid filters are proposed for realizing the prediction stages of a multiresolution lossless image compression structure. Optimal and adaptive Boolean filters are used for prediction in The proposed predictors performance is compared to the performance of other lossless multiresolution methods: the hierarchical interpolation s...

This paper presents several broadband active sound quality control algorithms based on delayless frequency-domain techniques and subband adaptive filters. This efficient algorithm provides faster convergence and reduced computational complexity as compared to a time-domain active noise equalizer. An equal-loudness compensation method is also introduced for designing the shaping filter to achiev...

This paper presents a lattice structure for adaptive Volterra systems. The stucture is applicable to arbitrary planes of support of the Volterra kernels. A fast least squares lattice and a fast QR-lattice adaptive nonlinear filtering algorithms based on the lattice structure are also presented. These algorithms share the fast convergence property of fast least squares transversal Volterra filte...

The quadratic constraint equation error (QCEE) method was proposed by Ho and Chan to achieve bias removal for the equation error adaptive IIR filters. However, this approach is limited to slow convergence in estimation when a small step size is used; large step sizes lead to significant misadjustment. This correspondence presents a variable step size (VSS) technique to greatly improve the QCEE ...

Among the various linear infinite impulse response (IIR) structures for adaptive filters, cascade IIR filters have advantages of easy stability monitoring and good sensitivity performance. However, their high cost for computing gradients is a problem. A novel technique of backpropagating the desired signal is proposed and then a cascade structure satisfying the requirements of this technique is...

Two well known optimization algorithms, the Genetic Algorithm (GA) and the Simulated Annealing Algorithm (SAA), are investigated for IIR adaptive phase equalizers. For non-convex error surfaces, gradient-based algorithms often fail to find the global optimum. This work compares the ability of the GA and the SAA to achieve the global minimum solution for multi-order all-pass adaptive filters to ...

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a ...

A near-end crosstalk (NEXT) cancellation system that uses frequency-domain leastmean-squares (FDLMS) adaptive filters is proposed. The new system is equipped with a mechanism whereby the NEXT signals are detected and then FDLMS adaptive filters are assigned to cancel only the significant NEXT signals. The paper also explores various schemes of assigning step sizes to the adaptive filters. It ha...