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An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

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Metallic nickel was electrodeposited from aqueous nickel(II) acetate dissolved in the lyotropic liquid crystalline phases of Brij 56 and Brij 78 surfactant templates to form metal films with hexagonal arrays of nanometer-sized channels. The applicability of these materials as inexpensive, large area and low-resistance current collectors was demonstrated by cyclic voltammetry. The redox charge capacity of the surface oxide in aqueous KOH was enhanced by 2 orders of magnitude over that of a nontemplated sample with no detectable impedance of the reaction rate.

A very fast FFT-based deconvolution method, which combines the well-known principles of least squares optimisation and regularisation, can be used for inverting systems comprising any number of inputs and outputs. The method was developed for the purpose of designing digital filters for multi-channel sound reproduction. It is typically several hundred times faster than a conventional steepest descent algorithm implemented in the time domain. A matrix of causal inverse FIR (finite impulse response) filters is calculated by optimising the performance of the filters at a large number of discrete frequencies. Consequently, this deconvolution method is useful only when it is feasible in practice to use relatively long inverse filters. The circular convolution effect in the time domain is controlled by zeroth-order regularisation of the inversion problem. It is necessary to set the regularisation parameter β to an appropriate value, but the exact value of β is usually not critical. For single-channel systems, a reliable numerical method for determining β without the need for subjective assessment is given. The deconvolution method is based on the analysis of a matrix of exact least squares inverse filters. The positions of the poles of those filters are shown to be particularly important.