Multi-channel Kalman filters for active noise control.

By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm.

Fast affine projections and the regularized modified filtered-error algorithm in multichannel active noise control.

In this paper, real-time results are given for broadband multichannel active noise control using the regularized modified filtered-error algorithm. As compared to the standard filtered-error algorithm, the improved convergence rate and stability of the algorithm are obtained by using an inner-outer factorization of the transfer path between the actuators and the error sensors, combined with a delay compensation technique using double control filters and a regularization technique that preserves the factorization properties. The latter techniques allow the use of relatively simple and efficient adaptation schemes in which filtering of the reference signals is unnecessary. Results are given for a multichannel adaptive feedback implementation based on the internal model control principle. In feedforward systems based on this algorithm, colored reference signals may lead to reduced convergence rates. An adaptive extension based on the use of affine projections is presented, for which real-time results and simulations are given, showing the improved convergence rates of the regularized modified filtered-error algorithm for colored reference signals.

Simulation of ultrasonic imaging with linear arrays in causal absorptive media.

Rigorous and efficient numerical methods are presented for simulation of acoustic propagation in a medium where the absorption is described by relaxation processes. It is shown how FFT-based algorithms can be used to simulate ultrasound images in pulse-echo mode. General expressions are obtained for the complex wavenumber in a relaxing medium. A fit to measurements in biological media shows the appropriateness of the model. The wavenumber is applied to three FFT-based extrapolation operators, which are implemented in a weak form to reduce spatial aliasing. The influence of the absorptive medium on the quality of images obtained with a linear array transducer is demonstrated. It is shown that, for moderately absorbing media, the absorption has a large influence on the images, whereas the dispersion has a negligible effect on the images.

Fast scan conversion algorithms for displaying ultrasound sector images.

Two fast algorithms for interpolation of ultrasonic sector-scans were developed. Both algorithms are based on line-drawing algorithms and are free from multiplications in the innermost loops. The algorithms were compared to the following conventional interpolators: 2-D windowed sinc, bicubic spline, 4 x 4 point bicubic spline, bilinear, and nearest neighbor. The most accurate of the two new algorithms is about eight times faster than nearest neighbor interpolation. The quantitative errors are of the same order as the errors of the nearest neighbor interpolator. The subjective image quality is between nearest neighbor and bilinear interpolation.