Carsten Hamm

Vibrational Error Extraction Method Based on Wavelet Technique

A key factor in developing and assessing any vibration attenuation technique for elastic systems is the measure that quantifies the occurring vibrations. In this paper, we propose a general and instantaneous vibration measure which allows for more subtle methods of localized vibration attenuation techniques. This measure is based on extracting the vibrational part from the conventional tracking error signal using wavelet technique. The paper also provides a method for constructing a wavelet function based on the system impulse response. This wavelet outperforms the existing ones in representing the system behavior while guaranteeing admissibility and providing sufficient smoothness and rate of decay in both time and frequency domains.

Spline multiresolution and wavelet-like decompositions

Splines are useful tools to represent, modify and analyze curves and they play an important role in various practical applications. We present a multiresolution approach to spline curves with arbitrary knots that provides good feature detection and localization properties for non-equally distributed geometric data. In addition, we show how equidistributed data and knot sequences can be efficiently handled using signal processing techniques.

Hermite Interpolation with Rational Splines with Free Weights

In this text we present an approach for Hermite interpolation with rational splines without predefined weight factors. We rearrange the equation of the derivative of the rational spline function into a homogeneous linear system of equations in homogeneous space. We use this linear system to formulate different interpolation problems, with the weight factors as well as the control points as a solution. In the first approach, we solve the linear system directly by adding only one inhomogeneous equation to normalise the weights. This approach has some significant constraints. The second approach uses the linear system as a secondary condition for maximizing the minimum weight. This way allows us to obtain method more open regarding the number of interpolation points. In the third approach, we reduce the number of interpolation points to approximate the values of the function between the interpolation points.