Recursive Computation of Signal Vector Norms

written by Katharina Rebbe, Gerhard Schmidt, and Tim Owe Wisch

This chapter is about numerically robust ways for recursive norm computation. In contrast to iterative norm computations, which are numerically very accurate and robust, recursive approaches offer a large reduction in computational complexity. However, after several thousand iterations error accumulation appears. To avoid this a mixed iterative and recursive approach is proposed that is cheap in complexity and robust with respect to error accumulation.

Removal of Signal Trends

written by Christin Bald, Julia Kreisel, and Gerhard Schmidt

This chapter is about the removal of the offset - also referred to as trend - of a signal. Therefore three different methods are introduced and compared against each other: subtracting a priori knowledge, highpass filtering, and a nonlinear, time-variant method. The presented methods are numerically robust and computationally efficient. The performances of the methods are demonstrated by removing the trend of a magnetically measured heart signal.

• Complex magnitude approximations (in progress)

• Design of crossover filters (in progress)

• Fast convolution without additional delay (in progress)

• Levinson-Durbin recursion (in progress)

• Prediction-based filter design (in progress)