This paper investigates the problem of reducing the deviation from a desired transfer function caused by the coefficient quantization errors of a three-dimensional (3-D) separable-denominator digital filter. First, a 3-D transfer function with separable denominator is represented with the cascade connection of three one-dimensional (1-D) transfer functions by applying a minimal decomposition technique. Next, the multiinput multi-output (MIMO) 1-D transfer function located in the middle of the cascade connection is realized by a minimal state-space model and then the l2/l2-sensitivity of the model is analyzed. Third, a technique for the optimal synthesis of the minimal state-space model is developed so as to minimize the l2-sensitivity subject to l2-scaling constraints. Finally, a numerical example is given to demonstrate the validity and effectiveness of the proposed technique.

We have developed a wearable airbag that incorporates a fall-detection system that uses both acceleration and angular velocity signals to trigger inflation of the airbag. The fall-detection algorithm was devised using a thresholding technique with an accelerometer and gyro sensor. Sixteen subjects mimicked falls, and their acceleration waveforms were monitored. Then, we developed a fall-detection algorithm that could detect signals 300 ms before the fall. This signal was used as a trigger to inflate the airbag to a capacity of 2.4 L. Although the proposed system can help to prevent fall-related injuries, further development is needed to miniaturize the inflation system.

A generalized form of the serial MSK (GSMSK)modem is presented. The impulse response of the conversion filter required to produce a GSMSK signal whose upward phase trellis arms have an arbitrary curvature is derived. Analysis is presented which shows that the proposed modem does not have intersymbol interference and that the BER performance is that of an antipodal signal set. Numerical results are shown for a particular trellis curvature.