In this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.

Humans perform complex sensorimotor tasks, such as walking on uneven terrain, in a seemingly effortless manner. However, even simple voluntary tasks, like lifting the arm to shake hands, require intricate adjustments to maintain balance. With experience, humans learn to produce the appropriate patterns of muscle activity necessary to maintain balance during everyday activities, as well as highly specialized motor tasks. Here, I investigated the neural feedback mechanisms controlling the formation of the muscle activity used during balance tasks. I hypothesized that humans use feedback from on-going balance perturbations to establish their muscular responses. Specifically, I investigated center-of-mass (CoM) kinematics as a control signal for the formation of these muscle activation patterns. Using an inverted pendulum model under delayed feedback control, I both reconstructed the temporal EMG patterns measured during experimental perturbations and predicted the optimal EMG patterns for responding to the same perturbations. By modulating four feedback parameters, this feedback law accounted for 91% of the variability in all experimentally-recorded EMG patterns - regardless of the mechanical action of the muscle or the response strategy chosen by the subject. To investigate the changes in postural control during motor learning, I used this feedback model to characterize responses while naïve subjects adapted to repetitive unidirectional and reversing perturbations. By adjusting feedback gains related to CoM velocity and displacement, subjects adapted their muscle activity to improve control over the CoM for both perturbation types. Though subjects were unable to use anticipatory strategies to reduce muscle onset latency or to mute inappropriate responses to reversing perturbations, more subtle feedforward adjustments to feedback-mediated postural responses were evident. With experience, subjects adapted their postural responses toward the optimal solution. The results of this work, when combined with on-going studies of muscle synergies, will provide a powerful tool for investigating the consequences that result from the changes in spatiotemporal muscle activity associated with aging, neurological dysfunction, musculoskeletal injury, and specialized training programs. This quantitative knowledge is critical to the development of diagnostic tools for balance and movement disorders, as well as for the design of effective interventional therapies, bipedal robots, and neural prostheses.