Orthonormal, moment preserving boundary wavelet scaling functions in Python

Abstract

In this paper we derive an orthonormal basis of wavelet scaling functions for L 2 ([0, 1]) motivated by the need for such a basis in the field of generalized sampling. A special property of this basis is that it includes carefully constructed boundary functions and it can be constructed with arbitrary smoothness. This construction makes assumptions about the signal outside the interval unnecessary. Furthermore, we provide a Python package implementing this wavelet decomposition. Wavelets defined on a bounded interval are widely used for signal analysis, compression, and for numerical solution of differential equations. We show that for many cases using the basis that we derive results in smaller error than the commonly used alternative.

Muscle Strength Weighting Based on Deep Learning and Wavelet Packet and Muscle Fatigue Analysis Based on L-Z Complexity

“…rough the measurement and statistics of the width of the muscle acoustic spectrum, the law of the change of the spectrum width of the muscle sound signal with the exercise time is obtained. It is found that in the early stage of exercise, the acoustic spectrum bandwidth of gastrocnemius muscle is wide [21][22][23], indicating that the muscle fibers participating in exercise are in the process of adapting to exercise load and rhythm, and various types of muscle fibers are mobilized to participate in exercise. In the middle of exercise, the muscle enters the adaptation period, the number of muscle fibers participating in exercise remain in a certain range, and the vibration spectrum is relatively stable.…”