Preparing Biomechanical Data for Functional Data Analysis

This chapter describes how to transform observed biomechanical data into smooth functions using B-spline or Fourier basis function expansions, using least-squares or penalised least-squares estimation approaches. It also discusses the characteristics of certain types of biomechanical data that might make other (e.g., wavelet or FPCA) basis function approaches more suitable. The second half of this chapter introduces phase variation in biomechanical data and describes approaches for separating phase and amplitude variation via registration. Various applications of registration to biomechanical data are discussed and their findings are detailed to develop guidance on its use. Some advanced analyses of phase variation and registration techniques from the statistics literature are reviewed to highlight possibilities for future applications.