Some of the sample observations

which seem like time series or discrete signals

are in fact smooth curves (functional data) corresponding to a latent continuous process.The smooth principal component analysis (PCA) focusing on functional data variation can fully characterize the dynamic features hidden in observations.The approaches smoothing discrete samples to continuous curves were introduced.The linear framework of smooth PCA was described as multivariate statistics in basis function spaces.The amplitude variation and phase variation embedded in smooth curves needed registration operations to separate themselves.The nonlinear framework of smooth PCA was discussed in two aspects:depicting two types of variation together with mixed data;depicting phase variation separately with differential manifolds in non-Euclidean space.Three groups of smooth PCA results were presented

which are raw gait data without registration

gait amplitude variation with registration and phase variation.Finally

the applications of smooth PCA in bio-signal processing were reviewed.