Cosine Series Representation

Abstract

We present a functional data analysis (FDA) framework based on explicit orthonormal basis expansion for modeling and denoising complex biomedical signals. Observed functional data are represented as smooth functions in a Hilbert space, and statistical inference is performed directly on their basis coefficients. This formulation provides a transparent and flexible approach to smoothing, regularization, and hypothesis testing. Applications to diffusion tensor imaging tract modeling and EEG denoising demonstrate the advantages of explicit basis representations for scalable and interpretable functional modeling.