  Multimodality and multichannel monitoring have become increasingly popular
and accessible in engineering, Internet of Things, wearable devices, and
biomedical applications. In these contexts, given the diverse and complex
nature of data modalities, the relevance of sensor fusion and sensor selection
is heightened. In this note, we study the problem of channel/modality selection
and fusion from an information theoretical perspective, focusing on linear and
nonlinear signal mixtures corrupted by additive Gaussian noise. We revisit and
extend well-known properties of linear noisy data models in estimation and
information theory, providing practical insights that assist in the
decision-making process between channel (modality) selection and fusion. Using
the notion of multichannel signal-to-noise ratio, we derive conditions under
which, selection or fusion of multimodal/multichannel data can be beneficial or
redundant. This contributes to a better understanding of how to optimize sensor
fusion and selection from a theoretical standpoint, aiming to enhance
multimodal/multichannel system design, especially for biomedical
multichannel/multimodal applications.
