Establish exact equivalence between HRV Studio and Kubios Smoothness Priors detrending

Establish whether HRV Studio’s implementation of Smoothness Priors detrending is exactly equivalent to Kubios HRV’s implementation, despite Kubios not exposing all internal processing details, in order to determine whether residual cross-platform differences can be attributed solely to subsequent spectral-analysis procedures.

Background

The paper compares HRV Studio with Kubios HRV under matched preprocessing conditions, including Smoothness Priors detrending based on the Tarvainen formulation. However, Kubios is a closed implementation whose internal processing details are not fully exposed. This prevents the authors from assuming that nominally identical detrending settings produce mathematically identical preprocessing outputs.

The unresolved equivalence matters because very-low-frequency power and absolute spectral power are highly sensitive to detrending and related preprocessing choices. Establishing implementation-level equivalence would help separate differences caused by detrending from those caused by spectral estimation, band integration, or other platform-specific operations.