Respiratory decomposition by orthogonal subspace projection¶
What it does¶
Orthogonal subspace projection separates uniformly sampled HRV modulation into a component represented by respiration and delayed copies of respiration, plus a residual outside that linear subspace.
When to use it¶
Use it to quantify or remove linear respiratory association when HRV modulation and respiration are synchronized on the same uniform sampling grid.
Canonical ID: hrv.osp
Inputs¶
| Name | Meaning | Type | Unit | Requirements |
|---|---|---|---|---|
m |
Uniformly sampled HRV modulation signal to be decomposed. | real vector | 1 | NaN allowed; finite |
resp |
Respiratory signal sampled on the same grid and time origin as the HRV modulation. | real vector | a.u. | NaN allowed; finite |
resp_pxx |
Respiratory power spectrum used to select a dominant respiratory frequency. | real vector | a.u.^2/Hz | minimum length: 2; no NaN; finite |
f |
Frequency grid associated with the respiratory spectrum. | real vector | Hz | minimum length: 2; no NaN; finite |
fs |
Common sampling frequency of the HRV modulation and respiratory signals. | real scalar | Hz | greater than: 0; no NaN; finite |
Parameters¶
| Name | Meaning | Type | Unit | Default | Requirements |
|---|---|---|---|---|---|
min_resp_frequency |
Lower bound applied to the selected respiratory frequency. | real scalar | Hz | 0.1 |
greater than: 0 |
Outputs¶
| Name | Meaning | Type | Unit |
|---|---|---|---|
m_resp |
HRV component represented by the delayed-respiration subspace. | real vector | 1 |
m_unrelated |
Residual HRV component outside the selected linear respiratory subspace. | real vector | 1 |
delay |
Adaptive number of respiratory regressors and first aligned output sample. | integer scalar | sample |
How it works¶
A dominant respiratory frequency sets an adaptive delayed-respiration model spanning approximately two cycles. HRV is projected onto that subspace, and the residual is obtained by subtraction. The dominant-frequency selection and minimum-frequency floor are empirical algorithm choices.
Interpretation and limitations¶
The related component measures linear association, not causal respiratory influence. Nonlinear effects, synchronization errors, artifacts, poor respiratory measurements, and unrelated dynamics can remain in the residual.
References¶
- Carolina Varon et al. (2017). Removal of Respiratory Influences from Heart Rate During Emotional Stress. Computing in Cardiology. doi:10.22489/CinC.2017.264-160
- Carolina Varon et al. (2019). Unconstrained Estimation of HRV Indices After Removing Respiratory Influences From Heart Rate. IEEE Journal of Biomedical and Health Informatics. doi:10.1109/JBHI.2018.2884644