## Appendix A Pseudocode of Proposed Doppler Envelope Extraction  
**Input**: \(P(v,t)\): Denoised Doppler map (velocity vs time),  
\(n_{\text{levels}}\): Number of contour levels (e.g., 7)  
**Output**: \(Spine(t)\), \(Leg(t)\), \(Foot(t)\): Estimated velocity envelopes  
```
1: Initialize \(contour\_levels\gets extract\_contours(P,n_{\text{levels}})\)
2:for each level \(i\) in \(contour\_levels\)do
3:for each time \(t\)do
4:\(M_{i}(t)\leftarrow\) mean of contour points at level \(i\) and time \(t\)
5:endfor
6: Smooth \(M_{i}(t)\) using moving average filter
7: Store \(M_{i}(t)\) as candidate envelope
8:endfor
9:for each time \(t\)do
10:\(A(t)\leftarrow\) velocity with maximum power in \(P\) at time \(t\)\(\triangleright\) baseline envelope
11:endfor

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