SVD Mathematical Framework
Hankel Matrix Construction:
H = [x(t), x(t+1), ..., x(t+m-1)]
where m is the embedding window size
H = [x(t), x(t+1), ..., x(t+m-1)]
where m is the embedding window size
Singular Value Decomposition:
H = U Σ VT
H = U Σ VT
Mode Extraction:
Mode k: xk(t) = σk · uk(t) · vk(t)
where σk is the k-th singular value
Mode k: xk(t) = σk · uk(t) · vk(t)
where σk is the k-th singular value
Frequency Analysis:
Frequency (cycles/day) = fHz × 24 / Δthours
Frequency (cycles/day) = fHz × 24 / Δthours