Karhunen–Loève decomposition of peripheral blood flow signal

The Karhunen–Loève expansion is applied to scalar signals and the effect of window length (tw), time lag (τ) and embedding dimension (d) is analysed for periodic signals and for signals modeled by the Lorenz equations. For τ≠k/2fi (fi are characteristic frequencies of the signal, k is positive integer), we obtain 2m modes from an m-periodic signal. For a large set of parameters a finite number of modes was not obtained from the Lorenz system. It is further shown that, on the time scale of a minute, the peripheral blood flow signal contains oscillatory modes that occur in pairs thereby confirming that the blood flow through the cardiovascular system is oscillatory. Some of the difficulties of applying Karhunen–Loève expansion to scalar signals are pointed out.