THE LSL ALGORITHM

I present here first the basic LSL algorithm as it is used for spectral analysis: its formalism, the definitions of the forward and backward residuals, and the recursion formulas. The proofs for the recursions implied are long, and heavy: I prefer to refer to Lee et al. (1981) for elegant geometric demonstrations. The recursion formulas also provide us with a statistical tool, describing the time-statistical variations in the data, which I will briefly explain. Finally, I derive a simple version of the general LSL algorithm; Friedlander (1982) had indeed derived such an algorithm, but in a ``normalized'' formalism, not easy to understand intuitively.