An inverse signal approach to computing the envelope of a real valued signal

We address the problem of estimating the envelope of a real valued signal, s(t) that is observed for a duration of T seconds. We model s(t) using a Fourier series, by considering periodic extensions of the signal. By using an analog of the auto-correlation method of linear prediction on the Fourier coefficients of s(t) the envelope of the signal is estimated without explicitly computing the analytic signal.