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 autocorrelation method of linear prediction on the Fourier coefficients of s(t), the envelope of the signal is estimated without explicitly computing the analytic signal through Hilbert transformation. Using this method the envelope of a non-stationary signal can be computed by processing the signal through a sliding T-second window