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

Abstract

We address the problem of estimating the envelope of a realvalued signal, st, that is observed for a duration of T seconds. We model st 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 st, 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.

Computation of Hilbert Transform via Discrete Cosine Transform

“…If the signal is buried by noise, the truncation of the DCT coefficients reduces noise in the computed HT and the envelope (Figure 2). In the FFT-based method (9), in Hartley transform assisted method [16] and in other algorithms described in literature [14][15] this usually cannot be made. In this context the DCT-based method is more robust to noise.…”

“…The theoretical basis of HT is well established, but the computational procedures are still being developed. The most frequently used methods are based on the fast Fourier transform (FFT) [12], but many other methods have been proposed, such as digital filtering [12,13], the parametric modelling approach [14,15] and the discrete Hartley transform [16].…”

Frequency Domain Linear Prediction Features for Replay Spoofing Attack Detection

“…The idea of linear prediction in the frequency domain was first proposed in [14] in the context of audio coding. Kumaresan et al [15,16] have also explored this concept, treating it as linear prediction in the spectral domain. In their approach, the envelope of the signal was obtained without computing the Hilbert transform of the signal, using linear prediction in the discrete Fourier transform (DFT) domain.…”