Extending coherence time for analysis of modulated random processes

Abstract

In this paper, we relax a commonly-used assumption about a class of nonstationary random processes composed of modulated wide-sense stationary random processes: that the fundamental frequency of the modulator is stationary within the analysis window. To compensate for the relaxation of this assumption, we define the generalized DEMON ("demodulated noise") spectrum representing modulation frequency, which we use to increase the coherence time of such signals. Increased coherence time means longer analysis windows, which provides higher SNR estimators. We use the example of detection on both synthetic and real-world passive sonar signals to demonstrate this increase.

Spectral Analysis for Nonstationary Audio

“…An alternate theory of locally stationary time series was developed by Dahlhaus [6] (see also [7] for a corresponding stationarity test). In a different context, frequency-modulated stationary signal were considered in [8], [9], and time warping models were analyzed in [10]. In several of these approaches, wavelet, time-frequency and similar representations happen to play a key role for the characterization of nonstationarity.…”

Enhancement and Recognition of Reverberant and Noisy Speech by Extending Its Coherence

“…Degottex and Stylianou [18] proposed another analysis/synthesis scheme for speech using an adaptive harmonic model that they claim is more flexible than the fan-chirp, as it allows nonlinear frequency trajectories. Wisdom et al showed that the fan-chirp transform can be used to build optimal detectors for nonstationary harmonics [19] and harmonically-modulated stationary processes with timevarying modulation frequency [20]. A preliminary version of this algorithm appeared in our REVERB challenge workshop paper [8].…”