Perceptual Effects Of Noise Disturbances On Phase Spectrum In Stft Analysis/synthesis Procedures. Application To Restoration Processes

Abstract

Restoration of audio recordings degraded by surface noise can be viewed as an analysWsynthesis procedure where the modulus of the Fouriex transform is replaced by an estimator before resynthesis. The goal is usually to find the best possible estimator in terms of noise power reduction. In current restoration procedures there are no modifications of the phase specuum, because most authors consider that the phase is perceptually irrelevant [l]. Therefore the prime objective of the work presented here was to check the validity of these assumptions, and put some emphasis on the degradation of the phase. For that purpose, an analysis/synthesis procedure simulating a restoration p m s has been carried out on artificially degraded signals. An overview of this procedure can be Seen in Fig. 1. addibve noise phase Original signal-EK""'"' phase Fig. 1 Simulation of a restoration process based on Short-Time-Fourier-Transform, with perfect modulus recovering and degraded phase. In these later experiments, the restored signal is obtained from the modulus of the original signal and from the phase of the degraded signal. Thus the estimator of the modulus is equivalent to the one which would be obtained through "perfect" cancellation of the noise. As a consequence, the remaining degradation of the restored signal is only due to the influence of the additive noise in the phase spectrum. The first goal of the work is to calculate an estimator for the phase deviation in the restored signal, which depends on both the noise characteristics and the parameters of the analysis/synthesis plocedure. The results are then compared with psychoacoustical data related to the perception of modulations. This comparison is aimed at providing an appropriate selection for the STFT parameters. Following Vary [2]. the noise component is assumed to be gaussian. For a sine wave of frequency fo = p Fe / N, where Fe is the sampling frequency and N the size of the window, it can be shown that the expectation for the maximum phase deviation at fo is given by