Spectral analysis for non-stationary audio

A. Meynard and B. Torrésani

Institut de Mathématiques de Marseille (I2M)

Aix-Marseille Université

Abstract :

A new approach for the analysis of non-stationary signals is proposed, with a focus on audio applications. Following earlier contributions, non-stationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is here on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This papers provides theoretical analysis of the approximations, and describes and analyses a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.

Keywords :

Non-stationary signals, deformation, wavelet analysis, local spectrum, Doppler effect

Link to the manuscript :

Spectral analysis for non-stationary audio

Link to the code :

JEFAS algorithm

Supplementary data :

Illustrations for the 3 test scripts provided with the paper :

Validation on a synthetic signal : starting from a random stationary gaussian process with given power spectrum, a non-stationary signal is generated by transforming it with given amplitude modulation and time warping. The simulation is used to provide quantitative assessment for the precision of estimators.

Doppler example : the signal is a sound originating from a moving racing car, recorded from a fixed location. Time warping is generated from Doppler effect, and amplitude modulation results from the variation of distance between the car and the recording device.

Singing female voice : the signal is a recording from a soprano singing a simple melody. Time warping models pitch variations.

Dolphin sound : the signal is a recording of a dolphin sound.

Wind sound : the signal is a recording of a wind sound.

Sound files :

Cross-synthesis :

To synthesize new sounds, we start from a stationarized sound obtained with JEFAS and we apply the deformation estimated from another nonstationarysound.

Cross-synthesis  : Matlab file enabling the cross-synthesis.