Spectral
estimation for non-stationary signal
classes
Adrien
Meynard1 and Bruno Torrésani2
1: Aix-Marseille
Université, CNRS,
Centrale Marseille, I2M, Marseille, France
2: CNRS,
Université de Montréal, CRM,
UMI 3457, Montréal, Canada
Supplementary
data
Abstract:
An approach to the spectral
estimation for some classes of non-stationary random signals is
developed, that addresses stationary random processes deformed by a
stationarity-breaking transformation. Examples include frequency
modulation, time warping, non-stationary filtering and others. Under
suitable smoothness assumptions on the transformation, approximate
expressions are obtained in adapted representation spaces. In the
Gaussian case, this leads to approximate maximum likelihood estimation
algorithms, which are illustrated on synthetic as well as real signals.
Illustration: processing of a
F1 engine sound
The input signal is a F1 engine sound, during acceleration stage (thus
the signal is not stationary). A time warping function is estimated,
and the signal is modified using the inverse warping function.
Time-scale
representations:
Below are represented the wavelet transform modulus of input and
processed signals
Spectral
representations:
The power spectra of input and processed signals are displayed below.
The harmonic structure clearly appears on the processed signal spectrum.
Audio files:
Original sound:
Modified sound:
Illustration: processing of a singing female voice
The input signal is a female voice singing a (non-stationary) melody.
Again a time warping function is estimated,
and the signal is modified using the inverse warping function.
Time-scale
representations:
Below are represented the wavelet transform modulus of input and
processed signals
Spectral
representations:
The power spectra of input and processed signals are displayed below.
The harmonic structure clearly appears on the processed signal spectrum.
