It is a well known fact that the time-frequency domain is very well adapted for representing audio signals. The
main two features of time-frequency representations of many classes of audio signals are sparsity (signals are
generally well approximated using a small number of coefficients) and persistence (significant coefficients are not
isolated, and tend to form clusters). This contribution presents signal approximation algorithms that exploit
these properties, in the framework of hierarchical probabilistic models.
Given a time-frequency frame (i.e. a Gabor frame, or a union of several Gabor frames or time-frequency
bases), coefficients are first gathered into groups. A group of coefficients is then modeled as a random vector,
whose distribution is governed by a hidden state associated with the group.
Algorithms for parameter inference and hidden state estimation from analysis coefficients are described. The
role of the chosen dictionary, and more particularly its structure, is also investigated. The proposed approach
bears some resemblance with variational approaches previously proposed by the authors (in particular the variational
approach exploiting mixed norms based regularization terms).
In the framework of audio signal applications, the time-frequency frame under consideration is a union of
two MDCT bases or two Gabor frames, in order to generate estimates for tonal and transient layers. Groups
corresponding to tonal (resp. transient) coefficients are constant frequency (resp. constant time) time-frequency
coefficients of a frequency-selective (resp. time-selective) MDCT basis or Gabor frame.
KEYWORDS: Time-frequency analysis, Convolution, Signal processing, Wavelets, Fourier transforms, Modulation, Signal analysis, Space operations, Linear filtering, Filtering (signal processing)
Time-frequency analysis and wavelet analysis are generally used for providing signal expansions that are suitable
for various further tasks such as signal analysis, de-noising, compression, source separation, ... However, time-frequency
analysis and wavelet analysis also provide efficient ways for constructing signals' transformations. They
are modelled as linear operators that can be designed directly in the transformed domain, i.e. the time-frequency
plane, or the time-scale half plane. Among these linear operators, transformations that are diagonal in the time-frequency
or time scale spaces, i.e. that may be expressed by multiplications in these domains, deserve particular
attention, as they are extremely simple to implement, even though their properties are not necessarily easy to
control.
This work is a first attempt for exploring such approaches in the context of the analysis and the design of
sound signals. We study more specifically the transformations that may be interpreted as linear time-varying
(LTV) systems (often called time-varying filters). It is known that under certain assumptions, the latter may
be conveniently represented by pointwise multiplication with a certain time frequency transfer function in the
time-frequency domain. The purpose of this work is to examine such representations in practical situations, and
investigate generalizations. The originality of this approach for sound synthesis lies in the design of practical
operators that can be optimized to morph a given sound into another one, at a very high sound quality.
We present a method based on local regularity analysis to detect glitch signatures in an interferometric signal. The regularity is given by the local value of the Holder exponent. This exponent can be derived using a Holderian analysis with a wavelet coefficients modulus calculation along wavelet transform modulus maxima lines (so called WTMML) in suitably selected regions of the time-scale half-plane. Glitches that are considered as a discontinuity on the signal show Holder exponent lower than a fixed threshold defined for a continuous signal (around -1). The method has been tested using computed histograms simulations derived from "HERSCHEL / SPIRE" theoretical signals. Statistics show that the optimization of the detection parameters should take into account variables such as sampling rate, signal to noise ratio but is almost independent of the glitch amplitude.
Several different approaches for joint detection/estimation of amplitude and frequency modulated signals embedded in stationary random noise with prescribed spectral density are considered and compared. Matched filter approaches are compared to time-frequency and time scale based approaches, together with “reassigned” versions. Particular attention is paid to the case of the so-called “power-law chirps”, characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered.
We give an algorithm for the estimation of the orientation of a planar surface with a homogeneous texture, viewed under perspective projection. We follow the two step procedure which is usually employed for this type of problem: First, a set of local distortion matrices is estimated - here we use wavelets -, then we determine the surface orientation which best fits the local distortions. In both parts the techniques we use are original.
We study local deformations of time-frequency and time-scale representations, in the framework of the so-called reassignment methods, which aim at `deblurring' time- frequency representations. We focus on deformations generated by appropriate vector fields defined on time- frequency or time scale plane, and constructed on the basis of geometric and group-theoretical arguments. Such vector fields may be used as such for signal analysis (as quantities generalizing instantaneous frequency or group delay) in the framework of reassignment algorithms.
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