Harmonic Decomposition of Audio Signals with Matching Pursuit

International audienceWe introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes

Damped and delayed sinuosidal model for transient modeling

International audienceIn this work, we present the Damped and De- layed Sinusoidal (DDS) model, a generalization of the sinu- soidal model. This model takes into account an angular fre- quency, a damping factor, a phase, an amplitude and a time- delay parameter for each component. Two algorithms are introduced for the DDS parameter estimation using a sub- band processing approach. Finally, we derive the Cramer- Rao Bound (CRB) expression for the DDS model and a simulation-based performance analysis in the context of a noisy fast time-varying synthetic signal and in the audio transient signal modeling context

Matching pursuit and atomic signal models based on recursive filter banks

The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictio- nary of time–frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal adaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm that provides a framework for deriving real-valued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric two-sided atoms constructed from underlying one-sided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that time–frequency atoms based on damped sinusoids are more suitable for represent- ing transients than symmetric Gabor atoms. The resulting atomic models are useful for signal coding and analysis modification synthesis

Sparse Representations in Power Systems Signals

This thesis seeks to detect transient disturbances in power system signals in a sparse framework. To this end, an overcomplete wavelet packet dictionary and damped sinusoid dictionary are considered, and for each dictionary Matching Pursuit is compared with Basis Pursuit. Previous work in developing waveform dictionary theory and sparse representation is reviewed, and simulations are run on a test signal in both noisy and noiseless environments. The solutions are viewed as time-frequency plane tilings to compare the accuracy and sparsity of these algorithms in properly resolving optimal representations of the disturbances. The advantages and disadvantages of each combination of dictionary and algorithm are presented