Matching pursuit with damped sinusoids

The matching pursuit algorithm derives an expansion of a signal in terms of the elements of a large dictionary of time-frequency atoms. This paper considers the use of matching pursuit for computing signal expansions in terms of damped sinusoids. First, expansion based on complex damped sinusoids is explored; it is shown that the expansion can be efficiently derived using the FFT and simple recursive filterbanks. Then, the approach is extended to provide decompositions in terms of real damped sinusoids. This extension relies on generalizing the matching pursuit algorithm to derive expansions with respect to dictionary subspaces; of specific interest is the subspace spanned by a complex atom and its conjugate. Developing this particular case leads to a framework for deriving real-valued expansions of real signals using complex atoms. Applications of the damped sinusoidal decomposition include system identification, spectral estimation, and signal modeling for coding and analysis-modification-synthesis.