Spectral representation of transient signals
Tarek A. Lahlou, Alan V. Oppenheim · 2014
Signal processing techniques exploiting natural and efficient representations of a class of signals with an underlying parametric model have been extensively studied and successfully applied across many disciplines. In this paper, we focus attention to the representation of one such class, i.e. transient structured signals. The class of transient signals in particular often results in computationally ill-conditioned problems which are further degraded by the presence of noise. We develop the Discrete Transient Transform, a biorthogonal transform to a basis parameterized by decay rate, along with algorithms for its implementation which mitigate these numerical issues and enable a spectral approach to parameter identification, estimation, and modeling for signals with transient behavior. The three algorithms developed have varying degrees of numerical robustness for generating the biorthogonal transient basis. Issues pertaining to transient spectral leakage and resolution are characterized and discussed in the context of an example related to Vandermonde system inversion.