Frequency-Damping Resolution of the Unit Disc: A Wavelet Idea

摘要

In this paper we introduce the numerical Laplace transform, a local timefrequency analysis method which applies to causal signals. The numerical Laplace transform resolves the identity, has good time-frequency resolution, and adapts resolution windows according to the time delay. The numerical Laplace transform is equivalent to a wavelet transform in the frequency domain. The discretized version of the numerical Laplace transform is invertible. The kernel vectors of the transform are frame vectors that are nearly tight over a fairly wide range of parameters. We demonstrate this with several numerical experiments. The numerical Laplace transform resolves a causal signal onto the s-plane. With a suitable mapping, the signal is resolved into the frequency damping unit disc.