A new family of wavelets derived from the Poisson distribution is intr
oduced. The associated wavelet transform is closely related to the Poi
sson transform. The Poisson wavelet transform is characterized by the
usual translation and scaling parameters and an additional discrete or
dering index. In this paper, the Poisson transform is reviewed, the pr
operties of the Poisson wavelet transform are developed, and two examp
les are provided to illustrate the utility of this transform for analy
zing time delayed signals that are exponentially damped and;for parame
ter identification. (C) 1997 Elsevier Science Ltd.