Wavelets and T-pulses

Summary form only given, as follows. One attractive application of the wavelet is as a basis function that is of compact support both in the original and in the transform domain. However, this is not possible from a theoretical point of view. Namely, a pulse that is limited in time cannot simultaneously be limited in frequency. However, from a practical point of view, one can concentrate (a percentage) of the energy in a particular band (say 99%). Moreover, wavelets have no \´DC\´ component. Hence a numerical optimization procedure can be designed to generate wavelets with such desired properties. From a users\´ point of view, additional constraints are required, for example zero intersymbol interference. This requirement guarantees that the waveshapes are orthogonal to its time shifted versions. For radar applications such a requirement would guarantee pulse to pulse orthogonality. A numerical optimization technique has been designed to generate a waveshape with such properties. Such waveshapes has been termed "T-pulses". The objective of this paper is to demonstrate the equivalence between T-pulses and wavelets. Examples are presented to illustrate how T-pulses can be used for efficient radar target identification applications.<>