Arbitrary Bandwidth Wavelet Sets

In this paper we consider an extension of the wavelet transform leading to the construction of wavelets with arbitrary band-width. The new wavelets are complete, orthonormal and dyadic; nevertheless their bandwidth is not constrained to be one oc-tave, rather it may be designed by selecting a set of parameters. The construction of the new bases starts in the discrete-time domain, exploiting properties of the Laguerre transform. Fur-thermore, we provide a procedure to define continuous-time warped wavelets. Flexibility of the bandwidth allocation allows for more and improved applications of the wavelet transform, such as signal coding, the design of auditory model based filter-banks and transient detection in pseudoperiodic signals, pointed out in the paper