Arbitrary bandwidth wavelet sets

In this paper we consider an extension of the wavelet transform leading to the construction of wavelets with arbitrary bandwidth. The new wavelets are complete, orthonormal and dyadic; nevertheless their bandwidth is not constrained to be one octave, 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. Furthermore, we provide a procedure to define continuous-time warped wavelets. The 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 filterbanks and transient detection in pseudoperiodic signals, pointed out in the paper