Wavelets based on splines: an application

In this paper, we describe the theory and implementation of a variable rate speech coder using the cubic spline wavelet decomposition. In the discrete time wavelet extrema representation, Cvetkovic, et. al. implement an iterative projection algorithm to reconstruct the wavelet decomposition from the extrema representation. Based on this model, prior to this work, we have described a technique for speech coding using the extrema representation which suggests that the non-decimated extrema representation allows us to exploit the pitch redundancy in speech. A drawback of the above scheme is the audible perceptual distortion due to the iterative algorithm which fails to converge on some speech frames. This paper attempts to alleviate the problem by showing that for a particular class of wavelets that implements the ladder of spaces consisting of the splines, the iterative algorithm can be replaced by an interpolation procedure. Conditions under which the interpolation reconstructs the transform exactly are identified. One of the advantages of the extrema representation is the 'denoising' effect. A least squares technique to reconstruct the signal is constructed. The effectiveness of the scheme in reproducing significant details of the speech signal is illustrated using an example.