B-spline signal processing using harmonic basis functions

Abstract

This paper deals with the concept of orthogonal transformation and proposes an orthogonal discrete spline transform (DSPLT) for processing and representation of signals in terms of modified spline basis functions. This work reinterprets the B-spline digital filtering techniques proposed by Unser et al. by introducing harmonic spline basis functions. The principle of periodic B-spline interpolation is explored. Based on the orthonormal properties of the eigenvectors of the periodic B-spline interpolation matrix, a complete set of orthonormal modified spline basis functions which constitute the basis set for the DSPLT is developed. A 16-point, not-in-place, radix-2, decimation-in-time fast DSPLT algorithm is presented. An efficient VLSI algorithm for computing the discrete spline transform coefficients of variable length is proposed. The spectral properties of the modified spline basis functions are explored. A multiresolution analysis (MRA) technique using wave-packets in terms of the modified spline basis is also developed. Finally, the present approach of B-spline coefficient extraction followed by interpolative signal reconstruction is compared with previous filtering methods.