B-spline signal processing using harmonic basis functions

This paper deals with the concept of orthogonal transformation and proposes an orthogonal discrete spline transform (DSPLT for processing and represen tation of signals in terms of modified spline basis functions. This work re interprets the B-spline digital filtering techniques proposed by Unser et a l, by introducing harmonic spline basis functions. The principle of periodi c B-spline interpolation is explored. Based on the orthonormal properties o f the eigenvectors of the periodic B-spline interpolation matrix, a complet e set of orthonormal modified spline basis functions which constitute the b asis set for the DSPLT is developed. A 16-point, not-in-place, radix-2, dec imation-in-time fast DSPLT algorithm is presented. An efficient VLSI algori thm for computing the discrete spline transform coefficients of variable le ngth is proposed. The spectral properties of the modified spline basis func tions are explored. A multiresolution analysis (MRA) technique using wave-p ackets in terms of the modified spline basis is also developed. Finally, th e present approach of B-spline coefficient extraction followed by interpola tive signal reconstruction is compared with previous filtering methods. (C) 1999 Elsevier Science B.V. All rights reserved.