Spline Wavelets of Small Support
Debao Chen · SIAM Journal on Mathematical Analysis · 1995
Every mth order cardinal spline wavelet is a linear combination of the functions $\{ N_{m + l}^{(l)} (2x - j),j \in {\bf Z}\} $. Here the function $N_m $ is the mth order cardinal B-spline. This paper proves that the single function $N_{m + l}^{(l)} (2x)$, or $N_{m + l}^{(l)} (2x - 1)$ is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases,the smoothness of the dual wavelet improves. Each wavelet is constructed by spline multiresolution analysis. The dual multiresolution analyses are given.