Wavelets: a tutorial in theory and applications
Wavelets: a tutorial in theory and applications
Wavelets and subband coding
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Multiresolution analysis adapted to irregularly spaced data
EURASIP Journal on Advances in Signal Processing
Hi-index | 0.00 |
This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we provide an explicit generalization allowing the construction of the scaling and wavelet bases on the nontraditional sequences. We show that the orthogonal decomposition is implemented using filter banks where the coefficients depend on the location of the knots on the sequence. Examples of orthonormal spline scaling and wavelet bases are provided. This approach can be used to interpolate irregularly sampled signals in an efficient way, by keeping the multiresolution approach.