ABSTRACT
This paper gives a self-contained presentation of Meyer and Mallat’s basic theory of multiresolution analysis and the construction of orthonormal wavelet bases in ℝ n . In fact, this is done in the more general setting of an arbitrary lattice in ℝ n with a strictly expanding matrix which preserves this lattice. The most familiar case is the integer lattice ℤ n with matrix equal to twice the identity. This general theory is applied to obtain a construction of Daubechies’ compactly supported wavelets. Also included is a discussion of subband coding, which gives an efficient algorithm for computing wavelet coefficients and for reconstructing a function from these coefficients.
