The construction of M-band tight wavelet frames

The theory of frame multiresolution analysis (FMRA) is a direct generalization of the (orthonormal) multiresolution analysis of Mallat. It provides conceptually new mathematical and signal processing results. We discuss tight wavelet frames associated with generating refinable functions with dilation factor M>2. We present a sufficient condition for finite number of functions to form a tight wavelet frame and establish general principles for constructing tight wavelet frames.