A Higher Density Discrete Wavelet Transform

This paper describes a new set of dyadic wavelet frames with two generators. The construction is simple, yet the wavelets cover the time–frequency plane in an arrangement that provides a higher sampling in both time and frequency. Specifically, the spectrum of the first wavelet is concentrated halfway between the spectrum of the second wavelet and the spectrum of its dilated version. In addition, the second wavelet is translated by half integers rather than whole integers in the frame construction. This arrangement leads to an expansive wavelet transform that is approximately shift invariant and has intermediate scales. The wavelet frames presented in this paper are compactly supported and have vanishing moments.