Multiwavelet packets and frame packets ofL2(ℝd)
The orthonormal basis generated by a wavelet ofL2(ℝ) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis ofL2(ℝd) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases ofL2(ℝd) from the multiwavelet packets.