This paper deals with the Fourier transform of wavelet packets relative to the scaling function . Included there are proofs of the following statements:
(i) ) = 0 for all .
(ii) for all for some , provided are continuous.
(iii) for .
(iv) for a.a. where .
Moreover, several theorems including a result on quadrature mirror filter are proved by using the Fourier transform of wavelet packets.
Cite this article
R. Kumar, K. Ahmad, L. Debnath, On Fourier Transforms of Wavelet Packets. Z. Anal. Anwend. 20 (2001), no. 3, pp. 579–588DOI 10.4171/ZAA/1032