On the phase condition and its solution for hilbert transform pairs of wavelet bases
Hüseyin Özkaramanlı, Runyi Yu · IEEE Transactions on Signal Processing · 2003
In this paper, the phase condition on the scaling filters of two wavelet bases that renders the corresponding wavelets as Hilbert transform pairs is studied. An alternative and equivalent phase condition is derived. With the equivalent condition and using Fourier series expansions, we show that the solution for which the corresponding scaling filters are offset from one another by a half sample is the only solution satisfying the phase condition.