A New Approach to the Common-Factor Design Technique for Hilbert-Pair of Wavelets

A Hilbert-Pair consists of a pair of filter banks whose corresponding wavelets are Hilbert transforms of each other. Selesnick [1] proposed the simple common-factor technique for its design. The filter transfer functions consist of the product of a factor that is common to both filter banks and a phase factor which gives the (approximate) half-sample-delay requirement. Previously the design of the phase factor has been based on designing an all-pass filter approximating the half-sample-delay. This paper proposes a different approach to designing the phase factor by exploiting a basic multirate identity. The downsampling approach allows greater flexibility and can yield filters and wavelets with better properties.