Parameterizations of masks for 3-band tight wavelet frames by symmetric extension of polyphase matrix

This paper deals with the construction of 3-band tight wavelet frames with symmetric properties using symmetric extension and parameterizations of the paraunitary matrix. Firstly, we construct a paraunitary matrix which is a symmetric extension of polyphase matrix corresponding to compactly supported wavelet frames with the least number generators. Further, we present symmetric characters and uniformity of wavelet frames with different filter lengths in terms of paraunitary matrix. Then, we focus on investigating the parameterizations of masks for 3-band tight wavelet frames with 3N filter length. Finally, examples of 3-band wavelet frames with good smoothness are constructed based on the parameterizations of masks.