Study on Several Problems of Normalized Tight Frame Super-wavelets
Bingjie Li · Journal of Air Force Engineering University · 2011
Three impotant results are given on normalized tight frame super-wavelets in the article.Firstly,A normalized tight frame super-wavelets of length in the space can be extended to a super-wavelets of length in the bigger space.That is a normalized tight super-wavelets frame in the space is extendable to an orthonormal basis in the bigger space.So the relationship between parseval super-wavelets and super-wavelets is found.Secondly,the equivalence of the normalized tight frame super-wavelets are studied by means of the unitary equivalence.The m-tuple remainly forms a normalized tight frame super-wavelets,when the final component of normalized tight frame super-wavelets is unitarily replaced by a normalized tight frame wavelet.Finally,the conditions of the normalized tight frame super-wavelets are improved.A sufficent condition on a normalized tight frame super-wavelets is given by using space theory.The three results are proofed by using functional analysis.These results function as the important theory basis for the signal processing in the space.