You Fa LI, Shou Zhi YANG, Tao QIN
Sampling theorem plays a key role in digital signal communication and image processing since a continuous signal is usually recovered and processed by using its discrete samples. In this paper, we shall study the extension of sampling theorem related to generalized interpolating refinable function vectors introduced in Han Bin [J. Comput. Appl. Math., 2009, 227: 254-270]. Precisely, for an existing generalized interpolating d-refinable function vector ø=(ø1,…,ør)T, i.e.øl(m/r + k)= δkδl-1-m,Ⅴk∈Z,m=0,1,…,r-1,l=1,…,r.we construct a set of functions{ør+1,...,ødr} such that ø#=(øT,ør+1,…,ødr)T is also a continuous d-refinable function vector and satisfies øl(m/dr+k)=δkδθd,r(l)-m, Ⅴk|∈Z,m=0,1,…,dr-1,l=r+1,…,dr,with θd,r(l)=l-r+Rl-1-r,d-1,Rl-1-r,d-1=[l-1-r/d-1].The multiwavelet sampling theorem associated with ø# is established. Obviously, the sampling theorem in the multiwavelet subspaces of ø is extended. Moreover, we estimate the truncated error of the sampling theorem, which is desirable for application.
