Publication

Abstract : In signal processing, rational pq -wavelets are preferable than the wavelets corresponding to dyadic MRA because it allows more variations in scale factors of signal components. In this paper, for a rational number pq,p,q∈N,p>q≥1,(p,q)=1 and α∈(0,qp−1) , we consider a collection Ap/qα , the space of all continuous functions in L2(R) that are linear on [pqk+plα,pqk+p(l+1)α] and [pqk+(p−1)pα,pqk+pq] for all l=0,1,…,p−2,k∈Z . For pq=32,43 , under certain conditions, we prove that, if 1q√ϕ(⋅q)∈Ap/qα generates a pq -MRA, then α=qp . Also, we show that if α=qp , there exists a function 1q√ϕ(⋅q)∈L2(R) , satisfying the above conditions, that generates pq -MRA. In addition, we construct orthonormal pq -wavelets corresponding to pq -MRA.