Joint 2-adic complexity is a new important index of the cryptographic security formultisequences. In this paper, we extend the usual Fourier transform to the case ofmultisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, forthe multisequences with pn-period, we discussthe relation between sequences and their Fourier coefficients. Based on the relation, wedetermine a lower bound for the number of multisequences with given joint 2-adiccomplexity.