An oversampled linear phase (LP) perfect reconstruction (PR) filter bank (FB) with a lattice structure involving a noise robust building block is presented. The structure is based on the generalized lapped pseudo-biorthogonal transform (GLPBT), which represents a large class of lapped transforms. Given an analysis bank of the GLPBT and a correlation matrix of noise, the proposed synthesis bank reduces the noise component and attains PR. Numerical results show that this class of filter bank is effective in transmission of oversampled data over noisy channels.