A block transform-based digital media codec achieves faster performance by re-mapping components of the digital media data into vectors or parallel units on which many operations of the transforms can be performed on a parallel or single-instruction, multiple data (SIMD) basis. In the case of a one-dimensional lapped biorthogonal transform, the digital media data components are re-mapped into vectors on which butterfly stages of both overlap pre-/post-filter and block transform portions of the lapped transform can be performed on a SIMD basis. In the case of a two-dimensional lapped biorthogonal transform, the digital media data components are re-mapped into vectors on which a Hadamard operator of both overlap pre-/post-filter and block transform can be performed on a SIMD basis.