The world of mobile devices is experiencing an ongoing trend of feature enhancement and generalpurpose multimedia platform convergence. This trend poses many grand challenges, the most pressing being their limited battery life as a consequence of delivering computationally demanding features. The envisaged mobile application features can be considered to be accelerated by a set of underpinning hardware blocks Based on the survey that this thesis presents on modem video compression standards and their associated enabling technologies, it is concluded that tight energy and throughput constraints can still be effectively tackled at algorithmic level in order to design re-usable optimised hardware acceleration cores. To prove these conclusions, the work m this thesis is focused on two of the basic enabling technologies that support mobile video applications, namely the Shape Adaptive Discrete Cosine Transform (SA-DCT) and its inverse, the SA-IDCT. The hardware architectures presented in this work have been designed with energy efficiency in mind. This goal is achieved by employing high level techniques such as redundant computation elimination, parallelism and low switching computation structures. Both architectures compare favourably against the relevant pnor art in the literature. The SA-DCT/IDCT technologies are instances of a more general computation - namely, both are Constant Matrix Multiplication (CMM) operations. Thus, this thesis also proposes an algorithm for the efficient hardware design of any general CMM-based enabling technology. The proposed algorithm leverages the effective solution search capability of genetic programming. A bonus feature of the proposed modelling approach is that it is further amenable to hardware acceleration. Another bonus feature is an early exit mechanism that achieves large search space reductions .Results show an improvement on state of the art algorithms with future potential for even greater savings.