Low-complexity Scaling Methods for DCT-II Approximations
This work addresses the need for low-complexity DCT approximations in signal processing applications, offering incremental improvements over prior methods.
The paper tackled the problem of generating efficient 2N-point DCT-II approximations by introducing new scaling methods based on Hou recursive matrix factorization, which outperform the existing JAM method in total error energy and mean squared error, as demonstrated through error analysis and hardware implementation.
This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.