Design of high-performance fixed-point transforms using the common factor method
Arianne T. Hinds · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
Fixed-point implementations of transforms such as the Discrete Cosine Transform (DCT) remain as fundamental building blocks of state-of-the-art video coding technologies. Recently, the 16x16 DCT has received focus as a transform suitable for the high efficiency video coding project currently underway in the Joint Collaboration Team - Video Coding. By its definition, the 16x16 DCT is inherently more complex than transforms of traditional sizes such as 4x4 or 8x8 DCTs. However, scaled architectures such as the one employed in the design of the 8x8 DCTs specified in ISO/IEC 23002-2 can also be utilized to mitigate the complexity of fixed-point approximations of higher-order transforms such as the 16x16 DCT. This paper demonstrates the application of the Common Factor method to design two scaled implementations of the 16x16 DCT. One implementation can be characterized by its exceptionally low complexity, while the other can be characterized by its relatively high precision. We review the Common Factor method as a method to arrive at fixed-point implementations that are optimized in terms of complexity and precision for such high performance transforms.