Twodimensional orthogonal DCT expansion in triangular and trapezoid regions It is known that the 2D DCT basis is complete and orthogonal in a rectangular region. In this paper, we introduce the way to generate the complete and orthogonal 2D DCT basis in a trapezoid region or a triangular region without using the complicated GramSchmidt method. Moreover, since a polygon can be decomposed several triangular regions, the proposed method is also suitable for the polygonal region. Our algorithm can much generalize the JPEG algorithm. Instead of dividing an image into 8 by 8 blocks, we can divide an image into trapezoid or triangular regions and then transform and code each of them. In addition to the DCT basis, our method can also be used for generating the 2D complete and orthogonal DFT basis, KLT basis, Legendre basis, Hadamard (Walsh) basis, and polynomial basis in the trapezoid and triangular regions.

A New Hardware Friendly 2DDCT HEVC Compliant Algorithm and its High Throughput and Low Power Hardware Design This paper presents a hardwarefriendly algorithm to maximize the throughput of the Discrete Cosine Transform (DCT) of the High Efficiency Video Coding (HEVC), together with its hardware design. The Fast DCT (FCT) algorithm is based on the CooleyTuckey algorithm for the Fast Fourier Transform (FFT) with pre and postprocessing required to maintain the compliance with the HEVC. The resulting algorithm allows high throughput while maintaining low power dissipation. The designed hardware was synthesized for a 45nm Nangate technology and it reaches a throughput of 81.28GSamples per second when consuming 12.33mW. Such energy efficiency and throughput surpass all related works in the literature.