VLSI Computational Architectures for the Arithmetic Cosine Transform

• Published in: IEEE transactions on computers Vol. 64; no. 9; pp. 2708 - 2715
• Main Authors: Rajapaksha, Nilanka, Madanayake, Arjuna, Cintra, Renato J., Adikari, Jithra, Dimitrov, Vassil S.
• Format: Journal Article
• Language: English
• Published: IEEE 01.09.2015
• Subjects: Arithmetic cosine transform; Complexity theory; Computer architecture; Discrete cosine transform; Discrete cosine transforms; fast algorithms; Hardware; Signal processing algorithms; Vectors; VLSI; fast algorithms; VLSI; arithmetic cosine transform; Discrete cosine transform
• ISSN: 0018-9340
• DOI: 10.1109/TC.2014.2366732

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier intensive, and accumulate round-off errors. Recently proposed fast algorithm arithmetic cosine transform (ACT) calculates the DCT exactly using only additions and integer constant multiplications, with very low area complexity, for null mean input sequences. The ACT can also be computed non-exactly for any input sequence, with low area complexity and low power consumption, utilizing the novel architecture described. However, as a trade-off, the ACT algorithm requires 10 non-uniformly sampled data points to calculate the eight-point DCT. This requirement can easily be satisfied for applications dealing with spatial signals such as image sensors and biomedical sensor arrays, by placing sensor elements in a non-uniform grid. In this work, a hardware architecture for the computation of the null mean ACT is proposed, followed by a novel architectures that extend the ACT for non-null mean signals. All circuits are physically implemented and tested using the Xilinx XC6VLX240T FPGA device and synthesized for 45 nm TSMC standard-cell library for performance assessment.