The paper presents the architecture and realization of a cost-effective FPGA realization of a Two-Dimensional Discrete Cosine Transform (2D DCT) for JPEG image compression. The architecture utilizes row-column decomposition of a fast 1D DCT algorithm implemented with distributed arithmetic. The work also used efficient multiplier architecture based on Urdhva-Tiryagbhyam sutra of ancient Indian Vedic mathematics. The paper explores the algorithmic evaluations, architectural design and development of Verilog models, verification methods, synthesis operations and timing analysis. This cost-effective design is optimized at different levels of abstraction, i.e., algorithm, architecture and gate levels. The design uses 1952 logic cells of one Vertex IV family FPGA and reaches an operating frequency of 85.12 MHz with the pipeline latency of 96 clock cycles.

Since multimedia applications on portable and low-power devices have become more prominent, the need for efficient, low-power image encoding and decoding techniques increases. The Discrete Cosine Transform (DCT) and the Inverse Discrete Cosine Transform (IDCT) form the transform pair in the JPEG, MPEG, H.261 and H.263 image and video compression standards. Its widespread use can be attributed to the energy compaction quality of the transform. DCT transformation of a natural image from the spatial to the frequency domain results in concentration of energy in low- order frequency coefficients. Other applications of the DCT include DCT domain algorithms such as translation, downscaling, filtering, masking and blue screen editing. Image enhancements such as brightness adjustment and detail enhancement also become more efficient in the DCT domain (Lee et al., 1997).

The JPEG image compression standard (Bhaskaran and Konstantinides, 1999; and Rana et al., 2011) was developed by Joint Photographic Expert Group (Amiri et al., 2007). The JPEG compression principle is the use of controllable losses to reach high compression rates. In this context, the information is transformed to the frequency domain through DCT. Since neighbor pixels in an image have high likelihood of showing small variations in color, the DCT output will group the higher amplitudes in the lower spatial frequencies (Pennebaker and Mitchell, 1992). Then, the higher spatial frequencies can be discarded, generating a high compression rate and a small perceptible loss in the image quality. The JPEG compression is recommended for photographic images, since drawing images are richer in high frequency areas that are distorted with the application of the JPEG compression (www.jpeg.org). The JPEG compression can be divided into five main stages: color space conversion, downsampling, 2D DCT, quantization and entropy coding, as shown in Figure 1. The first two operations are used only for color images.

Telecommunications Journal, Two-Dimensional Discrete Cosine Transform (2D DCT), Latency, FPGA.