Efficient, low complexity 8-point discrete tchebichef transform approximation for signal processing applications

Abstract

The Discrete Tchebichef Transform (DTT) is widely used in signal processing applications such as image and video compression and digital watermarking due to its coding and decorrelation properties. In embedded systems and real-time applications, the need for fast, low complexity, and energy efficient algorithms is increasingly important. However, there is a limited number of such algorithms available for efficient computation of the DTT compared to the discrete cosine transform. To address this issue, a new DTT approximation is proposed, which provides a low-complexity and efficient solution by exploiting the deviation from orthogonality. The suggested algorithm requires fewer additions and bit-shifting operations compared to the existing ones. The implementation of this DTT approximation on the Xilinx Virtex-6 XC6VSX475T-1FF1759-2 FPGA resulted in a 19.20% decrease in hardware resources and 2% reduction in energy consumption for 1-D 8 inputs compared to the best candidate DTT approximation. With a low deviation from orthogonality, the efficiency of the proposed approximation has been confirmed in image compression and digital watermarking. The experimental results show an average quality improvement of 0.25 dB over the latest DTT approximation.