One-dimensional Discrete Cosine Transform Research Articles

A fast algorithm for computing multidimensional dct on certain small sizes

This paper presents a new algorithm for the fast computation of multidimensional (m-D) discrete cosine transform (DCT) with size N/sub 1//spl times/N/sub 2//spl times//spl middot//spl middot//spl middot//spl times/N/sub m/, where N/sub i/ is a power of 2 and N/sub i//spl les/256, by using the tensor product decomposition of the transform matrix. It is shown that the m-D DCT or inverse discrete cosine transform (IDCT) on these small sizes can be computed using only one-dimensional (1-D) DCTs and additions and shifts. If all the dimensional sizes are the same, the total number of multiplications required for the algorithm is only 1/m times of that required for the conventional row-column method. We also introduce approaches for computing scaled DCTs in which the number of multiplications is considerably reduced.

Architectural Synthesis of Digital Signal Processing Algorithms Using IRIS

In this paper, we present the IRIS architectural synthesis system for high-performance digital signal processing. This tool allows non-specialists to automatically derive VLSI circuit architectures from high-level, algorithmic representations, and provides a quick route to silicon implementation. By incorporating a novel synthesis methodology, called the Modular Design Procedure, within the IRIS system, parameterised models of complex and innovative DSP hardware can be derived and automatically assembled to create new DSP systems. The nature of this synthesis methodology is such that designers can explore a large range of architectural alternatives, whilst considering all the architectural implications of using specific hardware to realise the circuit. The applicability of IRIS is demonstrated using the design examples of a second order Infinite Impulse Response filter and a one-dimensional Discrete Cosine Transform circuit.

A Fast 8 × 8 Pruned DCT Algorithm

El-Sharkawy, M., and Eshmawy, W., A Fast 8 × 8 Pruned DCT Algorithm,Digital Signal Processing6 (1996), 145–154.A new algorithm that computes the 8 × 8 pruned Discrete Cosine Transform (DCT) using the vector–radix approach is introduced. The vector–radix approach decomposes the 8 × 8 pruned DCT into four 4 × 4 pruned DCTs. The 4 × 4 pruned DCT is then decomposed into four one-dimensional pruned DCTs. The number of points that need to be calculated from each one-dimensional DCT depends on the allowed amount of pruning. The proposed algorithm does not require any bit reversal operations. To illustrate the usefulness of the proposed pruned DCT algorithm, we utilize it to compress images using a Joint Photographic Experts Group (JPEG) algorithm. The proposed 8 × 8 pruned DCT algorithm improves the compression ratio and reduces both the complexity and execution time of the modified JPEG algorithm.

Discrete Cosine Transform Coding for TV Signal

An efficient encoding technique using discrete cosine transform (DCT) for bandwidth compression is described. Real-time one-dimensional DCT has been developed by maintaining a balance between complexity of implementation and performance. Excellent performance is demonstrated in terms of subjective quality.