A refined fast 2-D discrete cosine transform algorithm

IEEE Transactions on Consumer Electronics, 1998

In this paper, a fast computation algorithm for the two-dimensional discrete cosine transform (2-D DCT) is derived based on index permutation. As a result, only the computation of N Npoint l-D DCT's and some postadditions are required for the computation of an (?JxN)-point 2-D DCT. Furthermore, as compared with [7], the derivation of the refined algorithm is more succinct, and the associated postaddition stage possesses a more regular butterfly structure. The regular structure of the proposed algorithm makes it more suitable for VLSI and parallel implementations.

IEEE Transactions on Signal Processing, 2000

A new fast algorithm for the type-II two-dimensional (2-D) discrete cosine transform (DCT) is presented. It shows that the 2-D DCT can be decomposed into cosine-cosine, cosine-sine, sine-cosine, and sine-sine sequences that can be further decomposed into a number of similar sequences. Compared with other reported algorithms, the proposed one achieves savings on the number of arithmetic operations and has a recursive computational structure that leads to a simplification of the input/output indexing process. Furthermore, the new algorithm supports transform sizes (1 2) (2 2), where 1 and 2 are arbitrarily odd integers, which provides a wider range of choices on transform sizes for various applications.

1994

Abstract The implementation of the two-dimensional discrete cosine transform (2D DCT) through the multiple onedimensional (row-by-column approach) and the direct 2D DCT is studied. It is observed that the execution times on different computer architectures using one-dimensional (1D) algorithms vary significantly although some of the examined algorithms have the same computational complexity (additions and multiplications). The direct 2D DCT outperforms all row-by-column approaches.

IEEE Transactions on Computers, 1980

An alternate algorithm to compute the discrete cosine transform (DCT) of sequences of arbitrary number of points is proposed. The algorithm consists of partitioning the DCT kernel into submatrices which by proper row and column shuffling and negations can be made equivalent to the group tables (or parts of them) of appropriate Abelian groups. The computations pertaining to the submatrices can be carried out using multidimensional cyclic convolutions. Algorithms are also developed to perform the computations associated with the submatrices that are parts of larger group tables. The new algorithms are more versatile and generally better in terms of the computational complexity in comparison with the existing algorithms.

Proc. the VII European Signal Processing Conf, 2007

Two pruning algorithms for the Vector-Radix Fast Cosine Transform are presented. Both are based on an in-place approach of the direct two-dimensional fast cosine transform (2D FCT). The first pruning algorithm concerns the computation of N 0 xN 0 out of NxN DCT points, where both N 0 and N are powers of 2. The second pruning algorithm is more general and concerns a recursive approach for the computation of any number of points of arbitrary shaped regions. A comparison with the row-column pruning method reveals that the proposed algorithms are more efficient in terms of total computational complexity, i.e. multiplications, additions and data transfers.

Electronics

Discrete cosine transforms (DCTs) are widely used in intelligent electronic systems for data storage, processing, and transmission. The popularity of using these transformations, on the one hand, is explained by their unique properties and, on the other hand, by the availability of fast algorithms that minimize the computational and hardware complexity of their implementation. The type-I DCT has so far been perhaps the least popular, and there have been practically no publications on fast algorithms for its implementation. However, at present the situation has changed; therefore, the development of effective methods for implementing this type of DCT becomes an urgent task. This article proposes several algorithmic solutions for implementing type-I DCTs. A set of type-I DCT algorithms for small lengths N=2,3,4,5,6,7,8 is presented. The effectiveness of the proposed solutions is due to the possibility of fortunate factorization of the small-size DCT-I matrices, which reduces the compl...

Circuits and Systems, 2016

Discrete cosine transform (DCT) is frequently used in image and video signal processing due to its high energy compaction property. Humans are able to perceive and identify the information from slightly erroneous images. It is enough to produce approximate outputs rather than absolute outputs which in turn reduce the circuit complexity. Numbers of applications like image and video processing need higher dimensional DCT algorithms. So the existing architectures of one dimensional (1D) approximate DCTs are reviewed and extended to two dimensional (2D) approximate DCTs. Approximate 2D multiplier-free DCT architectures are coded in Verilog, simulated in Modelsim to evaluate the correctness, synthesized to evaluate the performance and implemented in virtexE Field Programmable Gate Array (FPGA) kit. A comparative analysis of approximate 2D DCT architectures is carried out in terms of speed and area.

In this paper, the implementation of a unified 8 × 8 discrete cosine transform (DCT) and its inverse is described. First, the accuracy of the structure that has been reported earlier is analyzed with Matlab in order to have internal word length requirements for the implementation. Then, the structure is modeled as a data path structure with Synopsys Module Compiler. When synthesizing the model with 19-bit internal word length onto 0.11 µm CMOS technology, the resulting pipeline exhibits an operation frequency of 253 MHz and uses 40 000 equivalent gates. The latency for both trans- forms is 94 cycles. Finally, the comparison to another unified pipeline structure reveals up to 15% smaller estimated area.

IEEE Transactions on Signal Processing, 2000

Modification to the architecture-oriented fast algorithm for discrete cosine transform of type II from Astola and Akopian is presented, which results in a constant geometry algorithm with simplified parameterized node structure. Although the proposed algorithm does not reach the theoretical lower bound for the number of multiplications, the algorithm possesses the regular structure of the Cooley-Tukey FFT algorithms. Therefore, the FFT implementation principles can also be applied to the discrete cosine transform.

International Conference on Acoustics, Speech, and Signal Processing,

A new class of practical fast algorithms is introduced for the Discrete Cosine 'nunsfom (DCT), a n important transform that is of particular interest i n image compression. For a n 8-point DCT only 11 multiplications and 29 additions are required. A systematic approach is presented to generate t h e different members in this class all having the same mini m u m arithmetic complexity. T h e structure of many of t h e published algorithms can be found in members of this class. An extension of t h e algorithm for longer transformations is presented. As a result, the 16-point DCT requires only SI multiplications a n d 81 additions, which is, to our knowledge, less t h a n t h e currently published algorithms.