A 100-MHz 2-D discrete cosine transform core processor

A 100-MHz two-dimensional discrete cosine transform (DCT) core processor applicable to the real-time processing of HDTV signals is described. An excellent architecture utilizing a fast DCT algorithm and multiplier accumulators based on distributed arithmetic have contributed to reducing the hardware amount and to enhancing the speed performance. A layout scheme with a column-interleaved memory and a new ROM circuit are introduced for the efficient implementation of memory-based signal processing circuits. Furthermore, mean values of errors generated in the core were minimized to enhance the computational accuracy with the word-length constraints. Consequently, it features the fastest operating speed and the smallest area with sufficient accuracy to satisfy the specifications in CCITT recommendation H.261. The core integrates about 102 K transistors and occupies 21 mm² using 0.8-μm double-metal CMOS technology     

DCT/IDCT processor for HDTV developed with dsp silicon compiler

This article presents a discrete cosine transform (DCT) processor for high definition television (HDTV) by using an extended version of DSP Silicon Compiler. The extension is mainly concerned with module generation functions. A matrix-vector product module composed of multiply-accumulators (MACs) is newly added to the silicon compiler. The compiler accomplishes placement of leaf-cells and routing between the cells, referring to a prototype layout for the MAC. The prototype, which consists of a Booth multiplier and a carry look ahead adder, is carefully designed to attain high operation speed. The processor developed by the silicon compiler carries out 8×8 DCT and its inverse transform (IDCT). In order to evaluate the newly extended functions in the compiler, the architecture employed for the processor is based on the matrix-vector product method. By using DSP Silicon Compiler and 0.8 µm triple metal CMOS technology, the DCT processor is easily implemented with error-free environment and achieves a 50MHz data rate, which meets Japanese HDTV base line signal processing. The chip is implemented on a 12.80×12.57mm ² area.     

Mixed-radix discrete cosine transform

Presents two new fast discrete cosine transform computation algorithms: a radix-3 and a radix-6 algorithm. These two new algorithms are superior to the conventional radix-3 algorithm as they (i) require less computational complexity in terms of the number of multiplications per point, (ii) provide a wider choice of the sequence length for which the DCT can be realized and, (iii) support the prime factor-decomposed computation algorithm to realize the 2^m3ⁿ-point DCT. Furthermore, a mixed-radix algorithm is also proposed such that an optimal performance can be achieved by applying the proposed radix-3 and radix-6 and the well-developed radix-2 decomposition techniques in a proper sequence     

基于矩的快速离散余弦变换处理机的设计及实现

阐述了基于矩的离散余弦变换算法和易于ＶＬＳＩ实现的脉动阵列算法结构,然后从软硬件结构划分、电路实现技术等方面探讨离散余弦变换处理机系统的设计思路。最后给出用矩实现的计算框图、电路实现框图以及外围驱动软件的结构设计。     

The fractional discrete cosine transform

The extension of the Fourier transform operator to a fractional power has received much attention in signal theory and is finding attractive applications. The paper introduces and develops the fractional discrete cosine transform (DCT) on the same lines, discussing multiplicity and computational aspects. Similarities and differences with respect to the fractional Fourier transform are pointed out     

Block-diagonal structure of Walsh-Hadamard/discrete cosine transform

The A-matrix, the conversion matrix for Walsh-Hadamard/discrete cosine transform, is known for its efficient block-diagonal structure. This associates with the even/odd structure of the transform kernels. In the letter we present a direct matrix derivation by using the intrinsic properties of the discrete cosine transform and the Walsh-Hadamard transform.     

Computationally efficient discrete cosine transform algorithm

An algorithm is developed for evaluating the discrete cosine transform using DFT and polynomial transforms. It is shown to be computationally more efficient than existing algorithms.     

On the discrete cosine transform computation

A generalized signal flow graph for the forward and inverse discrete cosine transform (DCT) based on the Hou's recursive algorithm is described. The regular structure of the generalized signal flow graph enables to realize the DCT and inverse DCT computation for any given N = 2^m, m > 0, and is effectively implementable on a VLSI chip. Computer program for the DCT and inverse DCT computation is also presented.     

Pruning the fast discrete cosine transform

The matrix representation of the simple structured algorithm for the discrete cosine transform (DCT), which was first introduced by Y. Morikawa et al. (1985) based on the successive order reduction of the Tchebycheff polynomial, and retrieved by a simpler approach by Z. Wang (1988), is reviewed. A fast pruning algorithm for the DCT is then developed     

Fast odd discrete cosine transform algorithms

It is shown that an N point type I odd discrete cosine transform can be reformulated as a (2N-1) point DFT of a real-symmetric sequence efficiently computed by the real-symmetric PFA-FFT. Using simple index mappings, the type II and III ODCTs are efficiently computed from the ODCT-1 of the same length. The ODCT-IV are then computed from ODCT-II or III using simple recurrence formulas.<>     

Fast algorithms for the discrete cosine transform

Several fast algorithms for computing discrete cosine transforms (DCTs) and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced. Because the 1-D 8-point DCT and the 2-D 8×8-point DCT are so widely used, they are discussed in detail. Algorithms for computing scaled DCTs and their inverses are also presented. These have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization     

A derivation for the discrete cosine transform

The purpose of this letter is to derive the discrete cosine transform (DCT) as a limiting case of the Karhunen-Loève transform (KLT) of a first-order Markov process, as the correlation coefficient approaches 1.     

Concurrent computation of two-dimensional discrete cosine transform

In this paper, a novel VLSI algorithm for the computation of a two-dimensional discrete cosine transform is proposed. The 2D-DCT equation can be expressed by the sum of high order cosine functions, and the algorithm can be realized by combining a highly efficient first order recursive structure with some simplified matrix multiplications, which results in highly regular hardware architecture and simple routing. The algorithm has temporal and spatial locality of connection and can be segmentized for pipeline operations, so the computation time is greatly reduced. Owing to the simplicity in hardware structure, it is especially good for VLSI implementation.     

Fast algorithm for computing discrete cosine transform

An efficient method for computing the discrete cosine transform (DCT) is proposed. Based on direct decomposition of the DCT, the recursive properties of the DCT for an even length input sequence is derived, which is a generalization of the radix 2 DCT algorithm. Based on the recursive property, a new DCT algorithm for an even length sequence is obtained. The proposed algorithm is very structural and requires fewer computations when compared with others. The regular structure of the proposed algorithm is suitable for fast parallel algorithm and VLSI implementation     

Simple systolic arrays for discrete cosine transform

in this paper, simple 1-D and 2-D systolic array for realizing the discrete cosine transform (DCT) based on the discrete Fourier transform (DFT) fo an input sequence are presented. The proposed arrays are obtained by a simple modified DFT (MDFT) and an inverse DFT (IDFT) version of the Goertzel algorithm combined with Kung's approach. The 1-D array requiresN cells, one multiplier and takesN clock cycles to produce a completeN-point DCT. The 2-D array takes N clock cycles, faster than the 1-D array, but the area complexity is larger. A continuous flow of input data is allowed and no idle time is required between the input sequences.     

Fast computation of discrete cosine transform through fast Hartley transform

A relationship between the discrete cosine transform (DCT) and the discrete Hartley transform (DHT) is derived. It leads to a new fast and numerically stable algorithm for the DCT.     

Relationship between two algorithms for discrete cosine transform

Two contributions are made to the implementation of fast discrete cosine transform algorithms. The first uses Hadamard ordering to improve the regularity of the Lee fast cosine transform (FCT) algorithm for the discrete cosine transform (DCT). The second derives a close relationship between the Lee FCT and the recursive algorithm for the DCT.<>     

Variable temporal-length 3-D discrete cosine transform coding

Three-dimensional discrete cosine transform (3-D DCT) coding has the advantage of reducing the interframe redundancy among a number of consecutive frames, while the motion compensation technique can only reduce the redundancy of at most two frames. However, the performance of the 3-D DCT coding will be degraded for complex scenes with a greater amount of motion. This paper presents a 3-D DCT coding with a variable temporal length that is determined by the scene change detector. Our idea is to let the motion activity in each block be very low, while the efficiency of the 3-D DCT coding could be increased. Experimental results show that this technique is indeed very efficient. The present approach has substantial improvement over the conventional fixed-length 3-D DCT coding and is also better than that of the Moving Picture Expert Group (MPEG) coding.     

Normal bases expansion of the discrete cosine transform

In this correspondence, we show that the discrete cosine transform (DCT) can be obtained by projecting the discrete Fourier transform from the extension field to the basefield. Applying the framework of projection operator, a fast fully recursive algorithm for computing the DCT is also presented     

DGT与DCT在图像编码中的性能比较

介绍了二维实值离散Gabor变换（RDGT）的快速算法,并着重探讨了二维实值离散Gabor变换与二维离散余弦变换在图像编码中的性能及差异。