Algorithm for cosine transform of Toeplitz matrices

An algorithm for calculating the 2D cosine transform of a Toeplitz matrix is presented. The algorithm is based on the application of 1D cosine transforms. More specifically, four 1D cosine transforms of size N are needed to obtain the transform of a Toeplitz matrix of size N×N. This is an improvement over previously published algorithms. The algorithm is also simple and regular     

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     

Fast discrete cosine transform algorithm for systolic arrays

A fast algorithm for an N-point discrete cosine transform (DCT) is derived from a 4N-point Winograd Fourier transform algorithm (WFTA). This algorithm, which has the same form as Winograd's Fourier transform and convolution algorithms, is suitable for a high-speed implementation using one-bit systolic arrays.     

Algorithm for wavelet transform of Toeplitz matrices

An algorithm is presented for calculating the 2D wavelet transform of a Toeplitz matrix. The algorithm exploits the special form of the Toeplitz matrix in order to reduce the number of operations required. More specifically. It is shown that the number of 1D wavelet transformations that are necessary to carry out a sub-band decomposition can be reduced to eight     

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 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.     

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     

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.     

Fast recursive algorithms for short-time discrete cosine transform

Local adaptive signal processing can be carried out using the short-time discrete cosine transform (DCT). Two fast recursive algorithms for computing the short-time DCT are presented. The algorithms are based on a recursive relationship between three subsequent local DCT spectra. The computational complexity of the algorithms is compared with that of fast DCT algorithms     

A new two-dimensional fast cosine transform algorithm

The discrete cosine transform (2-D DCT) is based on a one-dimensional fast cosine transform (1-D FCT) algorithm. Instead of computing the 2-D transform using the row-column method, the 1-D algorithm is extended by means of the vector-radix approach. Derivation based on both the sequence splitting and Kronecker matrix product method are discussed. The sequence splitting approach has the advantage that all the underlying operations are shown clearly, while the matrix product representations are more compact and readily generalized to higher dimensions. The bit reversal operations are placed before the recursive additions so that the recursive operations can be performed in a very regular manner. This greatly simplifies the indexing problem in the software implementation of the algorithms. The vector-radix algorithm saves 25% multiplications as compared with the row-column method     

Fast Hartley transform algorithm

The discrete Hartley transform is a new tool for the analysis, design and implementation of digital signal processing algorithms and systems. It is strictly symmetrical concerning the transformation and its inverse. A new fast Hartley transform algorithm has been developed. Applied to real signals, it is faster than a real fast Fourier transform, especially in the case of the inverse transformation. The speed of operation for a fast convolution can thus be increased.     

An algorithm for calculation of the discrete cosine transform by paired transform

A new algorithm for splitting the one-dimensional (1-D) 2/sup r/-point discrete cosine transform (DCT) into a set of short 2/sup k/-point type-IV DCTs [k=1:(r-1)] is introduced. The splitting is performed by means of paired transformation that is defined by the paired representation of signals with respect to the cosine transform. A proposed method of calculating the 2/sup r/-point cosine transform requires 2/sup r-1/r multiplications and 2/sup r-1/(3r-2)+1 additions when r/spl ges/2.     

NEW FAST ALGORITHM OF 2-D DISCRETE COSINE TRANSFORM

In this paper, a new algorithm for the fast computation of a 2-D discrete cosine transform (DCT) is presented. It is shown that the N×N DCT, where N = 2m, can be computed using only N 1-D DCT's and additions, instead of using 2N 1-D DCT's as in the conventional row-column approach. Hence the total number of multiplications for the proposed algorithm is only half of that required for the row-column approach, and is also less than that of most of other fast algorithms, while the number of additions is almost comparable to that of others.     

Fast Hankel transform by fast sine and cosine transforms: theMellin connection

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure that does not require exponential sampling is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into a sine, a cosine, and an inversion transform, which can be implemented by means of fast sine and cosine transforms     

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     

基于小波变换和离散余弦变换的fisher脸识别

本文结合几种现有的人脸识别特征提取算法,先对人脸图像进行小波分解去噪;然后通过离散余弦变换对低频分量作进一步特征提取和压缩,保留人脸图像中对光照、姿态、表情变化不敏感的识别信息;接着利用PCA和LDA相结合得到最终的识别特征;最后采用欧式距离和最近邻分类器识别人脸。实验采用ORL标准人脸库验证了这种组合的有效性。     

Fast odd-factor algorithm for discrete W transform

The authors present an odd-factor algorithm for type-II discrete W transforms (DWTs). They show that for N=p*q, where q is an odd integer, the length-N DWT can be decomposed into p length-q type-III DCTs and q length-p type-II DWTs. This is particularly useful for the computation of DWTs of arbitrarily composite length. A reduction in computational complexity is also achieved compared to other existing fast algorithms     

Fast interpolation algorithm using fast Hartley transform

The use of fast Hartley transform for fast discrete interpolation is considered. The computational method uses the sprit-radix algorithm which requires the least number of operations compared with other Hartley algorithms. Results from this method are compared with those using the fast Fourier transform.     

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     

Fast dual-MGS block-factorization algorithm for dense MoM matrices

A robust method is introduced for efficiently compressing dense method of moments (MoM) matrices using a dual modified Gram-Schmidt block-QR-factorization algorithm based on low-rank singular value decomposition. The compression is achieved without generating the full matrix or even full subblocks of the matrix. The compressed matrix may then be used in the iterative solution of the MoM problem. The method is very robust because it uses a reduced set of the original matrix entries to perform the compression. Furthermore, it does not depend on the analytic form of the Green's function, so it may be applied to arbitrarily complex media.