Showing papers on "Modified discrete cosine transform published in 1990"

Discrete Cosine Transform: Algorithms, Advantages, Applications

Abstract: Discrete Cosine Transform. Definitions and General Properties. DCT and Its Relations to the Karhunen-Loeve Transform. Fast Algorithms for DCT-II. Two Dimensional DCT Algorithms. Performance of the DCT. Applications of the DCT. Appendices. References. Index.

Low bit rate transform coder, decoder and encoder/decoder for high-quality audio

Abstract: A low bit-rate (192 kBits per second) transform encoder/decoder system (44.1 kHz or 48 kHz sampling rate) for high-quality music applications employs short time-domain sample blocks (128 samples/block) so that the system signal propagation delay is short enough for real-time aural feedback to a human operator. Carefully designed pairs of analysis/synthesis windows are used to achieve sufficient transform frequency selectivity despite the use of short sample blocks. A synthesis window in the decoder has characteristics such that the product of its response and that of an analysis window in the encoder produces a composite response which sums to unity for two adjacent overlapped sample blocks. Adjacent time-domain signal samples blocks are overlapped and added to cancel the effects of the analysis and synthesis windows. A technique is provided for deriving suitable analysis/synthesis window pairs. In the encoder, a discrete transform having a function equivalent to the alternate application of a modified Discrete Cosine Transform and a modified Discrete Sine Transform according to the Time Domain Aliasing Cancellation technique or, alternatively, a Discrete Fourier Transform is used to generate frequency-domain transform coefficients. The transform coefficients are nonuniformly quantized by assigning a fixed number of bits and a variable number of bits determined adaptively based on psychoacoustic masking. A technique is described for assigning the fixed bit and adaptive bit allocations. The transmission of side information regarding adaptively allocated bits is not required. Error codes and protected data may be scattered throughout formatted frame outputs from the encoder in order to reduce sensitivity to noise bursts.

Discrete cosine transform processing system

Abstract: A three dimensional (3D) discrete cosine transform (DCT) uses one dimensional DCT networks for transforming and inverse-transforming blocks of data, such as image data. The 3D DCT configuration uses DCT transform coding to remove both the spatial and temporal redundancy of a sequence of image frames to achieve high bandwidth compression.

The ISO audio coding standard

Abstract: An ISO audio coding standard is being developed that will provide an audio quality comparable to that of a compact disc using a reduced bit rate of about 2*128 kb/s for a stereo sound signal instead of 2*706 kb/s. Four coding algorithms have been considered in order to develop the audio coding standard. Two of these coding algorithms have been tested and are outlined. The ASPEC algorithm uses a modified discrete cosine transform with overlapping blocks and dynamic windowing in order to map the input samples into frequency coefficients. The MUSICAM algorithm uses a subband analysis filter bank with 32 equally spaced subbands to map the input samples into frequency coefficients. Concepts for improvement of the coding algorithms are discussed which might be the basis for future ISO activities aiming at a bit rate of only 2*64 kb/s for a stereo sound signal. >

Interpolation using type I discrete cosine transform

Abstract: A novel interpolation method, using the type I discrete cosine transform (DCT-I), is introduced. The original definition of the DCT-I has been modified to suit this application. Three options for the modified DCT-I are proposed.

On computing 2-D systolic algorithm for discrete cosine transform

Abstract: A 2-D systolic array algorithm for the discrete cosine transform (DCT) is presented. It is based on the inverse discrete Fourier transform (DFT) version of the Goertzel algorithm via Horner's rule. This array requires N cells and multipliers, takes square root N+2 clock cycles to produce a complete N-point DCT, and is able to process a continuous stream of data sequences. >

A DCT chip based on a new structured and computationally efficient DCT algorithm

Abstract: A discrete cosine transform (DCT) algorithm and architecture that minimize both software and hardware costs are presented. The proposed approaches are either direct or indirect and are based on the decomposition of the DCT in three operations: permutation, fast Fourier transform, and rotation. The main characteristics of the VLSI implementation chosen for this DCT and inverse DCT algorithm are show. Its data path coupled with a twin-pages memory and its controller, which contains the microprograms of the DCT algorithm are described. The results in terms of data processing rate and silicon area are given. >

Fast cosine transform based on the successive doubling method

Abstract: An efficient and regular algorithm for computing the fast cosine transform (FCT) using the method of successive doubling is presented. The FCT is obtained by the composition of two elementary transforms. Its high regularity facilitates its implementation in VLSI technology.

Algorithm for prime length discrete cosine transforms

Abstract: A new algorithm is introduced such that we can realise a discrete cosine transform by correlations. This algorithm can be applied to any odd prime length DCT and is most suitable for VLSI implementation.

On asymmetrical performance of discrete cosine transform

Abstract: The discrete cosine transform (DCT) is considered as a suboptimum transform for many practical source-coding applications. Autoregressive order 1 (AR(1)) source models are good first approximations to several natural signals. It is known that the performance of the DCT depends on the sign of the autocorrelation coefficient of the AR(1) source. The authors explain theoretically this asymmetrical performance of the DCT as well as the behavior of the modified Hermite transform (MHT) and the discrete Hadamard transform (DHT), which perform symmetrically regardless of the sign of the autocorrelation coefficient. >

On compatibility of order-8 integer cosine transforms and the discrete cosine transform

Abstract: The author shows that integer cosine transforms (ICTs) are functionally compatible with discrete cosine transforms (DCTs) that are used in image coding. It is provided that the w-bit ICT can inversely transform exactly represented DCT coefficients with less mean-square-error than the w-bit DCT for w equal to 4, 3 and 2 and scaling factors of ICTs implemented using 8 bits. Conversely, an exactly represented DCT can inversely transform the coefficients from the w-bit ICT with less mean-square-error than the w-bit DCT. Therefore, the ICTs can be said to be compatible with the DCT. These ICTs, while being considered as new transforms, can also be regarded as alternative and better ways to implement the DCT when the number of bits for representing kernel components are restricted to 4, 3, and 2. >

Simple systolic arrays for discrete cosine transform

Abstract: 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.

A new convolution structure for the realisation of the discrete cosine transform

Abstract: A formulation for converting a length-N, where N=2/sup m/ and m is an integer, discrete cosine transform into two length-N/2 correlations is presented. This formulation enables the authors to realize the discrete cosine transform with a reduced number of operations compared to conventional approaches, and it also results in extremely regular structure, which is most suitable for a realization using distributed arithmetic. >

Transform coding algorithms for seismic data compression

Abstract: An investigation is presented of transform-based seismic data compression. The study concentrates on discrete orthogonal transforms such as the discrete Fourier transform (DFT), the discrete cosine transform (DCT), the Walsh-Hadamard transform (WHT), and the Karhunen-Loeve transform (KLT). Uniform and subband transform coding schemes were implemented, and comparative results are given for data rates ranging from 150 to 550 b/s. These results are also compared to existing linear prediction techniques. >

An algorithm for a fast two-dimensional discrete cosine transform

Abstract: The authors present an algorithm for the implementation of the two-dimensional discrete cosine transform (DCT) for 2/sup n/*2/sup n/ data points. This algorithm is based on a recently published fast one-dimensional DCT algorithm. The new algorithm is recursive, fast, and numerically stable. The two-dimensional decomposition in this new algorithm is based on the vector-radix approach. In this approach, the data matrix is partitioned into four subblocks, each of which, after some processing is transformed by a lower order DCT. The results from the lower order transforms are then combined to form the desired two-dimensional DCT. The overall complexity of the new transform is compared in terms of the number of multiplications and additions required to perform the two-dimensional DCT with those of a row/column implementation using the fast one-dimensional transform. >

Electrocardiogram compression using lapped orthogonal transform

Abstract: The results of a study to examine the feasibility of electrocardiogram (ECG) data compression using the lapped orthogonal transform (LOT) are presented. The blocking effects in the reconstructed signal are shown to be reduced, while the bit rate and the performance of the proposed scheme remain the same, as compared with the traditional discrete cosine transform. A fast computing algorithm of the LOT adaptable for VLSI architectures is described. >

Fast Algorithms for One- and Two-Dimensional Discrete Cosine Transforms

Abstract: The discrete cosine-transform (DCT) is closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the DCT and its inverse, which is based on the polynomial arithmetic with Chebyshev polynomials. In the case of radix-2 lengthy our algorithm possesses a simple structure and the same computational complexity as the best known DCT-algorithms. The extension to the two dimensional DCT is presented as well.

A novel systolic array implementation of DCT, DWT and DFT

Abstract: A novel systolic array architecture for computing discrete orthogonal transforms (such as the discrete cosine transform (DCT), the discrete W transform (DWT), or the discrete Fourier transform (DFT)) is proposed. The systolic algorithm is based on the FFCT proposed by Vetterli and Nussbaumer (1984) and the recursive equation of trigonometric functions. The author presents the processing elements based on a special butterfly computation and describes the systolic array implementations for computing DCT, DWT and DFT respectively. All these computations can be fulfilled in the real domain. It is argued that because of a high degree of simplicity, regularity, suitability and concurrency inherent to these designs, their VLSI implementation will be cost effective. >

Image coding using weighted cosine transform

Abstract: A new orthogonal transform, called weighted cosine transform (WCT), is developed for digital image coding applications. The new transform is characterized. The transform matrix is the weighted version of that in the discrete cosine transform (DCT). Various commonly used criteria based on the one-dimensional and two-dimensional Markov models have shown that the performance of the order-8 and order-16 WCT is better than the DCT and the phase-shift cosine transform (PSCT), which is an improved version of the DCT. A fast computational algorithm for the WCT is also derived, which, however, requires more computational efforts than the DCT. >

Discrete cosine transform encoding of two-dimensional processes

Abstract: The performance of a two-dimensional (2D) block discrete cosine transform (DCT) operating on 2D first-order separable autoregressive Gauss-Markov processes and real-world images is studied. In each case, Lloyd-Max and entropy-constrained quantizers with optimum rate-allocation are employed. These results are compared to the earlier developments for vector predictive quantizers and entropy-constrained 2-D differential pulse code modulation (DPCM). Relative performance improvements that can be obtained for the schemes under consideration, when operating on the same source (either stochastic or select real-world images), are established. The results obtained for real-world images indicate the degree to which the theoretical results can be extended to practical applications. >

Fast odd discrete cosine transform algorithms

Abstract: 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-I of the same length. The ODCT-IV are then computed from ODCT-II or III using simple recurrence formulas.