Received Aug 2, 2013 Revised Oct 14, 2013 Accepted Oct 28, 2013 The H.264/AVC standard achieves remarkable higher compression performance than the previous MPEG and H.26X standards. One of the computationally intensive units in the MPEG and H.26X video coding families is the Discrete Cosine Transform (DCT). In this paper, we propose an efficient implementation of the DCT, inverse DCTs and the H...

This paper presents an overview of the transform and quantization designs in H.264. Unlike the popular 8 8 discrete cosine transform used in previous standards, the 4 4 transforms in H.264 can be computed exactly in integer arithmetic, thus avoiding inverse transform mismatch problems. The new transforms can also be computed without multiplications, just additions and shifts, in 16-bit arithmet...

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebra...

The Discrete Sine and Cosine Transforms (DST and DCT) have already received considerable attention due to their use in source coding. The DCT of type-II (DCT-II) is at the core of standards for image and video compression, such as JPEG, H.26x-series, and MPEG 1-4 standards. The DST of type-I was suggested as a basis for Recursive Block Coding technique. The DCT and DST of type IV are used in de...

Image processing became a big challenge in the multimedia usage for processing the images with low power and high efficiency. For processing images, DCT (Discrete cosine transforms) are utilized for compression because of its advantages over the energy consumption. In existing methods, they used Approximate DCT with fast algorithm and regular pipelining structure for reducing the design complex...

Since the most efficient waveform coding methods use linear transforms before quantization and entropy coding, the methods designed to allow random access to compressed data normally have to deal with the result of these transforms. However, in some specialized technical applications the information needed is the result of non-linear operations. For instance, it is useful to have fast access to...

A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described. Different families of transforms are defined within the introduced class. All transforms of one family can be computed with fast algorithms similar in structure to each other. In particular, the family of Haar-like transforms consists of discrete or...

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...

Time-frequency analysis and the transforms that it gives rise to play an important role in digital signal processing. In lossy audio compression, for instance, it has been found that working in the transform domain leads to methods that achieve a much higher level of signal compression than could be achieved in the temporal domain. This article gives an introduction to time-frequency analysis t...

Two new design techniques for adaptive orthogonal block transforms based on vector quantization (VQ) codebooks are presented. Both techniques start from reference vectors that are adapted to the characteristics of the signal to be coded, while using different methods to create orthogonal bases. The resulting transforms represent a signal coding tool that stands between a pure VQ scheme on one e...