FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

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The Design and Implementation of FFTW3

For the past few years, a joint ISO/CCITT committee known as JPEG (Joint Photographic Experts Group) has been working to establish the first international compression standard for continuous-tone still images, both grayscale and color. JPEG’s proposed standard aims to be generic, to support a wide variety of applications for continuous-tone images. To meet the differing needs of many applications, the JPEG standard includes two basic compression methods, each with various modes of operation. A DCT-based method is specified for “lossy’’ compression, and a predictive method for “lossless’’ compression. JPEG features a simple lossy technique known as the Baseline method, a subset of the other DCT-based modes of operation. The Baseline method has been by far the most widely implemented JPEG method to date, and is sufficient in its own right for a large number of applications. This article provides an overview of the JPEG standard, and focuses in detail on the Baseline method.

https://www.ijg.org/files/Wallace.JPEG.pdf

The JPEG still picture compression standard

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

http://www.gbv.de/dms/ilmenau/toc/024184004richa.PDF

Remote sensing digital image analysis

1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

/pdf/wavelet-methods-for-time-series-analysis-1m2hg2nm53.pdf

Wavelet Methods for Time Series Analysis

A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loeve transform, which is known to be optimal. The performances of the Karhunen-Loeve and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion.

Discrete Cosine Transform

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.

Discrete Cosine Transform: Algorithms, Advantages, Applications

A tutorial-review paper on discrete orthogonal transforms and their applications in digital signal and image (both monochrome and color) processing is presented. Various transforms such as discrete Fourier, discrete cosine, Walsh-Hadamard, slant, Haar, discrete linear basis, Hadamard-Haar, rapid, lower triangular, generalized Haar, slant Haar and Karhunen-Loeve are defined and developed. Pertinent properties of these transforms such as power spectra, cyclic and dyadic convolution and correlation are outlined. Efficient algorithms for fast implementation of these transforms based on matrix partitioning or matrix factoring are presented. The application of these transforms in speech and image processing, spectral analysis, digital filtering (linear, nonlinear, optimal and suboptimal), nonlinear systems analysis, spectrography, digital holography, industrial testing, spectrometric imaging, feature selection, and patter recognition is presented. The utility and effectiveness of these transforms are evaluated in terms of some standard performance criteria such as computational complexity, variance distribution, mean-square error, correlated rms error, rate distortion, data compression, classification error, and digital hardware realization.

Orthogonal transforms for digital signal processing

A computationally simpler and effective method is proposed for estimating motion in a video sequence. The paper outlines a search technique based on conjugate directions [3], [4] and another simpler technique called the one-at-a-time search [3]. Based on the comparison of the two methods, the latter technique is adopted as the basis for further research. The adopted technique is compared with brute force search, existing 2-D logarithmic search [1], and a modified version of it [2], for motion compensated prediction [5].

Predictive Coding Based on Efficient Motion Estimation

1. Introduction. I. DIGITAL CODING TECHNIQUES. 2. Color Formats. 3. Quantization. 4. Predictive Coding. 5. Transform Coding. 6. Hybrid Coding and Motion Compensation. 7. Vector Quantization and Subband Coding. II. INTERNATIONAL STANDARDS FOR IMAGE, VIDEO AND AUDIO CODING. 8. JPEG Still Picture Compression Algorithm. 9. ITU-T H.261 Video Coder. 10. MPEG-1 Audiovisual Coder for Digital Storage Media. 11. MPEG-2 Generic Coding Algorithms. 12. MPEG-4 and H.263 Very Low Bit-rate Coding. 13. High Definition Television Services. 14. CMTT Digital Broadcasting S Standards. Appendix A. Manufactures and Vendors. Appendix B. Information on the Internet.

K. R. Rao

Papers

Discrete Cosine Transform

Discrete Cosine Transform: Algorithms, Advantages, Applications

Orthogonal transforms for digital signal processing

Predictive Coding Based on Efficient Motion Estimation

Techniques and Standards for Image, Video, and Audio Coding