Discrete cosine transform

A discrete cosine transform expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a used transformation technique in signal processing and data compression, it is used in most digital media, including digital images, digital video, digital audio, digital television, digital radio, speech coding. DCTs are important to numerous other applications in science and engineering, such as digital signal processing, communications devices, reducing network bandwidth usage, spectral methods for the numerical solution of partial differential equations; the use of cosine rather than sine functions is critical for compression, since it turns out that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform, but using only real numbers.

The DCTs are related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of a periodically extended sequence. DCTs are equivalent to DFTs of twice the length, operating on real data with symmetry, whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants; the most common variant of discrete cosine transform is the type-II DCT, called "the DCT". This was the original DCT, first proposed by Nasir Ahmed in 1972, its inverse, the type-III DCT, is correspondingly called "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform, equivalent to a DFT of real and odd functions, the modified discrete cosine transform, based on a DCT of overlapping data. Multidimensional DCTs are developed to extend the concept of DCT on MD signals. There are several algorithms to compute MD DCT. A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT.

One of these is the integer DCT, an integer approximation of the standard DCT, used in several ISO/IEC and ITU-T international standards. DCT compression known as block compression, compresses data in sets of discrete DCT blocks. DCT blocks can have a number of sizes, including 8x8 pixels for the standard DCT, varied integer DCT sizes between 4x4 and 32x32 pixels; the DCT has a strong "energy compaction" property, capable of achieving high quality at high data compression ratios. However, blocky compression artifacts can appear; the discrete cosine transform was first conceived by Nasir Ahmed, while working at Kansas State University, he proposed the concept to the National Science Foundation in 1972. He intended DCT for image compression. Ahmed developed a practical DCT algorithm with his PhD student T. Natarajan and friend K. R. Rao at the University of Texas at Arlington in 1973, they found that it was the most efficient algorithm for image compression, they presented their results in a January 1974 paper, titled "Discrete Cosine Transform".

It described what is now called the type-II DCT, as well as the type-III inverse DCT. It was a benchmark publication, has been cited as a fundamental development in thousands of works since its publication; the basic research work and events that led to the development of the DCT were summarized in a publication by Ahmed, "How I Came Up with the Discrete Cosine Transform". Since its introduction in 1974, there has been significant research on the DCT. In 1977, Wen-Hsiung Chen published a paper with C. Harrison Smith and Stanley C. Fralick presenting a fast DCT algorithm, he founded Compression Labs to commercialize DCT technology. Further developments include a 1978 paper by N. J. Narasinha and S. C. Fralick, a 1984 paper by B. G. Lee; these research papers, along with the original 1974 Ahmed paper and the 1977 Chen paper, were cited by the Joint Photographic Experts Group as the basis for JPEG's lossy image compression algorithm in 1992. In 1975, John A. Roese and Guner S. Robinson adapted the DCT for inter-frame motion-compensated video coding.

They experimented with the DCT and the fast Fourier transform, developing inter-frame hybrid coders for both, found that the DCT is the most efficient due to its reduced complexity, capable of compressing image data down to 0.25-bit per pixel for a videotelephone scene with image quality comparable to an intra-frame coder requiring 2-bit per pixel. The DCT was applied to video encoding by Wen-Hsiung Chen, who developed a fast DCT algorithm with C. H. Smith and S. C. Fralick in 1977, founded Compression Labs to commercialize DCT technology. In 1979, Anil K. Jain and Jaswant R. Jain further developed motion-compensated DCT video compression called block motion compensation; this led to Chen developing a practical video compression algorithm, called motion-compensated DCT or adaptive scene coding, in 1981. Motion-compensated DCT became the standard coding technique for video compression from the late 1980s onwards; the integer DCT is used in Advanced Video Coding, introduced in 2003, High Efficiency Video Coding, introduced in 2013.

The integer DCT is used in the High Efficiency Image Format


Kunustoria is a census town in Jamuria CD Block in Asansol Sadar subdivision of Paschim Bardhaman district in the Indian state of West Bengal. Kunustoria is located at 23°39′28″N 87°07′03″E; the Asansol-Durgapur region is composed of undulating laterite soil. This area lies between two mighty rivers -- the Ajay, they flow parallel to each other in the region – the average distance between the two rivers is around 30 km. For ages the area was forested and infested with plunderers and marauders; the discovery of coal led to industrialisation of the area and most of the forests have been cleared. As per the 2011 census, 83.33% of the population of Asansol Sadar subdivision was urban and 16.67% was rural. In 2015, the municipal areas of Kulti and Jamuria were included within the jurisdiction of Asansol Municipal Corporation. Asansol Sadar subdivision has 26 Census Towns.. As per 2011 Census of India Kunustoria had a total population of 5,127 of which 2,720 were males and 2,407 were females. Population below 6 years was 587.

The total number of literates in Kunustoria was 3,451. As of 2001 India census, Kunustoria had a population of 5,416. Males constitute 56% of the population and females 44%. Kunustoria has an average literacy rate of 67%, higher than the national average of 59.5%: male literacy is 77%, female literacy is 55%. In Kunustoria, 13% of the population is under 6 years of age; as per ECL website telephone numbers, operational collieries in the Kunustoria Area of Eastern Coalfields in 2018 are: Amritnagar Colliery, Amrasota Colliery, Bansra Colliery, Belbaid Colliery, Kunustoria Colliery, Mahabir OCP, North Searsole Colliery, Parasea Colliery, Parasea 6 & 7 Incline and Parasea OCP. Kunustoria has two primary schools, they provide mid day meals to the student like kichri which provide the poorer section an incentive to send their children to school for education as well as for food

ARA Rosales (P-42)

ARA Rosales is the second ship of the MEKO 140A16 Espora class of six corvettes built for the Argentine Navy. The ship is the fourth ship to bear the name of Colonel Leonardo Rosales, who fought in the Argentine Navy during Argentina's war of independence and the Cisplatine War; the Argentine Navy struggles to meet maintenance and training requirements because of financial problems and import restrictions. The operational status of Rosales is not clear. Rosales and her sister ships were part of the 1974 Naval Constructions National Plan, an initiative by the Argentine Navy to replace old World War II-vintage ships with more advanced warships; the original plan called for six MEKO 360H2 destroyers, four of them to be built in Argentina, but the plan was modified to include four MEKO destroyers and six corvettes for anti-surface warfare and patrol operations. Rosales was constructed at the Río Santiago Shipyard of the Astilleros y Fábricas Navales del Estado state corporation, her keel was laid on 1 April 1981 and was launched on 4 March 1983.

The ship was delivered to the Navy on 14 November 1986 and formally commissioned on 24 March 1987. First captain was Capitan de Navio Manuel Augusto Iricibar. In February 1991, as part of Task Group 88.1 Rosales along with ARA Bahía San Blas participated as part of the Coalition of the Gulf War in the United Nations-mandated blockade of Iraq following its invasion of Kuwait. She participated in patrol and escort missions as part of Operations Desert Shield and Desert Storm, returning to Argentina on July 1991 Rosales participated in several naval exercises and conducted fishery patrol duties in the Argentine exclusive economic zone, capturing two illegal fishing ships in 1992, she is homeported at Puerto Belgrano Naval Base and is part of the Navy's 2nd Corvette Division with her five sister ships. Guia de los buques de la Armada Argentina 2005-2006. Ignacio Amendolara Bourdette, ISBN 987-43-9400-5, Editor n/a