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# Topic: Discrete cosine transform

###### In the News (Fri 19 Jul 19)

 PlanetMath: discrete cosine transform The discrete cosine transforms (DCT) are a family of similar transforms closely related to the discrete sine transform and the discrete Fourier transform. This is version 14 of discrete cosine transform, born on 2002-01-13, modified 2007-08-22. DCT for 2 dimension, summation underscript, n=1 by mbutterfield on 2005-11-01 21:19:55 planetmath.org /encyclopedia/DiscreteCosineTransform.html   (282 words)

 Discrete cosine transform signal processor - Patent 3920974 The discrete cosine transform may be interpreted as a discrete Fourier transform of a symmetrized version of the image data block. This invention implements a discrete cosine transform of length N using only filters with 2N-1 taps, thus either reducing the filter length required or permitting a longer block to be transformed with filters of a given length. The discrete cosine transform of an input signal may be computed in prior art by symmetrizing the input signal, storing it in a memory, and computing the discrete Fourier transform of the resultant signal. www.freepatentsonline.com /3920974.html   (1682 words)

 DCT.str (Version 1.0) Transforms an 8x8 signal from the frequency domain to the signal domain using an inverse Discrete Cosine Transform in accordance with the IEEE specification for a 2-dimensional 8x8 iDCT. Transforms an 8x8 signal from the signal domain to the frequency domain using a Discrete Cosine Transform in accordance with the IEEE specification for a 2-dimensional 8x8 DCT. Transforms a 2D signal from the frequency domain to the signal domain using an inverse Discrete Cosine Transform. www.cag.lcs.mit.edu /streamit/mpeg/DCT.str.html   (1275 words)

 Discrete sine transform The discrete sine transform (DST) is a frequency transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is real and imaginary), where in some variants the input and/or output data are shifted by half a sample. A related transform is the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. www.ebroadcast.com.au /lookup/encyclopedia/di/Discrete_sine_transform.html   (539 words)

 DISCRETE COSINE TRANSFORM The DCT is a loss-less and reversible mathematical transformation that converts a spatial amplitude representation of data into a spatial frequency representation. One of the advantages of the DCT is its energy compaction property, that is, the signal energy is concentrated on a few components while most other components are zero or are negligibly small. The energy compaction property of the DCT is well suited for image compression since, as in most images, the energy is concentrated in the low to middle frequencies, and the human eye is more sensitive to the middle frequencies. vlsi1.engr.utk.edu /~gabi/552/dct/report/intro.html   (350 words)

 [No title] The DCT is the sampled version of the Cosine Transform, with the transform coefficients at discrete intervals in the frequency domain. DCT [7]: A two-dimensional DCT is performed on small blocks (8 pixels by 8 lines) of each component of the picture to produce blocks of DCT coefficients (Fig. When the DCT is used in the subsequent stages to produce the coefficient matrix, the presence of noise would result in a greater number of non-zero coefficients that the encoder cannot differentiate from the original signal. www.lycos.com /info/discrete-cosine-transform.html   (477 words)

 55:148 Dig. Image Proc. Chapter 11 The discrete Fourier transform is analogous to the continuous one and may be efficiently computed using the fast Fourier transform algorithm. The properties of linearity, shift of position, modulation, convolution, multiplication, and correlation are analogous to the continuous case, with the difference of the discrete periodic nature of the image and its transform. Note that the discrete cosine transform computation can be based on the Fourier transform - all N coefficients of the discrete cosine transform may be computed using a 2N -point fast Fourier transform. www.icaen.uiowa.edu /~dip/LECTURE/LinTransforms.html   (1478 words)

 Discrete cosine transform circuit - US Patent 5357453 A discrete cosine transform circuit including a shuffle circuit with n (n is an integer) shuffle stages, the n shuffle stages sequentially having 2 A path switching section is connected to the input stages of the shuffle circuit for changing a transfer path of output information from the output stages of the shuffle circuit according to whether the discrete cosine transform to be processed is a forward discrete cosine transform or an inverse discrete cosine transform. The first and second selection sections select information according to whether the discrete cosine transform to be processed is the forward discrete cosine transform or the inverse discrete cosine transform and apply the selected information to the first and second RACs, respectively. www.patentstorm.us /patents/5357453.html   (297 words)

 Modified discrete cosine transform: Definition and Links by Encyclopedian.com The modified discrete cosine transform (MDCT) is a frequency transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are 50% overlapped. As a lapped transform, the MDCT is a bit unusual compared to other frequency transforms in that it has half as many outputs as inputs (instead of the same number). In principle, x and y could have different window functions, and the window function could also change from one block to the next (especially for the case where data blocks of different sizes are combined), but for simplicity we consider the common case of identical window functions for equal-sized blocks. www.encyclopedian.com /md/MDCT.html   (1453 words)

 dicsrete cosine transform DCT (Discrete cosine transform) takes it's name because of the fact all signals can be interpreted as a sine/cosine wave. The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT"; its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. www.edaboard.com /ftopic132493.html   (490 words)

 Define DCT - Discrete Cosine Transform In the decoder, an inverse discrete transform is used to reverse the process. Discrete Cosine Transform is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The N frequencies of a 2N point DFT correspond to N points on the upper half of the unit circle in the complex frequency plane.Assuming a periodic input, the magnitude of the DFT coefficients is spatially invariant (phase of the input does not matter). www.birds-eye.net /definition/d/dct-discrete_cosine_transform.shtml   (923 words)

 The Discrete Cosine Transform (DCT) The DCT is similar to the discrete Fourier transform: it transforms a signal or image from the spatial domain to the frequency domain (Fig 7.8). F(u,v) is the DCT coefficient in row k1 and column k2 of the DCT matrix. The DCT input is an 8 by 8 array of integers. www.cs.cf.ac.uk /Dave/Multimedia/node231.html   (401 words)

 DCT - DiCTionary, Discrete Cosine Transform, Display Compression Technology Discrete Co-sine Transform: used to transform discrete data from the domain of time or space to the frequency domain, without analyzing the phase of the signal DCT is a process that converts images from three-dimensions (3D) to two-dimensions (2D) by using the Discrete Cosine (DC) coefficient to examine the luminance of each block of pixels used to form an image. In the decoder, an inverse discrete transform is used to reverse the process. www.auditmypc.com /acronym/DCT.asp   (392 words)

 Understanding the Discrete Cosine Transform in Java Another central component of JPEG compression is the Discrete Cosine Transform, which is the primary topic of this lesson. The definition of the DCT is very similar to the definition of the DFT but the computation of the imaginary part using the sine term simply isn't part of the definition. Listing 4 invokes the static transform method of the ForwardDCT01 class to compute the forward DCT of the time data and to save the results in the array referred to by realSpect, which was created in Listing 1. www.developer.com /java/data/article.php/3619081   (6709 words)

 Discrete Cosine Transform   (Site not responding. Last check: ) This transform, studied extensively for image compression, is extremely efficient for highly correlated data. The two-dimensional DCT can be obtained by performing a one-dimensional DCT on the columns and then, a one-dimensional DCT on the rows. The transformed output from the two-dimensional DCT is ordered so that the mean value (the DC coefficient) is in the upper left corner of the 8 x 8 coefficient block, and the higher frequency coefficients progress by distance from the DC coefficient. www.ctie.monash.edu.au /EMERGE/multimedia/JPEG/IMPL03A.HTM   (185 words)

 Discrete Cosine Transform. The DCT is similar to the discrete Fourier transform: it transforms a signal or image from the spatial domain to the frequency domain. The input image is N2 pixels wide by N1 pixels high; A(i,j) is the intensity of the pixel in row i and column j; B(k1,k2) is the DCT coefficient in row k1 and column k2 of the DCT matrix. The DCT input is an 8 by 8 array of integers. cobweb.ecn.purdue.edu /~ace/jpeg-tut/jpgdct1.html   (199 words)

 Understanding the 2D Discrete Cosine Transform in Java Another central component of JPEG compression is the two-dimensional Discrete Cosine Transform, which is the primary topic of this lesson. If the image were simply transformed from the image domain into the frequency domain and back into the image domain, the process would be almost lossless. One of the significant attributes of the two-dimensional Discrete Cosine Transform (2D-DCT) is that it is separable. www.developer.com /java/data/article.php/3634156   (8311 words)

 Image Transforms - Fourier Transform The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent. The logarithm of the magnitude of its Fourier transform is homepages.inf.ed.ac.uk /rbf/HIPR2/fourier.htm   (2177 words)

 ImageProcessing8.4 The discrete cosine transform (DCT) is an important transform in 2D signal processing. The DCT is used in two international image/video compression standards, Joint Photographic Experts Group (JPEG), and Motion Picture Experts Group (MPEG) [Pen90, Pen93]. The 1D discrete cosine transform (1D DCT) X[k] of a sequence x[n] of length N is defined as documents.wolfram.com /applications/digitalimage/UsersGuide/ImageTransforms/ImageProcessing8.4.html   (242 words)

 Apparatus for performing a discrete cosine transform of an input signal - Patent 4152772 The cosine transform is suitable for real-time television image processing, specifically for obtaining an acceptable picture when the number of bits of information available for describing the picture and/or the channel bandwidth are severely limited. This invention implements a discrete cosine transform of length N using only filters with N taps, thus either reducing the filter length required or permitting a longer block to be transformed with filters of a given length. The two types of DCT which are useful for reduced redundancy television image transmission are obtained by extending a length N data block to have even symmetry, taking the discrete Fourier transform (DFT) of the extended data block, and saving N terms of the DFT. www.freepatentsonline.com /4152772.html   (5302 words)

 Chapter 12 Image processing and analysis based on continuous or discrete image transforms is a classic processing technique. The discrete Fourier transform is analogous to the continuous one and may be efficiently computed using the fast Fourier discrete cosine transform may be computed using a 2N -point fast Fourier transform. www.eng.iastate.edu /ee528/sonkamaterial/chapter_11.htm   (1021 words)

 Discrete Cosine Transform :: Transforms (Image Processing Toolbox™) The discrete cosine transform (DCT) represents an image as a sum of sinusoids of varying magnitudes and frequencies. The DCT has the property that, for a typical image, most of the visually significant information about the image is concentrated in just a few coefficients of the DCT. For example, the DCT is at the heart of the international standard lossy image compression algorithm known as JPEG. www.mathworks.com /access/helpdesk/help/toolbox/images/f21-16366.html   (509 words)

 Welcome to Evertrust Technology Discrete cosine transform is a lossy compression algorithm that samples an image at regular intervals, analyzes the frequency components present in the sample, and discards those frequencies which do not affect the image as the human eye perceives it. DCT is the basis of standards such as JPEG, MPEG, H.261, and H.263. The standard uses DCT to compress the pixel data and is a form of lossy compression. www.etthk.com /LcompressionHistory.htm   (1042 words)

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