The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sampl...

Each Discrete Cosine Transform uses N real basis vectors whose components are cosines. In the DCT-4, for example, the jth component of v k is cos(j + 1 2)(k + 1 2) N. These basis vectors are orthogonal and the transform is extremely useful in image processing. If the vector x gives the intensities along a row of pixels, its cosine series P c k v k has the coeecients c k = (x; v k)=N. They are q...

In this paper a reversible discrete cosine transform (RDCT) is presented. N-point reversible transform is firstly presented, then 8-point RDCT is obtained by substituting the 2 and 4point reversible transforms for 2 and 4-point transforms which compose 8-point discrete cosine transform (DCT), respectively. Integer input signal can be losslessly recovered, although the transform coefficients are...

Discrete frequency transforms provide a method to obtain a global view of data within a window. Discrete cosine transform is the frequency transform for practical image processing because of its excellent energy compaction property. Another reason for its popularity is the existence of a fast implementation for the algorithm. In this article, the basics of the discrete cosine transform, its use...

The paper presents novel recursive algorithms for realization of one-dimensional type-II discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) of any length. By using some mathematical techniques, recursive expressions for DCT and IDCT have been developed. The number of additions and multiplications in the recursive algorithm for DCT are less in comparison with some other...

The transform properties of several orthogonal basis functions are analysed in detail in this report, and their performance compared using a set of grayscale test images, containing both natural and artificial scenes. Well-defined image quality measures are used to determine the type of images that are most suitable for compression for a given basis function. The particular transforms that we h...