Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
The JPEG still picture compression standard
Communications of the ACM - Special issue on digital multimedia systems
Digital Image Compression Techniques
Digital Image Compression Techniques
Fast multiplierless approximations of the DCT with the liftingscheme
IEEE Transactions on Signal Processing
Real-time fluid simulation using discrete sine/cosine transforms
Proceedings of the 2009 symposium on Interactive 3D graphics and games
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A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.