This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [lo] is used to parameterize all the DCTs and DSTs in terms of certain (2x2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with ...

This paper presents a new 3-D subband coding framework that is able to achieve a good balance between high compression performance and channel error resilience. Various data transform methods for the decorrelation of video were examined and compared, including subband filtering, discrete cosine transforms, discrete wavelet transforms, and lapped transforms. The coding stage of the algorithm is ...

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing – are introduced and their main properties and possible applications are discussed.

This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [lo] is used to parameterize all the DCTs and DSTs in terms of certain (2x2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with ...

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A,M,Φ), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and Φ generalizes the concept of the z-transform to bijective linear mappings from a vector sp...

 Abstract—Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for Fourier transform. In this letter, we derive a discrete Fresnel transform (DFnT) from the infinitely periodic optical gratings, as a linear trigon...

In the past decade, the advancement in data communications was significant during explosive growth of the Internet, which led to the demand for using multimedia in portable devices. Video and Audio data streams require a huge amount of bandwidth to be transferred in an uncompressed form. The objective of this paper is to minimize the number of bits required to represent an image and also the ac...