The multiplicative complexity of discrete cosine transforms

Discrete Cosine and Sine Transforms

The discrete fractional cosine and sine transforms

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

Discrete Cosine Transforms on Quantum Computers

A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size N ...

Comparison of Discrete Cosine Transforms (DCT), Discrete Fourier Transforms (DFT), and Discrete Wavelet Transforms (DWT) in Digital Image Watermarking

Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods w...

The discrete fractional random cosine and sine transforms

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given.