Composite Cosine Transforms

Discrete Cosine and Sine Transforms

Fractional Cosine and Sine Transforms

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.

Integral Transforms of Fourier Cosine Convolution Type

which has the following property Fc(f ∗ g)(x) = (Fcf)(x)(Fcg)(x). (3) The theory of integral transforms related to the Fourier and Mellin convolutions is well developed [2, 6, 10, 11, 12, 13, 19] and has many applications. Some other classes of integral transforms, that are not related to any known convolutions, are considered in [14, 15]. In this paper we investigate integral transforms of the...

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...

Fractional cosine, sine, and Hartley transforms

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...