Hartley-Fourier cosine generalized convolution inequalities

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

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...

A Generalized Convolution for Finite Fourier Transformations

Presented to the Society, April 16, 1948; received by the editors June 25, 1948. 1 The author wishes to thank Professor R. V. Churchill for his advice in the preparation of this paper. The content of this paper is part of a dissertation submitted in partial fulfillment of the requirements for the degree of doctor of philosophy in the University of Michigan. 2 The numbers in brackets refer to th...

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...

Fractional cosine and sine transforms in relation to the fractional Fourier and Hartley transforms

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