Applications of Generalized Convolutions Associated with the Fourier and Hartley Transforms
نویسنده
چکیده
In this paper we present new generalized convolutions with weight-function associated with the Fourier and Hartley transforms, and consider applications. Namely, using the generalized convolutions, we construct normed rings on the space L(R), provide the sufficient and necessary condition for the solvability of a class of integral equations of convolution type, and receive the explicit solutions of those equations.
منابع مشابه
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...
متن کاملBasefield transforms derived from character tables
We show that it is possible to de ne Hartley-like transforms for (generalized) character tables of nite groups. This large class of transforms include Hartley transforms for discrete Fourier transforms over abelian groups and Hartley-like transforms for the discrete cosine transform of type I.
متن کاملFractional 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.
متن کاملIntegral 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...
متن کاملImplicitly Dealiased Convolutions: Example Applications and Performance Comparison
Implicitly dealiasing is a recently-developed technique which improves upon conventional zero padding to compute linear convolutions via fast Fourier transforms. For onedimensional inputs, the memory requirements and performance are similar to conventional zero-padded convolutions, but implicitly dealiased convolutions are faster and require less memory when the data is multi-dimensional. We sh...
متن کامل