Cosine Products, Fourier Transforms, and Random Sums

Cosine Products, Fourier Transforms, and Random Sums

one gets the first actual formula for 7r that mankind ever discovered, dating from 1593 and due to Frangois Viete (1540-1603), whose Latinized name is Vieta. (Was any notice taken of the formula's 400th anniversary, perhaps by the issue of a postage stamp?) From the samples of a function t(x) at equally spaced points x", n E z, one can reconstruct the complete function with the aid of sin x/x, ...

1 7 N ov 2 00 4 Cosine Products , Fourier Transforms , and Random Sums ∗

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...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Unified Architecture for Discrete Fourier and Inverse Cosine Transforms

A unified architecture for radix-2 decimation-in-time fast Fourier transform and inverse discrete cosine transform of type II is presented based on constant geometry formulation of the algorithms. The parallelism of the architecture can be specified to meet various throughput and area requirements. The type and size of the transform in the architecture can be configured in run-time. In addition...