The fast Fourier transform (FFT) is one of the truly great computational developments of this
century. It has changed the face of science and engineering so much so that it is not an …

Two aspects of the Kronecker product are studied. First, we start with the Kronecker product
approximation problem. Given a matrix A and a factorization of its dimensions, we find …

Many versions of the fast Fourier transform require a reordering of either the input or the
output data that corresponds to reversing the order of the bits in the array index. There has …

A simple and efficient design and implementation of the two-dimensional (2D) parallel block-
filtering algorithm by fast number theoretic transforms is presented. The algorithm is …

This correspondence describes a new bit-reversal permutation algorithm based on a trivial
symmetry that has not been exploited until now. According to timing experiments, this …

The three dimensional discrete cosine transform (3D DCT) has been widely used in many
applications such as video compression. On the other hand, the kary n-cube is one of the …

An extension of one of the fastest existing algorithms for the computation of the two-
dimensional (2D) discrete cosine transform (DCT) is presented and a 2D fast cosine …

A novel fast recursive O (N) algorithm for bit-reversal permutation of a data array is
presented. Exploiting regularity in the bit-reversal and eliminating redundant computations …

Fast bit-reversal algorithms have been of strong interest for many decades, especially after
Cooley and Tukey introduced their FFT implementation in 1965. Many recent algorithms …

Data shuffling in a particular order is frequently required in signal processing applications.
The authors present fast recursive algorithms, of order O (N), for shuffling a data sequence in …