Search

Tensor algorithms for calculating the two-dimensional (2-D) discrete cosine transform (DCT) are examined. The approach used is based on the concept of partitions revealing transforms that leads the tensor representation of the 2-D DCT and effective tensor algorithms for computing the 2-D DCT with arbitrary orders.

Split manageable efficient algorithms have been developed for computing unitary transforms of arbitrary orders by using different partitioning in the frequency domain and new paired representation of the transforms. These are for the so-called paired transforms. The algorithms are described for the one-dimensional case and use the special partitioning in the frequency domain.

Use of Fibonacci p-codes enables the development of an VLSI architecture and a parallel decomposition algorithm to determine the output of a nonlinear digital stack filter. A running stack filtering VLSI architecture and algorithm are derived for a subclass of positive Boolean functions.

A new concept is presented for calculating fast discrete orthogonal transforms that leads to a general split manageable algorithm for computing discrete unitary transforms. A fast Fourier transform (FFT) algorithm is developed with less arithmetical complexity by replacing some of the arithmetical operations by others, such as shifting operations.

In this paper, the method of splitting or parallelization of calculation of the $N$-point discrete Fourier transform (DFT) by the DFTs of smaller orders is described. For that the concept of partitions revealing the one-dimensional (1-D) DFT of order $q2^r,$ where $r > 1$ and $q > 1$ is a positive odd number, is described. Two different partitions are considered and the corresponding effective algorithms of calculation of the $q2^r$ -point 1-D DFT are described for the $q=3$ case. The calculation of the transform is based on the paired representations, when the signal is represented as a set of 1-D signals which define the 1-D DFT in disjoint subsets of frequency-points which cover the set of all frequencies. The splittings of the $q2^r$ -point 1-D DFT are performed by the 1-D discrete 2- and $q$ -paired transforms which allow for calculating with a minimum number of operations. The examples of the paired transforms and computational complexity of the proposed algorithms for the $N=6$ and 12 cases are given. [ABSTRACT FROM PUBLISHER]