For two-dimensional (2-D) digital filters implemented by a block recursive equation, explicit relations between their frequency characteristics and those of scalar filter are obtained. Specifically, these include the relation between the discrete-time Fourier transform (DTFT) of the block recursive equation and that of the scalar 2-D difference equation, and the relation between the block matri...

A virtual instrument for time–frequency analysis is presented. Its realization is based on an order recursive approach to the time–frequency signal analysis. Starting from the short time Fourier transform and using the S-method, a distribution having the auto-terms concentrated as high as in the Wigner distribution, without cross-terms, may be obtained. The same relation is used in a recursive ...

An efficient procedure is proposed for the realization of robust short-time Fourier transform (STFT) based on the recursive realization of the standard STFT. In the initial stage it uses the robust STFT calculated by iterative or sorting procedures and, after that, the recursive relation is applied. Basic difference from the standard STFT realization is in limiting samples in the next instants,...

This paper presents a framework for synthesizing eecient out-of-core programs for block recursive algorithms such as the fast Fourier transform (FFT) and Batcher's bitonic sort. The block recursive algorithms considered in this paper are described using tensor (Kronecker) product and other matrix operations. The algebraic properties of the matrix representation are used to derive eecient out-of...

Algorithms are presented for maximally efficient computation of the crystallographic fast Fourier transform (FFT). The approach is applicable to all 230 space groups and allows reduction of both the computation time and the memory usage by a factor equal to the number of symmetry operators. The central idea is a recursive reduction of the problem to a series of transforms on grids with no speci...

An integrated algorithm for analyzing the real-time, running Fourier spectra is presented. When applying to the real-time analysis, the computational e$ciency and synchronization ability are highly improved by integrating the recursive procedure with the real-time implementation strategy. Given the FFT (frame) size N"2r and moving size M"2p, the algorithm implements the recursive procedure for ...

The computation of linear moment matrices, whose elements are defined as zeroth order integration values of an image, was recently introduced as a tool to reduce the computational cost required to obtain the geometric moments of an image. The main relevance of these matrices is twofold: on one hand, they can be eficiently obtained by means of accumulation filters, which only require additions; ...

This paper develops a prime radix transform algorithm that can be used to calculate the discrete Fourier transform (DFT) of a data block of length P, a prime, using fixed coefficient second order recursive filter sections: this simple hardware structure allows compact, high performance DFT processors to be developed. Further “massaging” of the prime radix algorithm produces the zero factor tran...

Discrete Fourier Transform (DFT) is probably the most popular signal processing tool. Wide DFT use is partly dedicated to fast Fourier Transform (FFT) algorithms (Cooley & Tukey, 1965, Oppenheim et al., 1999, Lyons, 2004). DFT may also be efficiently computed by recursive algorithms in the window sliding by one sample (Jacobsen & Lyons, 2003, Duda, 2010). Unfortunately, DFT has two main drawbac...