A divide and conquer algorithm is presented for computing arbitrary multi-dimensional discrete Fourier transforms. In contrast to standard approaches such as the row-column algorithm, this algorithm allows an arbitrary decomposition, based solely on the size of the transform independent of the dimension of the transform. Only minor modifications are required to compute transforms with different...

We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain “low frequency” Fourier components. The secon...

In this paper, we discuss the design and implementation of a high-speed, low power 1024-point pipeline FFT processor. Key features are flexible internal data length and a novel processing element. The FFT processor, which is implemented in a standard 035 pm CMOS process, is efficient in term of power consumption and chip area.

Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n logn 4 ∗ n) bit operations.

An improved approach to updating the electric field in simulations of Coulomb gases using the local lattice technique introduced by Maggs and Rossetto [1], is described and tested. Using the Fast Fourier Transform (FFT) an independent configuration of electric fields subject to Gauss’ law constraint can be generated in a single update step. This FFT based method is shown to outperform previous ...

Fourier descriptors are powerful features for the recognition of two-dimensional connected shapes. In this article, we propose a method to define Fourier descriptors even for broken shapes, i.e. shapes that can have more than one contour. The method is based on the convex hull of the shape and the distance to the closest actual contour point along the convex hull. We define different invariant ...

In some signal processing applications, the input data are real. In this case, the Bruun algorithm for computation of the Discrete Fourier Transform (DFT) is attractive. This correspondence offers a pipeline and a recirculated shuffle network implementation of the Bruun algorithm. The parallel pipeline and recirculated FFT structures are implemented based on the modified perfect shuffle network.