Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of FFT and propose a new presentation. Our heuristic description is helpful for students and programmers to grasp the algorithm entirely and deeply.

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...

Let Fq be the finite field with q elements and let ! be a primitive n-th root of unity in an extension eld Fqd of Fq. Given a polynomial P 2 Fq[x] of degree less than n, we will show that its discrete Fourier transform (P (1); P (!); :::; P (!n¡1)) 2Fqd n can be computed essentially d times faster than the discrete Fourier transform of a polynomial Q 2 Fqd[x] of degree less than n, in many case...

The methods of fast parallel calculation of multidimensional hypercomplex discrete Fourier transform (HDFT) are discussed. The theoretical and experimental estimation of parallelization efficiency is given. It is shown that proposed method has very high efficiency (up to 90%).

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 this section we discuss the theory of Fourier Series for functions of a real variable. In the next sections we will study an analogue which is the “discrete” Fourier Transform. Early in the Nineteenth century, Fourier studied sound and oscillatory motion and conceived of the idea of representing periodic functions by their coefficients in an expansion as a sum of sines and cosines rather tha...

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.

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and simulation of earthquake accelerograms. This paper is introduced a novel method based on discrete Hartley transform (DHT) and radial basis function (RBF) neural network for generation of artificial earthquake accelerograms from specific target spectrums. Acce...

at the target knots yj ∈ [−14 , 1 4 ], j = 1, . . . ,M , where σ = a + ib, a > 0, b ∈ R denotes a complex parameter. Fast Gauss transforms for real parameters σ were developed, e.g., in [15, 8, 9]. In [12], we have specified a more general fast summation algorithm for the Gaussian kernel. Recently, a fast Gauss transform for complex parameters σ with arithmetic complexity O(N log N + M) was int...