We compare several algorithms for computing the discrete Fourier transform of n numbers. The number of “operations” of the original Cooley-Tukey algorithm is approximately 2n A(n), where A(n) is the sum of the prime divisors of n. We show that the average number of operations satisfies (l/x)Z,,,2n A(n) (n2/9)(x2/log x). The average is not a good indication of the number of operations. For examp...

This paper presents an interpolation/extrapolation technique for sequence partitions. It consists of four steps: region parametrization, region interpolation, region ordering and partition creation. The evolution of each region is divided into two types: regular motion and random deformations. Both types of evolution are parametrized by means of the Fourier descriptors of the regions and they a...

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...

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...

لا ةصلاخ : نأ مو لعملا ن م ويد يفلا ة جلاعم ي ف ر مزلا ة آرح ريد قت (video) ً ار يبآ اً ئبع ل ثمي جلا عملا ةد حو ي ف يزآرملا (CPU) . ة مءَلاملاو ثحبلا يروط نيسحتل ةعيرس تا يمزراوخ ريوطت مت كلذل . تا يمزراوخلا هذ ه يناكملا لقحلا يف لمعت . تا يمزراوخ يف ةرفوتملا تاعرسلا نم ديفتست ةديدج ةيمزراوخ حرتقن لاقملا اذه يفو ةعيرسلا هييروف (FFT) . ددحت ةحرتقملا ةيمزراوخلاو مادختساب يعجرملا راطلإاو ةرفشملا ةر...

Automatic detection of image orientation is a very important operation in photo image management. In this paper, we propose an automated method based on the boosting algorithm to estimate image orientations. The proposed method has the capability of rejecting images based on the confidence score of the orientation detection. Also, images are classified into indoor and outdoor, and this classifi...

Discussion of the considerations involved in high-performance FFT implementations, which center largely on memory access and other non-arithmetic concerns, as illustrated by a case study of the FFTW

In this paper we study the effective thermal behaviour of 3D representative volume elements (RVEs) of two-phased composite materials constituted by a matrix with cylindrical and spherical inclusions distributed randomly, with periodic boundaries. Variations around the shape of inclusions have been taken into account, by corrugating shapes, excavating and/or by removing pieces of inclusions. The...