Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...

Typically, many of the modern buildings have concrete walls constructed from cinder block walls, that have periodic nature in their relative dielectric constant. This periodic nature excites higher-order Floquet harmonic modes at microwave frequencies, which leads to the propagation of scattered waves along with non-specular directions. Periodic structures exhibit different behaviors when illum...

1. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on R n (n = 3) 3. Fourier inversion on R 2 4. Fourier inversion on R n (general n) 5. Fourier inversion on spheres 6. Fourier inversion on complex projective space, and variants 7. Fourier inversion on hyperbolic space, and variants 8. Fourier inversion on strongly scattering manifolds 9. Hermite expansions an...

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

anomaly detection (ad) has recently become an important application of target detection in hyperspectral images. the reed-xialoi (rx) is the most widely used ad algorithm that suffers from “small sample size” problem. the best solution for this problem is to use dimensionality reduction (dr) techniques as a pre-processing step for rx detector. using this method not only improves the detection p...

due to its simplicity radix-2 is a popular algorithm to implement fast fourier transform. radix - 2 p algorithms have the same order of computational complexity as higher radices algorithms, but still retain the simplicity of radix-2 . by defining a new concept, twiddle factor template , in this paper we propose a method for exact calculation of multiplicative complexity for radix-2 p algorithm...

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...

s is a time-frequency transform based on the concept of short-time fourier transform and wavelet transform. the main property of this transform that separate it from the discrete short-time fourier transform is variable frequency resolution. but in this transform the change of resolution of high frequencies to low frequencies is very high. so another transform as a modified s transform is intro...

In this work we extend the qualitative reconstruction method for inverse source problems for time-harmonic acoustic and electromagnetic waves in free space, recently developed in [R. Griesmaier, M. Hanke, and T. Raasch, SIAM J. Sci. Comput., 34 (2012), pp. A1544–A1562], to a relevant three-dimensional setting. The reconstruction algorithm relies on the fact that a windowed Fourier transform of ...