the s-transform has widely been used in the analysis of non-stationary time series. a simple method to obtain depth estimates of gravity field sources is introduced in this study. we have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. this calculation procedure is based on replacement of the fourier transform with the s-tra...

for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

A direct sum theorem for two parties and a function f states that the communication cost of solving k copies of f simultaneously with error probability 1/3 is at least k · R1/3(f), where R1/3(f) is the communication required to solve a single copy of f with error probability 1/3. We improve this for a natural family of functions f , showing that the 1-way communication required to solve k copie...

for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

2 User reference: the sift function 1 2.1 Scale space parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Detector parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Descriptor parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Direct access to SIFT components . . . . . . . ....

Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω...

An arithmetical function f is said to be even (mod r) if f (n) = f ((n, r)) for all n ∈ Z + , where (n, r) is the greatest common divisor of n and r. We adopt a linear algebraic approach to show that the Discrete Fourier Transform of an even function (mod r) can be written in terms of Ramanujan's sum and may thus be referred to as the Discrete Ramanujan-Fourier Transform.

We show a pointwise estimate for the Fourier transform involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the...