We describe a new method for Automatic Gait Recognition based around the use of Fourier descriptors that model the periodic deformation of human gait. Fourier descriptors have been used successfully in the past to model the boundary of static or moving, rigid-bodied objects, but many objects actually deform in some way as they move. Here we use Fourier descriptors to model not only the object’s...

Currently the circle and the sieve methods are the key tools in analytic number theory. In this paper the unifying theme of the two methods is shown to be Ramanujan Fourier series.

The main aim of this paper is to investigate (Hp, Lp)-type inequalities for maximal operators of logarithmic means of one-dimensional bounded Vilenkin-Fourier series.

Two methods of calculation of the 2-D DFT are analyzed.  The q2r×q2r-point 2-D DFT can be calculated by the traditional columnrow method with 2(q2r) 1-D DFTs, and we also propose the fast algorithm which splits each 1-D DFT by the short transforms by means of the fast paired transforms.  The q2r×q2r-point 2-D DFT can be calculated by the tensor or paired representations of the image, when the...

Following the approach developed by S. Gurevich and R. Hadani, an analytical formula of the canonical basis of the DFT is given for the case N = p where p is a prime number and p ≡ 1 (mod 4).

By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval’s identity.

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.

Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms o...

In this work, the method of Fourier descriptors has been extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on t...

When n = 2, T is a Fourier multiplier, and it is well known that such operators are bounded on L, 1 < p < ∞, if m is a symbol of order 0. Coifman and Meyer [2]–[7], Kenig and Stein [14], and Grafakos and Torres [12] extended this result to the n > 2 case, showing that one had the mapping properties T : L1 × . . .× Ln−1 → Lpn (3) whenever 1 < pi ≤ ∞ (4) for i = 1, . . . , n− 1, 1/(n− 1) < pn <∞,...