We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elem...

We consider the recursive Fourier sampling problem (RFS), and show that there exists an interactive proof for RFS with an efficient classical verifier and efficient quantum prover.

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (WienerKhintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this probl...

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursiv...

We study additive properties of the set S of bijections (or permutations) {1, . . . , n} → G, thought of as a subset of Gn, where G is an arbitrary abelian group of order n. Our main result is an asymptotic for the number of solutions to π1 + π2 + π3 = f with π1, π2, π3 ∈ S, where f : {1, . . . , n} → G is an arbitary function satisfying ∑n i=1 f(i) = ∑ G. This extends recent work of Manners, M...

In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

| Based on the least mean squares (LMS) algorithm , the LMS spectrum analyzer can be used to re-cursively calculate the discrete Fourier transform (DFT) of a sliding window of data. In this paper, we compare the LMS spectrum analyzer with the straightforward non-adaptive implementation of the recursive DFT. In particular , we demonstrate the robustness of the LMS spectrum analyzer to the propag...

It is shown that a priori knowledge of the edges of an object is not sufficient to ensure that it can be uniquely reconstructed from the modulus of its Fourier transform (or from its autocorrelation function). Furthermore, even in those cases for which the ultimate solution is unique, in intermediate steps in the solution by the recursive Hayes-Quatieri algorithm there can be ambiguities. An ex...

This paper develops a recursive method for computing moments of 2D objects described by elliptic Fourier descriptors (EFD). To this end, Green’s theorem is utilized to transform 2D surface integrals into 1D line integrals and EFD description is employed to derive recursions for moments computations. A complexity analysis is provided to demonstrate space and time efficiency of our proposed techn...