Orthogonal Harmonic Signals of the Generalized Class

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Generalized orthogonal designs

Orthogonal Harmonic Analysis of Fractal Measures

We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis. Overview We study properties of pairs of Borel measures on R simultaneously generalizing Fourier series and the Fourier transform. We show that certain fractal measures fall within the class of measures admitting generalized Fourier series. The class of fractal measures considered in...

Nonlinear Estimation of Harmonic Signals

A nonlinear harmonic estimator (NHE) is proposed for extracting a harmonic signal and its fundamental frequency in the presence of white noise. This estimator is derived by applying an extended complex Kalman filter (ECKF) to a multiple sinusoidal model with staterepresentation and then efficiently specializing it for the case of harmonic estimation. The effectiveness of the NHE is verified usi...

Generalized Spiked Harmonic Oscillator

A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = − d dx + Bx + A x + λ xα ,where B > 0, A ≥ 0 , and α and λ denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schrödinger’s equation for the potential V (x) = Bx + A x . Compact closed-form expressions are obtai...