Nonlinear trigonometric approximation and the Dirac delta function

Nonlinear Function Approximation

Further Results on the Dirac Delta Approximation and the Moment Generating Function Techniques for Error Probability Analysis in Fading Channels

In this article, we employ two distinct methods to derive simple closed-form approximations for the statistical expectations of the positive integer powers of Gaussian probability integral [ ( )] p E Q γ β γ Ω with respect to its fading signal-to-noise ratio (SNR) γ random variable. In the first approach, we utilize the shifting property of Dirac delta function on three tight bounds/approximati...

Approximation By Trigonometric Polynomials

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Nonperiodic Trigonometric Polynomial Approximation

The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of x to powers of sin(px) where p is a parameter which depends on the dimension of the approximating subspace. The new set does not suf...

Monotone trigonometric approximation

Let f ∈ C[−ω, ω], 0 < ω < π, be nonlinear and nondecreasing. We wish to estimate the degree of approximation of f by trigonometric polynomials that are nondecreasing in [−ω, ω]. We obtain estimates involving the second modulus of smoothness of f and show that one in general cannot have estimates with the third modulus of smoothness.