Fourier-type integral transforms in modeling of transversal oscillation

Abstract

Envelope detection and measurement has important applications in many domains such as instrumentation, sensors characterization, analog and digital communications. Instead of other envelope detection methods that use analog circuits or digital filters, we propose an electronic circuit that operates measurement in coherent mode. After reproduction of the input wave frequency using direct digital synthesizer, we place the envelope on a new low reference frequency signal followed by an analog measurement block based on analog multipliers and low-pass filters. Design circuit, simulation and experimental results are presented to validate the measurement for different values of input and reference frequencies.

On Fourier–Bessel matrix transforms and applications

“…The reader may refer to, for example, previous studies. [1][2][3][4][5][6][7][8][9][10][11][12] Among the many classical integral transforms is Fourier-Bessel transform (also designated as Hankel transform) that is a fundamental tool in many areas of mathematical statistics, physics, engineering, probability theory, analytic number theory, data analysis, and so on (see, for instance, previous studies [13][14][15][16][17][18][19] ). Many researchers regard ℌ{g(𝜂); q} = ∫ ∞ 0 q 𝔍 m (𝜂q) g(𝜂) d𝜂, q > 0, (1.1) the standard Fourier-Bessel transform involving the mth-order Bessel function of the first kind 𝔍 m (𝜂) as a kernel.…”

“…They are also useful in evaluating integrals involving special functions. The reader may refer to, for example, previous studies 1–12 …”