Notes on the Theory of Modulation

Carson, John R.

doi:10.1109/jrproc.1922.219793

Cited by 187 publications

(42 citation statements)

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“…In we present a collection of classical formulae that are well known in the physics of telecommunications (Carson 1922; van der Pol 1930; Roder 1931). Some of the more complicated cases (multiple modulations, recursive or cascade modulations) were investigated by mathematicians who developed the theory of electrical sound synthesis in the 1960s and 1970s.…”

Section: Introductionmentioning

confidence: 99%

Blazhko RR Lyrae light curves as modulated signals

Benkő

Szabo

Paparó

2011

Monthly Notices of the Royal Astronomical Society

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We present an analytical formalism for the description of Blazhko RR Lyrae light curves. In this formalism the amplitude and frequency modulations are treated in a manner similar to the theory of electronic signal transmission. We consider monoperiodic RR Lyrae light curves to be carrier waves, and modulate their amplitude (AM), frequency (FM) and phase (PM); as a general case we discuss simultaneous AM and FM. The main advantages of this method are the following: (i) the mathematical formalism naturally explains numerous light‐curve characteristics found in the Blazhko RR Lyrae stars such as mean brightness variations, complicated envelope curves and non‐sinusoidal frequency variations; (ii) our elucidation also explains the properties of the Fourier spectra such as apparent higher order multiplets, amplitude distribution of the sidepeaks, the appearance of the modulation frequency itself and its harmonics. In addition, compared to the traditional methods, our light‐curve solutions reduce the number of necessary parameters. This formalism can be applied to any type of modulated light curves, not just to Blazhko RR Lyrae star light curves.

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Section: Introductionmentioning

confidence: 99%

Blazhko RR Lyrae light curves as modulated signals

Benkő

Szabo

Paparó

2011

Monthly Notices of the Royal Astronomical Society

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“…Indeed, IMFs can be defined as signals (in time or space) that are both amplitude-and frequency-modulated [14]. In [17], we have defined the total practical IMF bandwidth of such an AM-FM signal, as an extension to Carson's rule for FM signal bandwidth [6]:…”

Section: Vmd With Compact Spatial Supportmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L 1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

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“…Applying the Carson's bandwidth rule [18], an approximate evaluation of the ECD rise and fall times (t r ) is given by…”

Section: Effect Of the Ecd Rise/fall Timementioning

confidence: 99%

Characterization of electron clouds in the Cornell Electron Storage Ring Test Accelerator usingTE-wave transmission

Santis

Byrd

Billing

et al. 2010

Phys. Rev. ST Accel. Beams

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A relatively new technique for measuring the electron cloud density in storage rings has been developed and successfully demonstrated [S. De Santis, J. M. Byrd, F. Caspers, A. Krasnykh, T. Kroyer, M. T. F. Pivi, and K. G. Sonnad, Phys. Rev. Lett. 100, 094801 (2008).]. We present the experimental results of a systematic application of this technique at the Cornell Electron Storage Ring Test Accelerator. The technique is based on the phase modulation of the TE mode transmitted in a synchrotron beam pipe caused by the periodic variation of the density of electron plasma. Because of the relatively simple hardware requirements, this method has become increasingly popular and has been since successfully implemented in several machines. While the principles of this technique are straightforward, quantitative derivation of the electron cloud density from the measurement requires consideration of several effects, which we address in detail.

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Notes on the Theory of Modulation

Cited by 187 publications

References 1 publication

Blazhko RR Lyrae light curves as modulated signals

Blazhko RR Lyrae light curves as modulated signals

Two-Dimensional Compact Variational Mode Decomposition

Characterization of electron clouds in the Cornell Electron Storage Ring Test Accelerator usingTE-wave transmission

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