Measurement of complex signals by quadrature sampling with filtering

AbstractAriel’s ambitious goal to survey a quarter of known exoplanets will transform our knowledge of planetary atmospheres. Masses measured directly with the radial velocity technique are essential for well determined planetary bulk properties. Radial velocity masses will provide important checks of masses derived from atmospheric fits or alternatively can be treated as a fixed input parameter to reduce possible degeneracies in atmospheric retrievals. We quantify the impact of stellar activity on planet mass recovery for the Ariel mission sample using Sun-like spot models scaled for active stars combined with other noise sources. Planets with necessarily well-determined ephemerides will be selected for characterisation with Ariel. With this prior requirement, we simulate the derived planet mass precision as a function of the number of observations for a prospective sample of Ariel targets. We find that quadrature sampling can significantly reduce the time commitment required for follow-up RVs, and is most effective when the planetary RV signature is larger than the RV noise. For a typical radial velocity instrument operating on a 4 m class telescope and achieving 1 m s−1 precision, between ~17% and ~ 37% of the time commitment is spent on the 7% of planets with mass Mp < 10 M⊕. In many low activity cases, the time required is limited by asteroseismic and photon noise. For low mass or faint systems, we can recover masses with the same precision up to ~3 times more quickly with an instrumental precision of ~10 cm s−1.

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Why simple quadrature is just as good as Monte Carlo

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2055 ◽

2020 ◽

Vol 26 (1) ◽

pp. 1-16

Author(s):

Kevin Vanslette ◽

Abdullatif Al Alsheikh ◽

Kamal Youcef-Toumi

Keyword(s):

Monte Carlo ◽

Random Sampling ◽

Bayesian Probability ◽

Independent Factor ◽

Worst Case ◽

Statistical Equivalence ◽

Deterministic Sampling ◽

Quadrature Methods ◽

Quadrature Sampling ◽

Simple Quadrature

AbstractWe motive and calculate Newton–Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that MC random sampling is statistically indistinguishable from a method that uses deterministic sampling on a randomly shuffled (permuted) function. We use this statistical equivalence to regularize the form of permissible Bayesian quadrature integration priors such that they are guaranteed to be objectively comparable with MC. This leads to the proof that simple quadrature methods have expected variances that are less than or equal to their corresponding theoretical MC integration variances. Separately, using Bayesian probability theory, we find that the theoretical standard deviations of the unbiased errors of simple Newton–Cotes composite quadrature integrations improve over their worst case errors by an extra dimension independent factor {\propto N^{-\frac{1}{2}}}. This dimension independent factor is validated in our simulations.

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Acoustic tomography of dynamic processes in a sea shelf zone with the use of complex signals

Acoustical Physics ◽

10.1134/1.1435382 ◽

2002 ◽

Vol 48 (1) ◽

pp. 1-7 ◽

Cited By ~ 5

Author(s):

V. A. Akulichev ◽

V. V. Bezotvetnykh ◽

S. I. Kamenev ◽

E. V. Kuz’20min ◽

Yu. N. Morgunov ◽

...

Keyword(s):

Shelf Zone ◽

Dynamic Processes ◽

Acoustic Tomography ◽

Complex Signals

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A new quadrature sampling and reconstruction technique and computer simulation of its performances

2004 International Conference on Communications, Circuits and Systems (IEEE Cat. No.04EX914) ◽

10.1109/icccas.2004.1346304 ◽

2004 ◽

Cited By ~ 2

Author(s):

Ren Gang ◽

Xu Jiapin ◽

Wang HongHui ◽

Jiang Lu

Keyword(s):

Computer Simulation ◽

Reconstruction Technique ◽

Sampling And Reconstruction ◽

Quadrature Sampling

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Complex wave digital filters for the analysis of complex signals

10.1109/icassp.1986.1169298 ◽

2005 ◽

Author(s):

N. Nagai ◽

M. Suzuki

Keyword(s):

Digital Filters ◽

Complex Signals ◽

Complex Wave ◽

Wave Digital Filters

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Dynamics and Bifurcations in Networks Designed for Frequency Conversion

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421300378 ◽

2021 ◽

Vol 31 (12) ◽

pp. 2130037

Author(s):

Visarath In ◽

Antonio Palacios

Keyword(s):

Collective Behavior ◽

Frequency Conversion ◽

Signal Frequency ◽

Complex Signals ◽

Multiple Frequencies ◽

Basic Ideas ◽

The Individual ◽

Parallel Arrays ◽

To Receive ◽

Down Conversion

This article reviews recent progress in signal frequency up-conversion and down-conversion, both theory and experiments with network implementations. The fundamental idea is to exploit the inherent symmetry of networks to produce collective behavior in which certain oscillators tend to oscillate at different frequencies. This concept is significantly different from other techniques, e.g. master-slave systems, in the sense that the collective behavior arises naturally from the mutual interactions of the individual units, and without any external forcing. In this manuscript, we present a comprehensive review of the basic ideas, methods, and experiments of the symmetry-based phenomenon of frequency conversion. In addition, we present a review of a device implementation of a broad spectrum analyzer, which motivated the development of systematic methods to up- and down-convert frequencies of oscillations. This device is made up of large parallel arrays of analog nonlinear oscillators with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles.

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