Power Spectra of Point Processes

2014 ◽  
pp. 259-336
Author(s):  
Pierre Brémaud
Keyword(s):  
Point Processes ◽  
Power Spectra

scholarly journals Power spectra of random spike fields and related processes

2005 ◽  
Vol 37 (4) ◽  
pp. 1116-1146 ◽  
Author(s):  
Pierre Brémaud ◽  
Laurent Massoulié ◽  
Andrea Ridolfi
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Power Spectra ◽  
Sampling Point ◽  
Birth And Death Processes ◽  
Large Classes ◽  
Random Samples ◽  
Branching Point ◽  
Random Times ◽  
Random Impulse

In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

Power spectra of general shot noises and Hawkes point processes with a random excitation

2002 ◽  
Vol 34 (01) ◽  
pp. 205-222 ◽  
Author(s):  
P. Brémaud ◽  
L. Massoulié
Keyword(s):  
Point Process ◽  
Spectral Measure ◽  
Point Processes ◽  
Marked Point ◽  
Power Spectra ◽  
Random Excitation ◽  
Marked Point Process ◽  
Martingale Measure ◽  
Shot Noise Process ◽  
Power Spectral

We give (i) the Cramér power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.

Power spectra of general shot noises and Hawkes point processes with a random excitation

2002 ◽  
Vol 34 (1) ◽  
pp. 205-222 ◽  
Author(s):  
P. Brémaud ◽  
L. Massoulié
Keyword(s):  
Point Process ◽  
Spectral Measure ◽  
Point Processes ◽  
Marked Point ◽  
Power Spectra ◽  
Random Excitation ◽  
Marked Point Process ◽  
Martingale Measure ◽  
Shot Noise Process ◽  
Power Spectral

We give (i) the Cramér power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.

scholarly journals Power spectra of random spike fields and related processes

2005 ◽  
Vol 37 (04) ◽  
pp. 1116-1146 ◽  
Author(s):  
Pierre Brémaud ◽  
Laurent Massoulié ◽  
Andrea Ridolfi
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Power Spectra ◽  
Sampling Point ◽  
Birth And Death Processes ◽  
Large Classes ◽  
Random Samples ◽  
Branching Point ◽  
Random Times ◽  
Random Impulse

In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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