Power Spectra of Stationary Signals

2019 ◽  
pp. 175-191
Author(s):  
Wojbor A. Woyczyński
Keyword(s):  
Power Spectra ◽  
Stationary Signals

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.

Testing Parameterizations of Submesoscale Ocean Variability: Resolutions and Power Spectra

2007 ◽  
Author(s):  
Alexey Kaplan ◽  
Huei-Ping Huang ◽  
Enrique N. Curchitser ◽  
William G. Large
Keyword(s):  
Power Spectra ◽  
Ocean Variability

scholarly journals Aperiodic Flux Variability in A 0535+262

1996 ◽  
Vol 165 ◽  
pp. 313-319
Author(s):  
Mark H. Finger ◽  
Robert B. Wilson ◽  
B. Alan Harmon ◽  
William S. Paciesas
Keyword(s):  
Neutron Star ◽  
Gamma Ray ◽  
Beat Frequency ◽  
Power Spectra ◽  
Center Frequency ◽  
X Ray ◽  
Binary Pulsar ◽  
Transient Source ◽  
Flux Variability ◽  
Burst And Transient Source

A “giant” outburst of A 0535+262, a transient X-ray binary pulsar, was observed in 1994 February and March with the Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory. During the outburst power spectra of the hard X-ray flux contained a QPO-like component with a FWHM of approximately 50% of its center frequency. Over the course of the outburst the center frequency rose smoothly from 35 mHz to 70 mHz and then fell to below 40 mHz. We compare this QPO frequency with the neutron star spin-up rate, and discuss the observed correlation in terms of the beat frequency and Keplerian frequency QPO models in conjunction with the Ghosh-Lamb accretion torque model.

scholarly journals Bayesian modeling and significant features exploration in wavelet power spectra

2007 ◽  
Vol 14 (1) ◽  
pp. 79-88 ◽  
Author(s):  
D. V. Divine ◽  
F. Godtliebsen
Keyword(s):  
Data Analysis ◽  
Traditional Approach ◽  
Statistical Significance ◽  
Power Spectra ◽  
Simulated Data ◽  
Scale Space ◽  
Independent Random Variables ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Testing Procedures

Abstract. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.

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