On the realization of band-limited power spectra from partial covariance sequence

1993 ◽  
Vol 39 (4) ◽  
pp. 1395-1397 ◽  
Author(s):  
T. Chonavel ◽  
P. Loubaton
Keyword(s):  
Power Spectra ◽  
Limited Power ◽  
Band Limited

Band‐limited power flow into enclosures. II

1980 ◽  
Vol 67 (3) ◽  
pp. 823-826 ◽  
Author(s):  
L. D. Pope ◽  
J. F. Wilby
Keyword(s):  
Power Flow ◽  
Limited Power ◽  
Band Limited

scholarly journals A unifying principle underlying the extracellular field potential spectral responses in the human cortex

2015 ◽  
Vol 114 (1) ◽  
pp. 505-519 ◽  
Author(s):  
Ella Podvalny ◽  
Niv Noy ◽  
Michal Harel ◽  
Stephan Bickel ◽  
Gal Chechik ◽  
...  
Keyword(s):  
Field Potential ◽  
Neuronal Activation ◽  
Human Cortex ◽  
Neuronal Process ◽  
High Gamma ◽  
Neuronal Processes ◽  
Limited Power ◽  
Visuomotor Tasks ◽  
Band Limited ◽  
Spectrum Slope

Electrophysiological mass potentials show complex spectral changes upon neuronal activation. However, it is unknown to what extent these complex band-limited changes are interrelated or, alternatively, reflect separate neuronal processes. To address this question, intracranial electrocorticograms (ECoG) responses were recorded in patients engaged in visuomotor tasks. We found that in the 10- to 100-Hz frequency range there was a significant reduction in the exponent χ of the 1/ fχ component of the spectrum associated with neuronal activation. In a minority of electrodes showing particularly high activations the exponent reduction was associated with specific band-limited power modulations: emergence of a high gamma (80–100 Hz) and a decrease in the alpha (9–12 Hz) peaks. Importantly, the peaks' height was correlated with the 1/ fχ exponent on activation. Control simulation ruled out the possibility that the change in 1/ fχ exponent was a consequence of the analysis procedure. These results reveal a new global, cross-frequency (10–100 Hz) neuronal process reflected in a significant reduction of the power spectrum slope of the ECoG signal.

scholarly journals Different dynamic resting state fMRI patterns are linked to different frequencies of neural activity

2015 ◽  
Vol 114 (1) ◽  
pp. 114-124 ◽  
Author(s):  
Garth John Thompson ◽  
Wen-Ju Pan ◽  
Shella Dawn Keilholz
Keyword(s):  
Neural Activity ◽  
Attention Deficit Disorder ◽  
Resting State ◽  
Low Frequency ◽  
Resting State Fmri ◽  
Periodic Patterns ◽  
Limited Power ◽  
Band Limited ◽  
Additional Support ◽  
Network Mapping

Resting state functional magnetic resonance imaging (rsfMRI) results have indicated that network mapping can contribute to understanding behavior and disease, but it has been difficult to translate the maps created with rsfMRI to neuroelectrical states in the brain. Recently, dynamic analyses have revealed multiple patterns in the rsfMRI signal that are strongly associated with particular bands of neural activity. To further investigate these findings, simultaneously recorded invasive electrophysiology and rsfMRI from rats were used to examine two types of electrical activity (directly measured low-frequency/infraslow activity and band-limited power of higher frequencies) and two types of dynamic rsfMRI (quasi-periodic patterns or QPP, and sliding window correlation or SWC). The relationship between neural activity and dynamic rsfMRI was tested under three anesthetic states in rats: dexmedetomidine and high and low doses of isoflurane. Under dexmedetomidine, the lightest anesthetic, infraslow electrophysiology correlated with QPP but not SWC, whereas band-limited power in higher frequencies correlated with SWC but not QPP. Results were similar under isoflurane; however, the QPP was also correlated to band-limited power, possibly due to the burst-suppression state induced by the anesthetic agent. The results provide additional support for the hypothesis that the two types of dynamic rsfMRI are linked to different frequencies of neural activity, but isoflurane anesthesia may make this relationship more complicated. Understanding which neural frequency bands appear as particular dynamic patterns in rsfMRI may ultimately help isolate components of the rsfMRI signal that are of interest to disorders such as schizophrenia and attention deficit disorder.

scholarly journals DAYENU: a simple filter of smooth foregrounds for intensity mapping power spectra

2020 ◽  
Vol 500 (4) ◽  
pp. 5195-5213
Author(s):  
Aaron Ewall-Wice ◽  
Nicholas Kern ◽  
Joshua S Dillon ◽  
Adrian Liu ◽  
Aaron Parsons ◽  
...  
Keyword(s):  
Large Scale ◽  
Dynamic Range ◽  
Fourier Transforms ◽  
Power Spectra ◽  
High Dynamic Range ◽  
Spectrum Estimation ◽  
Sampled Data ◽  
Optimal Basis ◽  
Intensity Mapping ◽  
Band Limited

ABSTRACT We introduce DPSS Approximate lazY filtEriNg of foregroUnds (dayenu), a linear, spectral filter for H i intensity mapping that achieves the desirable foreground mitigation and error minimization properties of inverse co-variance weighting with minimal modelling of the underlying data. Beyond 21-cm power-spectrum estimation, our filter is suitable for any analysis where high dynamic-range removal of spectrally smooth foregrounds in irregularly (or regularly) sampled data is required, something required by many other intensity mapping techniques. Our filtering matrix is diagonalized by Discrete Prolate Spheroidal Sequences which are an optimal basis to model band-limited foregrounds in 21-cm intensity mapping experiments in the sense that they maximally concentrate power within a finite region of Fourier space. We show that dayenu enables the access of large-scale line-of-sight modes that are inaccessible to tapered discrete Fourier transform estimators. Since these modes have the largest SNRs,dayenu significantly increases the sensitivity of 21-cm analyses over tapered Fourier transforms. Slight modifications allow us to use dayenu as a linear replacement for iterative delay clean ing (dayenurest). We refer readers to the Code section at the end of this paper for links to examples and code.

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

2007 ◽  
Vol 98 (5) ◽  
pp. 2795-2806 ◽  
Author(s):  
Alexander B. Neiman ◽  
Tatyana A. Yakusheva ◽  
David F. Russell
Keyword(s):  
Power Spectra ◽  
Qualitative Change ◽  
Sine Wave ◽  
Spike Trains ◽  
Broadband Noise ◽  
Noise Stimulus ◽  
Similar Frequency ◽  
Best Response ◽  
Band Limited

The response properties of ampullary electroreceptors of paddlefish, Polyodon spathula, were studied in vivo, as single-unit afferent responses to external electrical stimulation with varied intensities of several types of noise waveforms, all Gaussian and zero-mean. They included broadband white noise, Ornstein–Uhlenbeck noise, low- or high-frequency band-limited noise, or natural noise recorded from swarms of Daphnia zooplankton prey, or from individual prey. Normally the afferents fire spontaneously in a tonic manner, which is actually quasiperiodic due to embedded oscillators. 1) Weak noise stimuli increased the variability of afferent firing, but it remained tonic. 2) In contrast, stimulation with less-weak broadband noise led to a qualitative change of the firing patterns, to parabolic bursting, even though the mean firing rate was scarcely affected. 3) The transition to afferent bursting was marked by the development of two well-separated timescales: the fast frequency of spiking inside bursts at ≤250 spikes/s and the slow frequency of burst occurrences at about 9 (range 5–13) bursts/s. These two timescales were manifested as two regimes in afferent power spectra, bimodal interspike interval histograms, return maps, and autocorrelation functions of afferent spike trains. 4) The stochastic approximately 9-Hz bursts were not simply driven by similar-frequency components of noise stimuli because bursts could be dissociated from stimulus waveforms using high-pass filtered noise, or a 0.1-Hz sine-wave stimulus. 5) Arrhenius plots showed that the threshold noise intensity required to elicit bursting depended on the frequency content of a noise stimulus, being lowest, about 1.2 μV/cm, for stimuli matching the 1- to 20-Hz best response band of these cathodally excited ampullary electroreceptors. This is only slightly higher than previous behavioral estimates of the electrosensory threshold as 0.5 μV/cm. 6) Comparable threshold values for bursting came from an alternate analytical approach, based on correlation times of spike trains. 7) Simultaneous recordings from pairs of afferents showed that their bursting frequencies (bursts/s) always converged as the amplitude of a noise stimulus was raised. Thus the slow timescale of bursting is similar for different electroreceptors, even though their mean spiking rates can differ. In conclusion, the ampullary electroreceptors of paddlefish have two distinct modes of operation: their spontaneous tonic firing is modulated by the weakest stimuli, but they switch to bursting output for less-weak stimuli. We propose that afferent bursting may mediate close-range tracking of planktonic prey.

The determination of the instantaneous velocity of axonally transported organelles from filmed records of their motion

1982 ◽  
Vol 60 (5) ◽  
pp. 670-679 ◽  
Author(s):  
K. J. Koles ◽  
K. D. McLeod ◽  
R. S. Smith
Keyword(s):  
Power Spectra ◽  
Computational Procedure ◽  
Dark Field ◽  
Nerve Fibers ◽  
Low Noise ◽  
Instantaneous Velocity ◽  
Mean Velocity ◽  
Myelinated Nerve ◽  
Motion Picture Film ◽  
Band Limited

A computational procedure is described for obtaining reproducible, low noise estimates of the instantaneous velocity of axonally transported organelles. Axonally transported organelles were detected in myelinated nerve fibers from Xenopus laevis by dark-field microscopy. The motion of the organelles was recorded on motion picture film at 3 frames/s, and the position of organelles travelling in the retrograde direction was obtained as a pair of x (axial) and y (transverse) coordinates at each 0.33-s interval. The trend in organelle movement with time was calculated for each of the series of x and y coordinates by linear regression. This trend was removed from the measurements of x and y to yield sets of trend-free displacements. The trend yielded a measure of the mean velocity of the organelle in each of the two orthogonal directions. Power spectra of the deviations in x and y about the trend were calculated. For 133 particles studied, 99% of the power in the trend-free deviations occurred at frequencies below 0.3 Hz. The peak power in the x and y deviations occurred at a frequency of 0.1 Hz or less. Positional deviations about the trend were treated with a discrete 21-term differentiating filter that attenuated frequencies above 0.3 Hz. Instantaneous velocities for the organelles were obtained by adding the result of the band-limited differentiation to the appropriate estimates of mean velocity. The 21-term method was compared with a commonly used 2-term approximation to a differentiator and was shown to produce velocity estimates with about one order of magnitude less error. Estimates of organelle velocity obtained with the 21-term method indicate that saltatory particle motion may be viewed either as a smooth variation of particle velocity with respect to time or as an irregular, or discontinuous, variation of velocity with respect to particle position.

scholarly journals Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

2020 ◽  
Author(s):  
Qingguang Zhang ◽  
Kyle W. Gheres ◽  
Patrick J. Drew
Keyword(s):  
Neural Activity ◽  
Power Distribution ◽  
Tissue Oxygenation ◽  
Field Potential ◽  
Two Photon ◽  
Stochastic Fluctuations ◽  
Discrete Nature ◽  
Limited Power ◽  
Band Limited ◽  
The Brain

AbstractThe concentration of oxygen in the brain spontaneously fluctuates, and the power distribution in these fluctuations has 1/f-like dynamics. Though these oscillations have been interpreted as being driven by neural activity, the origins of these 1/f-like oscillations is not well understood. Here, to gain insight of the origin of the 1/f-like oxygen fluctuations, we investigated the dynamics of tissue oxygenation and neural activity in awake behaving mice. We found that oxygen signal recorded from the cortex of mice had 1/f-like spectra. However, band-limited power in the local field potential, did not show corresponding 1/f-like fluctuations. When local neural activity was suppressed, the 1/f-like fluctuations in oxygen concentration persisted. Two-photon measurements of erythrocyte spacing fluctuations (‘stalls’) and mathematical modelling show that stochastic fluctuations in erythrocyte flow and stalling could underlie 1/f-like dynamics in oxygenation. These results show discrete nature of erythrocytes and their irregular flow, rather than neural activity, could drive 1/f-like fluctuations in tissue oxygenation.

scholarly journals Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

PLoS Biology ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. e3001298
Author(s):  
Qingguang Zhang ◽  
Kyle W. Gheres ◽  
Patrick J. Drew
Keyword(s):  
Neural Activity ◽  
Tissue Oxygenation ◽  
Field Potential ◽  
Low Frequencies ◽  
Two Photon ◽  
Stochastic Fluctuations ◽  
Discrete Nature ◽  
Limited Power ◽  
Band Limited ◽  
Distribution Of Power

The concentration of oxygen in the brain spontaneously fluctuates, and the distribution of power in these fluctuations has a 1/f-like spectra, where the power present at low frequencies of the power spectrum is orders of magnitude higher than at higher frequencies. Though these oscillations have been interpreted as being driven by neural activity, the origin of these 1/f-like oscillations is not well understood. Here, to gain insight of the origin of the 1/f-like oxygen fluctuations, we investigated the dynamics of tissue oxygenation and neural activity in awake behaving mice. We found that oxygen signal recorded from the cortex of mice had 1/f-like spectra. However, band-limited power in the local field potential did not show corresponding 1/f-like fluctuations. When local neural activity was suppressed, the 1/f-like fluctuations in oxygen concentration persisted. Two-photon measurements of erythrocyte spacing fluctuations and mathematical modeling show that stochastic fluctuations in erythrocyte flow could underlie 1/f-like dynamics in oxygenation. These results suggest that the discrete nature of erythrocytes and their irregular flow, rather than fluctuations in neural activity, could drive 1/f-like fluctuations in tissue oxygenation.

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