On the existence of discrete Wigner distributions

O'Neill, J.C.; Flandrin, Patrick; Williams, William J.

doi:10.1109/97.803429

Cited by 47 publications

(22 citation statements)

References 5 publications

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“…This distribution, which, here, is called R-WD, satisfies mathematical properties analogous to those satisfied by the continuous WD. Note that (2) has also been proposed by O'Neill et al for odd-length signals [5]. The authors have used an axiomatic approach, which was extended in [6] to derive a discrete Cohen class.…”

Section: A Discrete Wdsmentioning

confidence: 99%

“…The detection problem considered has been solved in the continuous-time continuous-frequency domain in [2]. Here, it is considered in the discrete case as (5) where is the Gaussian signal to be detected, characterized by the mean and the covariance . The additive noise is zero-mean, Gaussian, and white with variance .…”

Section: Discrete Tf Formulations Of Optimum Detectionmentioning

confidence: 99%

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Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions

Richard

2002

IEEE Trans. Signal Process.

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Abstract-During the last decade, a comprehensive theory for optimum time-frequency (TF)-based detection has been developed. This was originally proposed in the continuous-time continuous-frequency case. This paper deals with detectors operating on discrete-time discrete-frequency Wigner distributions (WDs). The purpose is to discuss some existing definitions of this distribution within the context of TF-based detection and selecting those that do not affect the performance of the decision device with which they are associated. This question is of interest since there exist several approches for discretizing the WD, sometimes resulting in a loss of fundamental properties. First, the discrete-time discrete-frequency formulations of optimum detection are investigated. Next, the problem of the design of TF-based detectors from training data, keeping in mind severe effects of the curse of dimensionality, is considered.

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Section: A Discrete Wdsmentioning

confidence: 99%

Section: Discrete Tf Formulations Of Optimum Detectionmentioning

confidence: 99%

Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions

Richard

2002

IEEE Trans. Signal Process.

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“…The instantaneous amplitude related to the AC cardiac, venous and the DC PPG signals were estimated by using SPWVD technique. For a discrete sequence s[n], the discrete SPWVD [14], [15] can be expressed as shown in Eq. 4.…”

Section: B Instantaneous Saturation Estimationmentioning

confidence: 99%

Estimation of Venous oxygenation saturation using the finger Photoplethysmograph (PPG) waveform

Shafqat

Langford

Pal

et al. 2012

2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-In this study, finger photoplethysmograph data obtained from twelve patients undergoing cardiothoracic surgery were analyzed in order to estimate the venous saturation utilizing the modulations created by the positive pressure ventilation in the AC Photoplethysmograph (PPG) signals. The PPG signals were analyzed in the time-domain using a conventional pulse oximetry algorithm to produce estimations of arterial oxygen saturation. The instantaneous arterial and venous saturations were estimated by utilizing time-frequency analysis technique of Smoothed-pseudo Wigner-Ville Distribution (SPWVD). The results showed that there was no significant difference in the traditionally-derived (time-domain) arterial saturation and the instantaneous arterial saturation. However, the instantaneous venous saturation was found to be significantly lower than the time-domain estimated and instantaneous arterial saturation (P=<0.001).

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“…The time-frequency analysis was carried out using SPWVD instead of more basic Short-Time Fourier transform method as it provides better temporal and frequency resolution, by allowing independent adjustment of frequency and time window lengths. The SPWVD representation for a discrete sequence s[n] can be expressed as (3) (Richman et al;1998;O'Neill et al;1999).…”

Section: Arterial and Venous Blood Oxygen Saturation Estimationmentioning

confidence: 99%

Estimation of instantaneous venous blood saturation using the photoplethysmograph waveform

2015

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Non-invasive estimation of regional venous saturation (SxvO2) using a conventional pulse oximeter could provide a means of obtaining clinically relevant information. This study was carried out in order to investigate the hypothesis that SxvO2 could be estimated by utilising the modulations created by positive pressure ventilation in the photoplethysmograph (PPG) signals. The modulations caused by the mechanical ventilator were extracted from oesophageal PPG signals obtained from 12 patients undergoing cardiothoracic surgery. The signals analysed in this work were acquired in a previous study. For the purpose of this analysis the raw PPG signal was considered to have three major components, ac PPG signal (cardiac related component), a static component or dc PPG signal (created mostly by the absorption of light by surrounding tissue) and the ventilator modulation component. These components were then used to estimate instantaneous arterial blood oxygen saturation (SpO2) and SxvO2 by utilising time-frequency analysis technique of smoothed-pseudo Wigner–Ville distribution (SPWVD). The results showed that there was no significant difference in the traditionally-derived (time-domain) arterial saturation and the instantaneous arterial saturation. However, the instantaneous venous saturation was found to be significantly lower than the estimated time-domain and instantaneous arterial saturation (P = < 0.001, n = 12).

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On the existence of discrete Wigner distributions

Cited by 47 publications

References 5 publications

Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions

Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions

Estimation of Venous oxygenation saturation using the finger Photoplethysmograph (PPG) waveform

Estimation of instantaneous venous blood saturation using the photoplethysmograph waveform

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