Uncertainties of a window mixing estimator for the noise power spectrum of digital signals

The statistical characteristics of several estimators of the noise power spectrum are analysed in this work. Averaged periodogram, Kim’s large subimage and small subimage methods [1] together with windowed periodogram methods using rectangular and Hamming windows and a new window mixing method are studied to obtain their biasing and standard deviation.Sample means and sample standard deviations of the NPS calculations following the different methods are obtained using synthetic images that simulate noise in digital radiography images. In addition, biasing and variance characteristics of the windowed periodograms and the window mixing methods are derived theoretically.Biasing, characteristic of estimators based in periodograms, is eliminated by modifying the periodogram in such a way that it is obtained as the discrete Fourier transform of the unbiased sampled covariance of the signal. Simulations show that Kim’s methods considerably improve the precision of the averaged periodogram, obtaining an important reduction in the sampled standard deviation. Also, the window mixing method, using a convex combination of windowed periodograms with rectangular and Hamming windows, improves the Kim’s methods in terms of standard deviation and has similar biasing.Finally, it is shown that NPS estimators based in the windowed periodogram and in the window mixing methods are unbiased and mean-square consistent, provided that the support of the autocorrelation function of the system PSF is finite.     

Spectral Estimation by Variable Span Log Periodogram Smoothing: An Application to Annual Lynx Numbers

Spectral estimation is commonly based on smoothing the periodogram or its logarithm. In such a smoothing exercise, it is not entirely sensible to use the same bandwidth for all frequencies, since the smoothness of the underlying spectrum may vary. This note describes the use of a variable span smoother in estimating the log spectrum. An application to annual lynx data is presented.     

The significance threshold for coherence when using the Welch's periodogram method: Effect of overlapping segments

A classical tool to identify coupling mechanisms between two biological signals is transfer function (TF) analysis, commonly estimated by the Welch's periodogram method. However, the reliability of TF estimation depends on the coherence function, an index of linear coupling in the frequency domain. Thus, a threshold value has to be determined before assuming a coupling between two signals at a given frequency.Koopmans (The spectral analysis of time series) proposed a theoretical expression in the case of non-overlapping segments. Overlapping segments, however, improves the estimation of TF.In the present study, a modification of the expression by Koopmans is proposed for taking into account the effect of the overlapping procedure, including the most common case of a 50% overlapping ratio. Simulation tests were done on non-coherent signals (using the Hanning window), and a Kolmogorov–Smirnov test was used to check for the adequacy with the proposed threshold formula. The results showed that for an overlapping ratio of 50%, no statistical difference could be found (P > 0.05), except when using less than seven segments.The method has been applied to the computation of the transfer function between systolic blood pressure and heart rate.     

Bright Light Therapy: Improved Sensitivity to Its Effects on Rest-Activity Rhythms in Alzheimer Patients by Application of Nonparametric Methods

Sleep-wake rhythm disturbances in patients with Alzheimer's disease (AD) make a strong demand on caregivers and are among the most important reasons for institutionalization. Several previous studies reported that the disturbances improve with increased environmental light, which, through the retinohypothalamic tract, activates the suprachiasmatic nucleus (SCN), the biological clock of the brain. The data of recently published positive and negative reports on the effect of bright light on actigraphically assessed rest-activity rhythms in demented elderly were reanalyzed using several statistical procedures. It was demonstrated that the light-induced improvement in coupling of the rest-activity rhythm to the environmental zeitgeber of bright light is better detected using nonparametric procedures. Cosinor, complex demodulation, and Lomb-Scargle periodogram-derived variables are much less sensitive to this effect because of the highly nonsinusoidal waveform of the rest-activity rhythm. Guidelines for analyses of actigraphic data are given to improve the sensitivity to treatment effects in future studies.     

24‐H entrainment and ultradian fluctuations in the activity of the lizard Gallotia galloti galloti (sauria‐lacertidae)

Abstract

Activity data from two experimental lizard groups were analysed in order to search for 24 h‐entrained and ultradian periodicities. The data of a first group were obtained through motion sensitive platforms situated under the animals’ cage and continuously for up to 12 consecutive days; those from a second group were collected by manual recording of the behaviour patterns of individual animals for 2 h each day over a 10‐day period. Lizards from both groups were situated in cages inside isolated chambers in which a light‐dark cycle (12:12), a temperature of 28°C ±1° and a relative humidity of 50–60% were maintained. Periodogram analysis showed the existence of a significant period peak (p < 0.01) at 24 h. Autocorrelation functions and spectral analysis of different data‐segment lengths showed that ultradian periodicities were present in the daily motor activity, appearing as noisy though frequency‐band limited. Differences in the frequency band‐limited fluctuations were found between morning and afternoon activities: during the morning ultradian activity appears distributed in two bands (4.5–36 c/day and 63–94 c/day), the power being mainly concentrated in the second one, while during the afternoon it was in the 4.5–36 c/day band. Results from the second lizard group showed only one band (24–60 c/day) overlapped with the first one from the latter group. Although activity recording methods and some experimental conditions are discussed as possible sources of these differences, the possibility of endogenous ultradian variation within the individuals is also suggested.     

Predictability of baroreflex sensitivity induced by phenylephrine injection via frequency domain indices computed from heart rate and systolic blood pressure signals during deep breathing

Diminished baroreflex sensitivity (BRS) is related to increased risk of sudden cardiac death in myocardial infarction patients and can be used as an indicator for risk level. The BRS is traditionally estimated invasively using vasoactive drugs, such as phenylephrine injection. This method has been widely accepted as a standard in clinical research. Due to its clinical importance, alternative BRS assessment methods have been investigated over the years to eliminate the use of drugs. In this study, the BRS obtained by drug-based (pharmacological) assessment was predicted from a subset of non-pharmacological indices computed from heart rate and systolic pressure signals. In the first phase of a two-phase experimental paradigm, 16 subjects were asked to perform two deep breathings with a 2-min delay in between. In the second phase, the BRS was measured by phenylephrine injection. Indices computed from the first phase describing the spectral and time domain properties of the heart rate and systolic pressure signals were used as predictors to estimate the pharmacological BRS of each subject. In addition to individual spectrum of beat-to-beat interval and systolic blood pressure, indices from cross-spectrum were also computed and evaluated as predictors. A leave one out method was employed to estimate the generalization capacity of the system and explore subset of indices, which gives the highest correlation between pharmacological and predicted BRS. Two predictors provided the highest correlation (r = 0.87, p = 1.16 × 10⁻⁵) with pharmacological BRS. The algorithm selected consistently normalized cross-power about the Mayer frequency and average magnitude square coherence in the high frequency band as predictors. These results indicate that the pharmacological BRS can be estimated from the combination of non-pharmacological spectral indices computed from beat-to-beat interval and systolic blood pressure signals obtained during deep breathing and therefore may eliminate the use of drugs.     

Bright Light Therapy: Improved Sensitivity to Its Effects on Rest-Activity Rhythms in Alzheimer Patients by Application of Nonparametric Methods

Sleep-wake rhythm disturbances in patients with Alzheimer's disease (AD) make a strong demand on caregivers and are among the most important reasons for institutionalization. Several previous studies reported that the disturbances improve with increased environmental light, which, through the retinohypothalamic tract, activates the suprachiasmatic nucleus (SCN), the biological clock of the brain. The data of recently published positive and negative reports on the effect of bright light on actigraphically assessed rest-activity rhythms in demented elderly were reanalyzed using several statistical procedures. It was demonstrated that the light-induced improvement in coupling of the rest-activity rhythm to the environmental zeitgeber of bright light is better detected using nonparametric procedures. Cosinor, complex demodulation, and Lomb-Scargle periodogram-derived variables are much less sensitive to this effect because of the highly nonsinusoidal waveform of the rest-activity rhythm. Guidelines for analyses of actigraphic data are given to improve the sensitivity to treatment effects in future studies.     

TRANSIENT CHAOS IN INTRACELLULAR DYNAMICS?

Periodogram analyses of the temporal variations of several cellular oscillations occasionally reveal the existence of short duration bands containing a wide range of frequencies. The possibility is considered that these are due to the transient compliance with chaotic conditions.     

Temporal patterns of citrus greasy spot‐induced defoliation of sweet orange cultivars in Brazil

Recôncavo Baiano is an area favourable for the occurrence of citrus greasy spot (CGS) (Mycosphaerella citri), but there has been no study of this pathosystem in Brazil. This work aimed to characterise the temporal patterns of CGS‐induced defoliation in sweet orange cultivars ‘Bahia’ (Washington Navel) and ‘Pêra’. Temperature, rainfall and relative humidity were recorded, as well as weekly defoliation (fallen leaves/canopy m² or m³). Considering the mean of fallen leaves per canopy m², and mean canopy area, the total annual defoliation was estimated to be around 32 000 leaves per plant for ‘Bahia’ and 18 500 for ‘Pêra’ sweet orange. Spectral density analysis showed that defoliation has a 5‐week‐long main cycle for both cultivars. The proportion of symptomatic fallen leaves was never below 0.97. The monthly number of fallen leaves per canopy area was positively correlated with the mean CGS incidence on leaves. Defoliation was significant, resulting in a low leaf density throughout the year. Many defoliation cycles and the very high proportion of symptomatic fallen leaves assure a constant inoculum supply. Based on these results, CGS cannot be considered a minor disease, at least in Recôncavo Baiano.