Fourier Entropy Research Articles

Monitoring thermally-induced phase transitions in porcine cornea with the use of fluorescence micro-imaging analysis

Thermal modifications induced in corneal stroma were investigated with the use of fluorescence microscopy. Tissue samples were heated in a water bath at temperatures in the 35-90 degrees C range. Fluorescence images of the structural modifications induced were acquired after staining with Indocyanine Green (ICG). Discrete Fourier Transform (DFT) and entropy analyses of each image made it possible to characterize the thermally-induced phase transitions in the stroma, and to indicate a threshold value for high thermal damage. The procedure could be proposed as the basis for a real-time controlling system for surgical techniques based on induced thermal effects.

Climatic and geomagnetic influences on the Lac du Bouchet palaeomagnetic SV record through the last 110 000 years

Abstract Palaeomagnetic secular variation records stacked from five cores ∼ 20 m long extend back through the last glacial cycle to ∼ 100 000 years ago. The time-scale has been constructed from conventional and accelerator radiocarbon ages back to ∼ 45 Ka BP and beyond this by comprehensive pollen studies which identify forest and steppe cycles that have been related to marine oxygen isotopic stages 4 and 5. Spectral analyses of the intensity and directional records using both Fourier and maximum entropy methods reveal strong low-frequency components which fall in the range of the Milankovitch obliquity and precession periodicities (40-20 Ka). It is concluded that although part of this signal may have fed indirectly into the natural remanence via the influence of climatic change on sediment facies, part has been impressed directly by perturbation of the geomagnetic dynamo process at the core-boundary by variations in the Earth's obliquity and precession. These long periods envelop a well-defined pattern, registered also by the independent ‘Mackereth’ core stack back to 50 Ka BP, of irregular secular oscillations of the geodynamo with periods of a few thousands of years.

A Comparison of Traditional Fourier and Maximum Entropy Spectral Methods for Vibration Analysis

The structural vibrations monitored on a process plant often contain burst phenomena where several discrete frequencies are present. Spectral analysis of these vibration signals by Fourier transform methods is generally considered incapable of resolving discrete frequencies close together in a short time slice. The power spectral density estimates computed by traditional Fourier transform methods are compared with those computed by more recent maximum entropy spectral analysis (MESA) methods for both data from a test system where the outputs of two tuned filters, excited by pseudo-random binary noise, are summed, and the vibration signals from an accelerometer mounted on a die in an extrusion process. The frequency resolution characteristics of the two methods are compared, and the problems associated with the choice of an optimum order autoregressive prediction error filter for the MESA method are discussed.

Frequency resolution of Fourier and maximum entropy spectral estimates

An analytic determination of the frequency resolution for maximum entropy and conventional Blackman‐Tukey spectral estimates is made for the case of known autocorrelation. As the signal‐to‐noise ratio decreases, the maximum entropy resolution is no better than that achievable by the Blackman‐Tukey spectral estimate. The mean resolution of an ensemble of spectra constructed from sampled data sequences agrees with the analytic result.