An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Four-week short chain fructo-oligosaccharides ingestion leads to increasing fecal bifidobacteria and cholesterol excretion in healthy elderly volunteers

<p>Abstract</p> <p>Background</p> <p>Short-chain fructo-oligosaccharides (scFOS) are increasingly used in human diet for their prebiotic properties. We aimed at investigating the effects of scFOS ingestion on the colonic microflora and oro-fecal transit time in elderly healthy humans.</p> <p>Methods</p> <p>Stools composition, oro-fecal transit time, and clinical tolerance were evaluated in 12 healthy volunteers, aged 69 ± 2 yrs, in three consecutive periods: basal period (2 weeks), scFOS (Actilight^®) ingestion period (8 g/d for 4 weeks) and follow-up period (4 weeks). Two-way ANOVA, with time and treatment as factors, was used to compare the main outcome measures between the three periods.</p> <p>Results</p> <p>Fecal bifidobacteria counts were significantly increased during the scFOS period (9.17 ± 0.17 log cfu/g vs 8.52 ± 0.26 log cfu/g during the basal period) and returned to their initial values at the end of follow-up (8.37 ± 0.21 log cfu/g; P < 0.05). Fecal cholesterol concentration increased during the scFOS period (8.18 ± 2.37 mg/g dry matter vs 2.81 ± 0.94 mg/g dry matter during the basal period) and returned to the baseline value at the end of follow-up (2.87 ± 0.44 mg/g dry matter; P < 0.05). Fecal pH tended to decrease during scFOS ingestion and follow-up periods compared to the basal period (P = 0.06). Fecal bile acids, stool weight, water percentage, and oro-fecal transit time did not change throughout the study. Excess flatus and bloating were significantly more frequent during scFOS ingestion when compared to the basal period (P < 0.05), but the intensity of these symptoms was very mild.</p> <p>Conclusion</p> <p>Four-week 8 g/d scFOS ingestion is well tolerated and leads to a significant increase in fecal bifidobacteria in healthy elderly subjects. Whether the change in cholesterol metabolism found in our study could exert a beneficial action warrants further studies.</p