Shear madness: new orthonormal bases and frames using chirpfunctions

The proportional-bandwidth and constant-bandwidth time-frequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tessellations of the time-frequency plane. While much effort has gone into methods for designing nice wavelet and window functions for these frameworks, little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time-frequency tilings. The authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear, or chirp, in the time-frequency plane, in addition to translate and scale. The new scale-shear fan bases and shift-shear chevron bases are obtained by operating on an existing: wavelet, Gabor (1946), or Wilson basis set with two special unitary warping transformations. In addition to the theoretical benefit of broadening the class of valid time-frequency plane tilings, these new bases could possibly also be useful for representing certain types of signals, such as chirping and dispersed signals     

Pseudo affine Wigner distributions: definition and kernelformulation

We introduce a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand (1992), these new time-scale distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the proportional bandwidth smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components. To formalize their place within the echelon of the affine class of time-scale distributions (TSDs), we introduce and study an alternative set of generators for this class     

An adaptive optimal-kernel time-frequency representation

Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal-dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line implementation or for tracking signal components with characteristics that change with time. The time-frequency representation developed in the present paper, based on a signal-dependent radially Gaussian kernel that adapts over time, surmounts these difficulties. The method employs a short-time ambiguity function both for kernel optimization and as an intermediate step in computing constant-time slices of the representation. Careful algorithm design provides reasonably efficient computation and allows on-line implementation. Certain enhancements, such as cone-kernel constraints and approximate retention of marginals, are easily incorporated with little additional computation. While somewhat more expensive than fixed kernel representations, this new technique often provides much better performance. Several examples illustrate its behavior on synthetic and real-world signals     

Signal transform covariant to scale changes

A unitary signal transformation that is covariant by translation to scale changes (dilations and compressions) in the signal is formulated and justified. Unlike the Mellin transform, which is invariant to scale changes, this new transform is a true indicator of the scale content of a signal.<>     

Unitary equivalence: a new twist on signal processing

Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature     

Nasal secretion analysis in allergic rhinitis, cystic fibrosis, and nonallergic fibromyalgia/chronic fatigue syndrome subjects

Vascular surgery can be safely performed in approximately 60% of patients with advanced peripheral vascular disease, because of the high frequency of concomitant coronary artery disease and consequent increased risk of perioperative cardiac complications. The aim of this study was to validate the hypothesis that endovascular revascularization could be safely applied to high-cardiac-risk patients with a lower incidence of perioperative cardiac complications. One hundred and fourteen patients with peripheral vascular disease referred for revascularization underwent preoperatively a clinical and echocardiographic evaluation, at rest and under dipyridamole stress test, to assess the cardiac risk. Patients with high clinical score (according to Goldman and Detsky), or low left ventricular ejection fraction at rest, or positive dipyridamole stress test, were considered at high cardiac risk. To record adverse cardiac events, all patients were monitored during surgery, postoperatively, and followed up for 18 months after hospital discharge. Forty-eight patients (42%) were found to be at high cardiac risk. In this high-cardiac-risk group, endovascular surgery was performed in 37/48 patients (77%) (group A), while the remaining 11/48 patients (23%) were bypassed with open surgery (group B). Postoperative cardiac complications occurred in 16% of patients in group A and in 45% of patients in group B with two deaths (p < 0.05). At follow-up, 51% of patients in group A and 44% of patients in group B had suffered late cardiac events (p=ns), with 10 deaths in group A and three deaths in group B (p=ns). Limb salvage rate was similar in the two groups (95% group A, 100% group B; p=ns). These data show that high-cardiac-risk patients with limb-threatening ischemia have significantly less perioperative cardiac complications when treated by endovascular procedures instead of bypass surgery. Follow-up data on cardiac events confirm the severity of concomitant coronary artery disease in patients with peripheral vascular disease.     

Aminopeptidase activity in human nasal mucosa

BACKGROUND: Aminopeptidases activate bradykinin and degrade many inflammatory peptides. OBJECTIVE: The objective of this study was to identify the types of aminopeptidase activities in human nasal mucosa. METHODS: Human nasal mucosa was homogenized (n = 12), and cytoplasmic (S2) and membrane-rich (P2) fractions were obtained. Several aminopeptidase (Ap) activities were defined by (1) substrate specificity with leucine-enkephalin (leu-Ap) and alanine-nitroanilide (ala-Ap), (2) inhibitor studies with puromycin and bestatin, (3) enzyme activity histochemistry (zymography), (4) immunohistochemistry, and (5) gel electrophoresis. Human volunteers had methacholine, histamine, and allergen nasal provocations to determine the mechanisms controlling nasal aminopeptidase secretion in vivo. RESULTS: P2 was the largest reservoir of puromycin-resistant aminopeptidase activity (630 pmol leu-enk/min/mg protein). S2 contained 32 pmol leu-enk/min/mg activity, with 80% representing puromycin-resistant activity and 20% puromycin-sensitive aminopeptidase (PS-Ap). Ala-Ap was detected in both P2 and S2 fractions and was localized by zymography to epithelial and gland cells. Anti-rat brain-soluble PS-Ap IgG detected immunoreactive material in epithelium, glands, and endothelium. In nasal provocation studies, leu-AP correlated with glandular exocytosis but not vascular leak. CONCLUSIONS: The predominant aminopeptidase in human nasal epithelial and submucosal gland cells was membrane-bound puromycin-resistant aminopeptidase. A novel soluble puromycin-resistant aminopeptidase and lower amounts of soluble PS-Ap were also detected.     

Joint Distributions of Arbitrary Variables Made Easy

We propose a simple framework for studying certain distributions of variables beyond time-frequency and time-scale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, the method can generate many distributions previously attainable only by the general construction of Cohen, including distributions of time versus inverse frequency, time versus Mellin transform (scale), and time versus chirp. In addition to providing insight into these new signal analysis tools, warp-based distributions have efficient implementations for potential use in applications.     

Locating available bandwidth bottlenecks

The spatio-temporal available bandwidth estimator (STAB), a new edge-based probing tool, locates thin links - those links with less available bandwidth than all the links preceding them - on end-to-end network paths. By localizing thin links, STAB facilitates network operations and troubleshooting, provides insight into what causes network congestion, and aids network-aware applications. The tool uses special chirp-probing trains, featuring an exponential flight pattern of packets, which have the advantage of employing few packets while giving an accurate estimate of available bandwidth.