Fourier Analysis Of Signals Research Articles

On harmonic analysis of vector‐valued signals

A vector‐valued signal in N dimensions is a signal whose value at any time instant is an N‐dimensional vector, that is, an element of . The sum of an arbitrary number of such signals of the same frequency is shown to trace an ellipse in N‐dimensional space, that is, to be confined to a plane. The parameters of the ellipse (major and minor axes, represented by N‐dimensional vectors; and phase) are obtained algebraically in terms of the directions of oscillation of the constituent signals, and their phases. It is shown that the major axis of the ellipse can always be determined algebraically. That is, a vector, whose value can be computed algebraically (without decisions or comparisons of magnitude) from parameters of the constituent signals, always represents the major axis of the ellipse. The ramifications of this result for the processing and Fourier analysis of signals with vector values or samples are discussed, with reference to the definition of Fourier transforms, particularly discrete Fourier transforms, such as have been defined in several hypercomplex algebras, including Clifford algebras. The treatment in the paper, however, is entirely based on signals with values in . Although the paper is written in terms of vector signals (which are taken to include images and volumetric images), the analysis clearly also applies to a superposition of simple harmonic motions in N dimensions. Copyright © 2016 John Wiley & Sons, Ltd.

A Document Retrieval Model Based on Digital Signal Filtering

Information retrieval (IR) systems are designed, in general, to satisfy the information need of a user who expresses it by means of a query, by providing him with a subset of documents selected from a collection and ordered by decreasing relevance to the query. Such systems are based on IR models, which define how to represent the documents and the query, as well as how to determine the relevance of a document for a query. In this article, we present a new IR model based on concepts taken from both IR and digital signal processing (like Fourier analysis of signals and filtering). This allows the whole IR process to be seen as a physical phenomenon, where the query corresponds to a signal, the documents correspond to filters, and the determination of the relevant documents to the query is done by filtering that signal. Tests showed that the quality of the results provided by this IR model is comparable with the state-of-the-art.

THERMOELASTIC STRESS ANALYSIS BY MEANS OF A STANDARD THERMOCAMERA

Thermoelastic analysis is a recently developed full-field, no-contact technique based on detecting temperature changes induced by a dynamic load proportional to its amplitude and synchronous with load history.1 In fact, it is known that a specimen changes its temperature when subjected to cyclic stresses; if the strain is elastic, the temperature change is produced by two main effects: elastoplasticity and thermoelasticity. The first phenomenon is due to microplasticity and energy dissipation inside a material, which causes mechanical energy to be converted into heat. Thermoelasticity can be explained by means of the first law of thermodynamics, whereby an increase in volume under adiabatic conditions is associated with a decrease in temperature, and vice versa.1 Thermoelasticity and elastoplasticity produce very different temperature patterns. The first induces a periodic temperature change, synchronous with loading history and proportional to the actual load amplitude, and the second produces a continuous temperature increment, which is related to both load amplitude and the number of cycles performed, and persists until thermal equilibrium is reached. The thermoelastic effect is usually neglected in standard thermography because it induces very small temperature changes compared to elastoplasticity, but it can be used for stress analysis because it is proportional to the amplitude of the first stress invariant (sum of principal stresses): this can be demonstrated for all isotropic material, with a linear stress/strain behaviour, on the basis of the first law of thermodynamics. In order to detect very small temperature changes (about 0.1 K in steel stressed at 100 MPa), thermoelastic stress measurements require suitable equipment; this is usually obtained by means of highly sensitive infrared detectors and a lock-in amplifier able to isolate that part of the temperature signal that is coherent with the load. Most modern differential thermocameras are equipped with focal plane array detectors and provide a full-field thermoelastic map in few seconds. In the literature, thermoelastic stress analysis (TSA) is usually undertaken using differential thermocameras,2,3 while standard thermocameras are mainly used for thermographic measurements in fatigue limit determination4 and only occasionally for TSA.5 In a previous study,6 the authors introduced a methodology to investigate the thermoelastic effect by means of an ordinary thermocamera; however, the experimental conditions were so strict that they seriously limited the applicability and usefulness of the methodology itself: the specimen had to be uniformly stressed and its constitutive material had to be isotropic. In the present study, these limitations have been overcome, thanks to the availability of a new thermocamera equipped with array detectors and the possibility of validating the results obtained against those provided by a differential thermocamera. The proposed methodology is based on a Fourier analysis of signals, performed through routines in Matlab™ code (The MathWorks, Natick, MA), whereby an accurate full-field thermoelastic map can be obtained from a sequence of standard thermographic images acquired by an ordinary thermocamera if the thermoelastic signal amplitude is estimated after flat-top windowing. As a result, this technique makes it possible to perform a meaningful TSA using a standard thermocamera, of particular benefit whenever, for reasons of cost or infrequent use, it is not possible to justify investing in a differential thermocamera

Wavelet Analysis for Gas Turbine Fault Diagnostics

The application of wavelet analysis to diagnosing faults in gas turbines is examined in the present paper. Applying the wavelet transform to time signals obtained from sensors placed on an engine gives information in correspondence to their Fourier transform. Diagnostic techniques based on Fourier analysis of signals can therefore be transposed to the wavelet analysis. In the paper the basic properties of wavelets, in relation to the nature of turbomachinery signals, are discussed. The possibilities for extracting diagnostic information by means of wavelets are examined, by studying the applicability to existing data from vibration, unsteady pressure, and acoustic measurements. Advantages offered, with respect to existing methods based on harmonic analysis, are discussed as well as particular requirements related to practical application.

Second-order susceptibility determination by Fourier analysis

The macroscopic tensor components of the nonlinear surface susceptibilityXs(2) of monomolecular organic thin films have been determined with high precision using Fourier analysis of signals obtained by polarization rotation of the incident fundamental radiation. Our analysis clearly shows the presence of three complex-valued susceptibility-tensor components and hence the inapplicability of Kleinman's conjecture for a thin film of rotational symmetry around the surface normal. The description of the susceptibility in terms of three tensor components of different phase and magnitude indicates that the usual description within the model of non-interacting rod-like molecules is insufficient to describe the optical nonlinearity of a well-organized Langmuir-Blodgett-type thin film.

Optoelectronic transducer for in vivo recording of oviductal contractile activity.

An optoelectronic instrument to record oviductal muscular activity in chronically instrumented animals was evaluated in in vitro and in vivo experiments. The intensity of red light transmitted through the oviduct was modulated by contractions of the oviductal wall producing an optical analog of the mechanical events. Accuracy of the analog was tested by Fourier analysis of signals from mechanical and optoelectronic transducers placed at the same site on the oviduct; the results validated the use of the optical device as a contraction event sensor. Contractions of the tubal mesenteries had less effect on the optical signal than on signals from extraluminal mechanical transducers. Optical and photographic recordings of luminal transport in exposed oviducts showed a correspondence of intraluminal movements to events in the optical contraction signal. This instrument does not alter tubal function, and thus it is an especially useful experimental tool to investigate the role of oviductal muscular activity in fertility.