Orthogonally aliased fourier transforms for the analysis of sparsely populated frequency spectra

1977 ◽  
Vol 124 (6) ◽  
pp. 508 ◽  
Author(s):  
R. Benjamin
Keyword(s):  
Fourier Transforms ◽  
Frequency Spectra

Diagnose Method Based on Spectral Analysis of Measured Parameters

2014 ◽  
Vol 1036 ◽  
pp. 535-540 ◽  
Author(s):  
Radu Vilău ◽  
Marin Marinescu ◽  
Octavian Alexa ◽  
Marian Truta ◽  
Valentin Vinturis
Keyword(s):  
Frequency Analysis ◽  
Fourier Transforms ◽  
Power Spectra ◽  
Time History ◽  
Point Of View ◽  
Mechanical Parameter ◽  
Accurate Analysis ◽  
Frequency Spectra ◽  
Time Frequency ◽  
History Of

The paper presents a possible method to diagnose a mechanical fault of an automotive system. Starting from the point of view that every fault of a mechanical system should introduce an abnormal component within the signal that describes the time history of a mechanical parameter we tried to find a way to reveal it.We were performing some tests involving a military vehicle with respect to the performances of its braking system. The tests were aiming at identifying a way to bring up-to-date the old weapon system from the braking systems point of view. During these tests we observed some anomalies concerning the pressure evolution within the braking cylinders of the vehicle. Some unusual but also systematic noises occurred. As a main issue at this point, the source of the noise should have been identified and filtered if necessary. We had to decide whether the noisy component of the signal is just a noise that should be removed by filtering the signal or it is a physical component of the mechanical parameter itself (not noise but a useful information).These procedures take time and they also request accurate knowledge as well as fine expertise in automotive testing. Since our Dept. has a long and rich practice in this respect, we assumed to processing data and give them a thorough interpretation. So, the first thing we did was to perform a frequency analysis, using classical methods. Usually, a simple frequency analysis cant provide information about a time variation of the frequency spectra due to the Fourier Transforms behavior, since it freezes the signal in time. A much more accurate analysis is the time-frequency analysis. However, observing both the amplitude and power spectra can lead to a useful conclusion. We concluded that the noise we met within the signal is due to the brake drums loss of circular shape (they turned into an oval, the process being known as ovalization). Hence, we cant talk about a noise as it is usually defined.

A Novel Approach to Evaluation of Vibration Source Separation Based on Spatial Distribution of Sensors and Fourier Transforms

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ali Mahvash ◽  
Aouni A. Lakis
Keyword(s):  
Spatial Distribution ◽  
Fourier Transforms ◽  
A Priori ◽  
Source Separation ◽  
Experimental Tests ◽  
Spatial Distance ◽  
Vibration Source ◽  
Mathematical Methods ◽  
Frequency Spectra ◽  
Multiple Sensors

An obstacle in diagnosis of multicomponent machinery using multiple sensors to acquire vibration data is firstly found in the data acquisition itself. This is due to the fact that vibration signals collected by each sensor are a mixture of vibration produced by different components and noise; it is not evident what signals are produced by each component. A number of research studies have been carried out in which this problem was considered a blind source separation (BSS) problem and different mathematical methods were used to separate the signals. One complexity with applying such mathematical methods to separate vibration sources is that no metric or standard measure exists to evaluate the quality of the separation. In this study, a method based on statistical energy analysis (SEA) is proposed using Fourier transforms and the spatial distance between sensors and components. The principle of this method is based on the fact that each sensor, with respect to its location in the system, collects a different version of the vibration produced in the system. By applying a short time Fourier transform to the signals collected by multiple sensors and making use of a priori knowledge of the spatial distribution of sensor locations with respect to the components, the source of the peaks on the frequency spectra of the signals can be identified and attributed to the components. The performance of the method was verified using a series of experimental tests on synthetic signals and real laboratory signals collected from different bearings and the results confirmed the efficacy of the method.

scholarly journals Comparative structural vibration analysis of machinery and GFRP with Al7075

2018 ◽  
Vol 144 ◽  
pp. 01009
Author(s):  
K. Vinoth Kumar ◽  
T. G. Loganathan ◽  
A. Bharath ◽  
B. Shyam Sundar ◽  
K. K. Abishek
Keyword(s):  
Fourier Transforms ◽  
Fast Fourier Transforms ◽  
Structural Vibration ◽  
Vibrational Properties ◽  
Frequency Spectra ◽  
Metal Fabrication ◽  
Current Scenario ◽  
Vibration Signature ◽  
Vibration Signatures ◽  
A Company

The current scenario of the industries is that the major losses in efficiency of a machine are due to vibration and friction. To reduce the detrimental effects of vibration we need to decrease the frequency and amplitude of vibration or completely eliminate vibration. To do that one must quantify vibration that already occurs in machinery and structural components. Which is the aim of this paper. The intention of the paper is to obtain and characterize the vibration signature of equipment used in a company and composite material. We have designed a setup to vibrational properties composites, vibrational signature of industrial equipment .To study vibration properties, micro-electrical mechanical systems (MEMS) based accelerometers are used to measure acceleration of the material about the datum when displaced. The data obtained is processed in MATLAB using ARDUINO relayed to computer to convert the data to frequency spectra using Fast-Fourier transforms (FFT). We ultimately compared the vibrational properties of two lathes used at a metal fabrication plant operating at different Conditions and quantified the vibration results using Fast Fourier Transforms (FFT) algorithm. The vibration signatures of a composite is studied along with which various properties like Damping Coefficient, Free Vibration, GFRP, Natural Frequency applications are studied.

Observational Data: Detailed Characteristics in the Frequency Domain

2017 ◽  
Author(s):  
Sarbani Basu ◽  
William J. Chaplin
Keyword(s):  
Frequency Domain ◽  
Observational Data ◽  
Frequency Spectrum ◽  
Fourier Transforms ◽  
Frequency Spectra ◽  
The Impact ◽  
Frequency Domain Properties

This chapter details the frequency-domain properties of observational data on stars. It is from the analysis of the frequency spectrum of the observations that the asteroseismic parameters are usually extracted. The chapter looks at each of the intrinsic stellar contributions in turn, always with an eye to how each must be handled in the asteroseismic analysis. It also considers the impact on the analysis of gaps in the data. In performing the analyses, this chapter begins by covering practical fundamentals associated with estimation of the frequency spectra, which underpin everything that follows. In addition, this chapter will be making use of Fourier transforms in studying the data.

Reconciliation of the discrete and integral Fourier transforms

Geophysics ◽  
1982 ◽  
Vol 47 (2) ◽  
pp. 237-243 ◽  
Author(s):  
Lindrith Cordell ◽  
V. J. S. Grauch
Keyword(s):  
High Frequency ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Large Data ◽  
Fourier Integral ◽  
Input Function ◽  
Frequency Spectra ◽  
Discrete Fourier Analysis ◽  
Band Limited ◽  
Discrete Transform

In the application of harmonic analysis to potential‐field geophysical studies, relationships derived in terms of the continuous Fourier integral transform are evaluated in terms of the discrete Fourier transform. The discrete transform, obtained by transforming a finite number of equispaced samples of the actual aperiodic continuous function, is too low at the dc level and increasingly too high in the high frequencies, compared with the theoretical integral transform. As a consequence, overly restrictive limitations must be placed on high‐frequency‐amplifying operators such as differentiation and downward continuation. Also, a spurious and troublesome azimuthal distortion occurs in the discrete Fourier analysis of three‐dimensional (3-D) (map) data represented as grids. The discrete transform can be made essentially equivalent to the integral transform if, before sampling, the continuous aperiodic input function is made periodic by shifting the function by integer multiples of the data interval and summing. Doing so requires extrapolation of the data function beyond the limits of the data interval. An equivalent‐source technique illustrates the principle. For practical application to large data sets, a high‐frequency band‐limited filter determined by the low‐frequency spectra accomplishes an analogous extrapolation in the frequency domain.

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

Observations of Frozen-Hydrated Microtubules

1990 ◽  
Vol 48 (1) ◽  
pp. 504-505
Author(s):  
D. Chrétien ◽  
D. Job ◽  
R.H. Wade
Keyword(s):  
Fourier Transforms ◽  
Structural Complexity ◽  
Image Contrast ◽  
Phase Behaviour ◽  
Experimental Conditions ◽  
Thin Sections ◽  
Surface Lattice ◽  
Cilia And Flagella ◽  
Outstanding Question

Microtubules are filamentary structures found in the cytoplasm of eukaryotic cells, where, together with actin and intermediate filaments, they form the components of the cytoskeleton. They have many functions and show various levels of structural complexity as witnessed by the singlet, doublet and triplet structures involved in the architecture of centrioles, basal bodies, cilia and flagella. The accepted microtubule model consists of a 25 nm diameter hollow tube with a wall made up of 13 paraxial protofilaments (pf). Each pf is a string of aligned tubulin dimers. Some results have suggested that the pfs follow a superhelix. To understand how microtubules function in the cell an accurate model of the surface lattice is one of the requirements. For example the 9x2 architecture of the axoneme will depend on the organisation of its component microtubules. We should also note that microtubules with different numbers of pfs have been observed in thin sections of cellular and of in-vitro material. An outstanding question is how does the surface lattice adjust to these different pf numbers?We have been using cryo-electron microscopy of frozen-hydrated samples to study in-vitro assembled microtubules. The experimental conditions are described in detail in this reference. The results obtained in conjunction with thin sections of similar specimens and with axoneme outer doublet fragments have already allowed us to characterise the image contrast of 13, 14 and 15 pf microtubules on the basis of the measured image widths, of the the image contrast symmetry and of the amplitude and phase behaviour along the equator in the computed Fourier transforms. The contrast variations along individual microtubule images can be interpreted in terms of the geometry of the microtubule surface lattice. We can extend these results and make some reasonable predictions about the probable surface lattices in the case of other pf numbers, see Table 1. Figure 1 shows observed images with which these predictions can be compared.

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