scholarly journals Theoretical Description of the Fourier Transform of the Absolute Amplitude Spectra and Its Applications

10.5772/15368 ◽  
2011 ◽  
Author(s):  
Levente Csoka ◽  
Vladimir Djokovic
Keyword(s):  
Fourier Transform ◽  
Theoretical Description ◽  
Amplitude Spectra ◽  
Absolute Amplitude ◽  
The Absolute ◽  
The Fourier Transform

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

A transient technique for seismograph calibration

1962 ◽  
Vol 52 (4) ◽  
pp. 767-779
Author(s):  
A. F. Espinosa ◽  
G. H. Sutton ◽  
H. J. Miller
Keyword(s):  
Fourier Transform ◽  
Steady State ◽  
Input Pulse ◽  
Electrical Signal ◽  
Experimental Results ◽  
Response Curves ◽  
Amplitude Response ◽  
Transient Technique ◽  
Absolute Amplitude ◽  
The Fourier Transform

abstract A transient technique for seismograph calibration was developed and tested by a variety of methods. In the application of this technique a known transient in the form of an electrical signal is injected, through (a) a Willmore-type calibration bridge or (b) an independent coil, into the seismometer and the corresponding output transient of the system is recorded. The ratio of the Fourier transform of this transient to that of the input pulse yields phase and relative amplitude response of the seismograph as a function of period. Absolute amplitude response may be calculated if two easily determined constants of the seismometer are known. This technique makes practical the daily calibration of continuously-recording seismographs without disturbing the instruments more than a very few minutes. The transient technique was tested and proven satisfactory with results of more conventional steady-state methods, using both digital and analog analyses of the output transients. A variety of output transients corresponding to various theoretical response curves has been calculated for two standard input transients. By comparison of the calculated output transients with experimental results it is possible to obtain the response of the instrument with considerable precision quickly and without computation.

scholarly journals Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
J. A. Tenreiro Machado ◽  
António M. Lopes
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Vector Field ◽  
System Dynamics ◽  
Power Law ◽  
System Behavior ◽  
Amplitude Spectra ◽  
The Fourier Transform ◽  
Complex Phenomena ◽  
Power Law Parameters

AbstractIn this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

scholarly journals 27. Intensity distribution across the Cygnus and Cassiopeia sources

1957 ◽  
Vol 4 ◽  
pp. 159-161
Author(s):  
R. C. Jennison
Keyword(s):  
Fourier Transform ◽  
Angular Distribution ◽  
Intensity Distribution ◽  
Phase Measurement ◽  
Frame Of Reference ◽  
Absolute Amplitude ◽  
A New Technique ◽  
The Fourier Transform ◽  
Aerial Systems ◽  
Phase Angles

Measurements of the angular distribution of intensity across the intense discrete sources in Cassiopeia and Cygnus have previously been handicapped by lack of knowledge of the phase of the Fourier transform at very long aerial spacings. The technical difficulties of measuring the phase of the transform and also of calibrating the absolute amplitude have been solved by a new technique involving three stations. This method enables the phase to be measured relative to a frame of reference within the source and obviates the need for retaining the phase angles accurately constant on the removal of one of the aerial systems to a new site. The phase measurement is not limited to observations of the central fringe, and useful measurements may be made on all the fringes contained within the aerial polar diagrams.

Amplitude Spectra of Fitness Landscapes

1998 ◽  
Vol 01 (01) ◽  
pp. 39-66 ◽  
Author(s):  
Wim Hordijk ◽  
Peter F. Stadler
Keyword(s):  
Fourier Transform ◽  
Topological Structure ◽  
Empirical Studies ◽  
Amplitude Spectrum ◽  
Fitness Landscapes ◽  
Configuration Spaces ◽  
Amplitude Spectra ◽  
Different Types ◽  
Reliable Procedure ◽  
The Fourier Transform

Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying configuration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used for classification and comparison purposes. We consider here three very different types of landscapes using both mutation and recombination to define the topological structure of the configuration spaces. A reliable procedure for estimating the amplitude spectra is presented. The method is based on certain correlation functions that are easily obtained from empirical studies of the landscapes.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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