Investigation of the Fourier Transform for Analyzing Spectroscopic Data by Computerized Learning Machines

1971 ◽  
Vol 25 (2) ◽  
pp. 203-207 ◽  
Author(s):  
L. E. Wangen ◽  
N. M. Frew ◽  
T. L. Isenhour ◽  
P. C. Jurs
Keyword(s):  
Fourier Transform ◽  
Data Storage ◽  
Spectroscopic Data ◽  
Weighted Average ◽  
Learning Machines ◽  
Frequency Representation ◽  
Data Points ◽  
The Fourier Transform ◽  
Time Required

This paper investigates the use of the fast Fourier transform as an aid in the analysis and classification of spectroscopic data. The pattern obtained after transformation is viewed as a weighted average and/or as a frequency representation of the original spectroscopic data. In pattern recognition the Fourier transform allows a different (i.e., a frequency) representation of the data which may prove more amenable to linear separation according to various categories of the patterns. The averaging property means that the information in each dimension of the original pattern is distributed over all dimensions in the pattern resulting from the Fourier transformation. Hence the arbitrary omission or loss of data points in the Fourier spectrum has less effect on the original spectrum. This property is exploited for reducing the dimensionality of the Fourier data so as to minimize data storage requirements and the time required for development of pattern classifiers for categorization of the data. Examples of applications are drawn from low resolution mass spectrometry.

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.

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.

scholarly journals Calculation of signal spectrum by means of stochastic inversion

2010 ◽  
Vol 28 (7) ◽  
pp. 1409-1418 ◽  
Author(s):  
T. Nygrén ◽  
Th. Ulich
Keyword(s):  
Fourier Transform ◽  
Sampling Rate ◽  
Digital Signal ◽  
Close Relation ◽  
Signal Spectrum ◽  
Inversion Method ◽  
Stochastic Inversion ◽  
Data Points ◽  
Sinusoidal Functions ◽  
The Fourier Transform

Abstract. The standard method of calculating the spectrum of a digital signal is based on the Fourier transform, which gives the amplitude and phase spectra at a set of equidistant frequencies from signal samples taken at equal intervals. In this paper a different method based on stochastic inversion is introduced. It does not imply a fixed sampling rate, and therefore it is useful in analysing geophysical signals which may be unequally sampled or may have missing data points. This could not be done by means of Fourier transform without preliminary interpolation. Another feature of the inversion method is that it allows unequal frequency steps in the spectrum, although this property is not needed in practice. The method has a close relation to methods based on least-squares fitting of sinusoidal functions to the signal. However, the number of frequency bins is not limited by the number of signal samples. In Fourier transform this can be achieved by means of additional zero-valued samples, but no such extra samples are used in this method. Finally, if the standard deviation of the samples is known, the method is also able to give error limits to the spectrum. This helps in recognising signal peaks in noisy spectra.

scholarly journals The method of automatic identification of motor vehicle users

2020 ◽  
Vol 2 (2) ◽  
pp. 63-71
Author(s):  
Tadeusz Niedziela
Keyword(s):  
Fourier Transform ◽  
Physical Properties ◽  
Motor Vehicle ◽  
Automatic Recognition ◽  
Automatic Identification ◽  
Image Function ◽  
Characteristic Features ◽  
The Fourier Transform

This paper presents a method of automatic recognition of fingerprint diffraction images of motor vehicle users. The proposed method is based on the basic physical properties of the Fourier transform. It creates the possibility of reducing the problem of recognition to the Fourier transform of the image function, extraction of characteristic features vector and classification of input images.

GRAVITY PROFILE INTERPRETATION USING THE FOURIER TRANSFORM

Geophysics ◽  
1974 ◽  
Vol 39 (6) ◽  
pp. 862-866 ◽  
Author(s):  
S. J. Collins ◽  
A. R. Dodds ◽  
B. D. Johnson
Keyword(s):  
Fourier Transform ◽  
Horizontal Cylinder ◽  
Direct Interpretation ◽  
Data Points ◽  
Lateral Extent ◽  
The Fourier Transform ◽  
Interpretation Method ◽  
Data Length ◽  
Gravity Profile

A number of attempts have been made to perform direct interpretation of gravity profiles using the Fourier transform of the profile. Of these, the methods of Odegard and Berg (1965) and Sharma et al. (1970) appear to be most applicable. The purpose of this study was to take one of the proposed models (Odegard and Berg’s horizontal cylinder) and determine the applicability of the interpretation method in terms of the number and lateral extent of the data points. The relative accuracies of the estimates of the depth and mass of a cylinder were determined as criteria for estimating the effects of data length and number of data points. In addition, the interpretation was extended to include the separation of two cylinders.

scholarly journals Regularized Simple Graph Convolution (SGC) for improved interpretability of large datasets

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Phuong Pho ◽  
Alexander V. Mantzaris
Keyword(s):  
Large Datasets ◽  
Journal Articles ◽  
Relevant Research ◽  
Research Papers ◽  
Ongoing Research ◽  
Network Information ◽  
Research Task ◽  
Data Points ◽  
Time Required

Abstract Classification of data points which correspond to complex entities such as people or journal articles is a ongoing research task. Notable applications are recommendation systems for customer behaviors based upon their features or past purchases and in academia labeling relevant research papers in order to reduce the reading time required. The features that can be extracted are many and result in large datasets which are a challenge to process with complex machine learning methodologies. There is also an issue on how this is presented and how to interpret the parameterizations beyond the classification accuracies. This work shows how the network information contained in an adjacency matrix allows improved classification of entities through their associations and how the framework of the SGC provide an expressive and fast approach. The proposed regularized SGC incorporates shrinkage upon three different aspects of the projection vectors to reduce the number of parameters, the size of the parameters and the directions between the vectors to produce more meaningful interpretations.

scholarly journals Algorithm for B-scan Image Reconstruction in Optical Coherence Tomography

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kranti Patil ◽  
Anurag Mahajan ◽  
Balamurugan Subramani ◽  
Arulmozhivarman Pachiyappan ◽  
Roshan Makkar
Keyword(s):  
Optical Coherence Tomography ◽  
Fourier Transform ◽  
Optical Coherence ◽  
Cross Sectional ◽  
Image Construction ◽  
Data Points ◽  
Maximum Penetration ◽  
The Fourier Transform ◽  
Processing Techniques

Optical coherence tomography (OCT) is an evolving medical imaging technology that offers in vivo cross-sectional, sub-surface images in real-time. OCT has become popular in the medical as well as non-medical fields. The technique extensively uses for food industry, dentistry, dermatology, and ophthalmology. The technique is non-invasive and works on the Michelson interferometry principle, i.e., dependent on back reflections of the signal and its interference. The objective is to develop an algorithm for signal processing to construct an OCT image and then to enhance the quality of the image using image processing techniques like filtering. The image construction was primarily based on the Fourier transform (FT) of the dataset obtained by data acquisition. This FT could be performed rapidly with the extensively used algorithm of fast Fourier transform (FFT). The depth-wise information could be extracted from each A-scan, i.e., axial scan and also the B-scan was obtained from the A-scan to see the structure of sample. The maximum penetration depth achieved with proposed system was 2.82mm for 1024 data points. First and second layer of leaf were getting at thickness of 1mm and 1.6mm, respectively. A-scans for Human fingertip gave its first, second and third layer was at a thickness of 0.75mm, 0.9mm and 1.6mm, respectively. A-scans for foam sheet gave its first, second and third layer was at a thickness of 0.6mm, 0.75mm, and 0.85mm, respectively.

A SIGNAL-TUNED GABOR TRANSFORM WITH APPLICATION TO EEG ANALYSIS

2013 ◽  
Vol 24 (04) ◽  
pp. 1350017 ◽  
Author(s):  
JOSÉ R. A. TORREÃO ◽  
SILVIA M. C. VICTER ◽  
JOÃO L. FERNANDES
Keyword(s):  
Experimental Study ◽  
Fourier Transform ◽  
Input Signal ◽  
Fourier Component ◽  
Gabor Transform ◽  
Eeg Analysis ◽  
Time Frequency ◽  
Frequency Representation ◽  
S Transform ◽  
The Fourier Transform

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

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