scholarly journals Insight into the Fourier Transform Band Pass Filtering Technique

2008 ◽  
Vol 43 (4) ◽  
Author(s):  
Waldemar Popiński
Keyword(s):  
Fourier Transform ◽  
Band Pass ◽  
Filtering Technique ◽  
The Fourier Transform ◽  
Insight Into

scholarly journals Measures with locally finite support and spectrum

2016 ◽  
Vol 113 (12) ◽  
pp. 3152-3158 ◽  
Author(s):  
Yves F. Meyer
Keyword(s):  
Fourier Transform ◽  
Finite Support ◽  
Locally Finite ◽  
Aperiodic Order ◽  
Finite Set ◽  
Dirac Comb ◽  
The Fourier Transform ◽  
Insight Into

The goal of this paper is the construction of measures μ on Rn enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ^ of μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These unexpected patterns strongly differ from quasicrystals, they provide us with unusual Poisson's formulas, and they might give us an unconventional insight into aperiodic order.

scholarly journals Fourier-Transform-Based Surface Measurement and Reconstruction of Human Face Using the Projection of Monochromatic Structured Light

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2529
Author(s):  
Bingquan Chen ◽  
Hongsheng Li ◽  
Jun Yue ◽  
Peng Shi
Keyword(s):  
Fourier Transform ◽  
Structured Light ◽  
Surface Measurement ◽  
Human Face ◽  
Image Processing Algorithm ◽  
Optical Filtering ◽  
Linearly Polarized ◽  
Potential Applications ◽  
Filtering Technique ◽  
The Fourier Transform

This work presents a new approach of surface measurement of human face via the combination of the projection of monochromatic structured light, the optical filtering technique, the polarization technique and the Fourier-transform-based image-processing algorithm. The theoretical analyses and experimental results carried out in this study showed that the monochromatic feature of projected fringe pattern generated using our designed laser-beam-based optical system ensures the use of optical filtering technique for removing the effect of background illumination; the linearly-polarized characteristic makes it possible to employ a polarizer for eliminating the noised signal contributed by multiply-scattered photons; and the high-contrast sinusoidal fringes of the projected structured light provide the condition for accurate reconstruction using one-shot measurement based on Fourier transform profilometry. The proposed method with the portable and stable optical setup may have potential applications of indoor medical scan of human face and outdoor facial recognition without strict requirements of a dark environment and a stable object being observed.

A Hilbert space approach to distributions

1990 ◽  
Vol 115 (3-4) ◽  
pp. 275-288 ◽  
Author(s):  
Rainer H. Picard
Keyword(s):  
Fourier Transform ◽  
Hilbert Spaces ◽  
Sobolev Type ◽  
Sequential Approach ◽  
Tempered Distributions ◽  
Schwartz Distributions ◽  
The Fourier Transform ◽  
Image Position ◽  
Insight Into ◽  
Space Approach

SynopsisA compact chain of Sobolev type Hilbert spaces , n integer, is introduced that is invariant withrespect to the Fourier transform ℱ. The spaces are related to powers of the adjoint of the so-called tempered derivative introduced in the sequential approach to distributions. It turns out that the intersection of all these Hilbert spaces coincides with the space of rapidly decaying C∞-functions and their union leads to the space of tempered distributions. Moreover, the naturally induced convergence concepts coincide with the usual ones. The approach provides not only a new and arguably more elementary approach to distributions it also provides a deeper insight into the action of the Fourier transform which is a unitary mapping in each space of the chain. Finally the Schwartz distributions are incorporated in the approach as locally tempered distributions.

scholarly journals Fourier transform of single particle wave functions in extremely deformed nuclei: Towards the momentum distribution of scission neutrons

2018 ◽  
Vol 169 ◽  
pp. 00020 ◽  
Author(s):  
M. Rizea ◽  
N. Carjan
Keyword(s):  
Fourier Transform ◽  
Single Particle ◽  
Fourier Transforms ◽  
Wave Packets ◽  
Wave Functions ◽  
Time Dependent ◽  
Dependent Potential ◽  
The Fourier Transform ◽  
Several Intervals ◽  
Insight Into

The Fourier transform of single particle wave functions in cylindrical coordinates is applied to the study of neutrons released during scission. We propagate the neutron wave packets in time through the bi-dimensional time dependent Schrödinger equation with time dependent potential. We separate the parts of these wave packets that are in the continuum and calculate their Fourier transforms at different times: immediately after scission (T = 1×10-22 s) and at several intervals afterwards (until T = 50×10-22 s). The momentum distributions corresponding to these Fourier transforms are then estimated. The evolution of these distributions in time provides an insight into the separation of the neutron from the fissioning system and asymptotically gives the kinetic energy spectrum of that particular neutron.

scholarly journals Wavelet Transforms Applications and Interpretation Based on the Signal Genesis

2019 ◽  
Vol 9 (1S) ◽  
pp. 30-37
Keyword(s):  
Fourier Transform ◽  
Wavelet Transforms ◽  
Wavelet Decomposition ◽  
Ct Scanner ◽  
Additional Signal ◽  
Spectral Components ◽  
Radar Echo ◽  
Frequency Components ◽  
The Fourier Transform ◽  
Insight Into

A signal from any measurement system provides insight into its genesis, thereby enabling an understanding of a certain activity or phenomenon. Seismic signals, radar echo signals, physiological signals, signals from specially fabricated instruments such as MRI, CT scanner all provide information by using an analysis that resolves the signal into its frequency components. While the Fourier transform and its fast – evaluating algorithm known as FFT are standard for such analysis, there are presently additional signal transforms in use, of which “ Wavelets” or Wavelet transform or wavelet decomposition are becoming very important. If the Fourier transform resolved the signal into its spectral components of Sine and Cosine waves, the Wavelets do the same in terms of non- sinusoidal oscillatory wave-shapes of burst – like appearance. This paper deals with the choice of wavelet transforms based on signal genesis and the interpretation required from the analysis of the signal, that one is expected to infer.

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.

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