Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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TL;DR: A WFT-based algorithm is described and theoretically analysed for fault detection and demonstrations using both simulated and real fringe patterns are carried out.
Abstract: Windowed Fourier transform (WFT), a tool of spatial-frequency analysis, is able to characterize the local frequency at any location in a fringe pattern. Changes in fringe frequency characterize defects in optical interferometric-based systems. Hence, the WFT is suitable for fault detection and condition monitoring in optical NDT. In this paper, a WFT-based algorithm is described and theoretically analysed for fault detection. This is followed by demonstrations using both simulated and real fringe patterns. Comparisons with the traditional Fourier transform approach and normalized cross correlation approaches are also carried out.
39 citations
01 Jan 1985
TL;DR: In this paper, it was shown that bit rates as low as 0.3 bit per pixel can be achieved by encoding a combination of the Fourier phase and amplitude data, which is achieved by low-pass filtering together with a clustering procedure in Fourier plane which seeks out the more important Fourier amplitude coefficients and their associated phases.
Abstract: The scientific advantages are pointed out from the Fourier transform encoding optical and electron microscope images and source data for computer-plotted Fourier-plane holograms, especially if bit compression ratios may be achieved, with comparable reconstructions, at the level found for the adaptive cosine transform. The relative importance is considered of image reconstruction based on the Fourier phase data alone and on combined phase and amplitude data. It is shown that bit rates as low as 0.3 bit per pixel can be achieved by encoding a combination of the Fourier phase and amplitude data. This is achieved by low-pass filtering together with a clustering procedure in the Fourier plane which seeks out the more important Fourier amplitude coefficients and their associated phases.
39 citations
TL;DR: The first two parts of this article will discuss concepts associated with the fast Fourier transform (FFT), an implementation of the DFT, and two applications are analyzed: a bat chirp and atmospheric sea-level pressure differences in the Pacific Ocean.
Abstract: The discrete Fourier transform (DFT) provides a means for transforming data sampled in the time domain to an expression of this data in the frequency domain. The inverse transform reverses the process, converting frequency data into time-domain data. Such transformations can be applied in a wide variety of fields, from geophysics to astronomy, from the analysis of sound signals to CO/sub 2/ concentrations in the atmosphere. Over the course of three articles, our goal is to provide a convenient summary that the experimental practitioner will find useful. In the first two parts of this article, we'll discuss concepts associated with the fast Fourier transform (FFT), an implementation of the DFT. In the third part, we'll analyze two applications: a bat chirp and atmospheric sea-level pressure differences in the Pacific Ocean.
39 citations
TL;DR: A computationally efficient algorithm is proposed to estimate the parameters of a real sinusoidal signal in noise using the fast Fourier Transform and achieves the Cramér–Rao lower bound.
Abstract: We propose and comprehensively analyze a computationally efficient algorithm to estimate the parameters of a real sinusoidal signal in noise. This method uses the fast Fourier Transform and is, therefore, computationally efficient. Accounting for the interference due to the negative spectral component allows the frequency to be estimated very accurately. Estimates of the amplitude and phase are derived in the process and are necessary for the suppression of the leakage. Theoretical analysis establishes that the estimator is asymptotically unbiased and achieves the Cramer–Rao lower bound. Simulation results are presented to verify the theory and demonstrate that the estimation performance is superior to other estimators in the literature.
39 citations
Patent•
18 Oct 2002TL;DR: In this article, a method for coding in frequency, module and phase a digital representation, in the space field, of a ring-shaped element, including the steps of: applying to any point of the element a polar conversion at constant angle, whereby the element is unfolded in rectangular form; transferring, to the frequency field, any points of the converted rectangular shape by means of a Fourier transform; filtering the discrete data resulting from the transfer by at least one real, bidimensional, band-pass filter, oriented along the phase axis; applying a Hilbert transform to the filtering results
Abstract: A method for coding in frequency, module and phase a digital representation, in the space field, of a ring-shaped element, including the steps of: applying to any point of the element a polar conversion at constant angle, whereby the element is unfolded in rectangular form; transferring, to the frequency field, any point of the converted rectangular shape by means of a Fourier transform; filtering the discrete data resulting from the transfer by means of at least one real, bidimensional, band-pass filter, oriented along the phase axis; applying a Hilbert transform to the filtering results; applying an inverse Fourier transform to the results of the Hilbert transform; and extracting phase and module information in the space field.
39 citations