Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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TL;DR: The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms and has interesting properties and Fourier transform relations.
Abstract: The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily bandlimited, periodic masks at some specific distances.
34 citations
TL;DR: It is shown that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal windowfunction in the time domain.
Abstract: We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processing, which is suitable for optical implementation. We also systematically analyze the selection of the window functions, especially those based on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inverse STFT and the inverse WT. A couple of optical architectures based on Fourier-domain processing for the STFT and the WT, by which real-time signal processing can be realized, are proposed.
34 citations
TL;DR: Simulation and experimental results show that the convergence stage of both the phase difference and time interval calculations has been largely shortened with higher accuracy of the CMF, as compared with the existing method based on the sliding Goertzel algorithm.
Abstract: There is a long convergence stage when using the sliding Goertzel algorithm to measure the phase difference between signals of a Coriolis mass flowmeter (CMF) because the contribution of negative frequency is neglected in the algorithm. A novel method for CMF signal processing is proposed based on the recursive discrete-time Fourier transform (DTFT) algorithm with negative frequency contribution. First, an adaptive lattice notch filter is applied to filter the sensor output signals of the CMF and calculate the frequency. Then, a new method based on the recursive DTFT algorithm with negative frequency contribution is introduced to calculate the real-time phase difference between two enhanced signals. With the frequency and the phase difference obtained, the time interval of the two signals is calculated, and then, the mass flowrate is derived. The method is validated in experiments using CMF signals acquired for different flowrates. Simulation and experimental results show that the convergence stage of both the phase difference and time interval calculations has been largely shortened with higher accuracy of the CMF, as compared with the existing method based on the sliding Goertzel algorithm.
34 citations
TL;DR: In this paper, an analysis of the corrugated-surface twist polarizer is presented, which finds application in the design of scanning reflector antennas using the spectraI-interation technique, a novel procedure which combines the use of the Fourier transform method with an iterative procedure.
Abstract: An analysis of the corrugated-surface twist polarizer which finds application in the design of scanning reflector antennas is presented. The spectraI-interation technique, a novel procedure which combines the use of the Fourier transform method with an iterative procedure is employed. The first step in the spectral-iteration method is the conversion of the original integral equation for the interface field into a form which is suitable for iteration using a method developed previously. An important feature of the technique is that it takes advantage of the discrete Fourier transform (DFT) type of kernel of the integral equation and evaluates the integral operators efficiently using the fast Fourier transform (FFT) algorithm. Thus, in contrast to the conventional techniques, e.g., the moment method, the spectral-iteration approach requires no matrix inversion and is capable of handling a large number of unknowns. Furthermore the method has a built-in check on the satisfaction of the boundary conditions at each iteration.
34 citations
TL;DR: A recurrence technique is described that enables the use of proven efficient Fourier transform techniques to be applied to the expansion of a given function in terms of spherical harmonics.
Abstract: A recurrence technique is described that enables the use of proven efficient Fourier transform techniques to be applied to the expansion of a given function in terms of spherical harmonics.
34 citations