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: In this article, the Fourier transform and the wavelet transform were used to process the fringe carrier pattern resulting from speckle-shearing inteferometry, in which the carrier frequency is modulated by deformation of a bending plate.
Abstract: The Fourier transform (FT) and the wavelet transform (WT) methods are used to process the fringe carrier pattern resulting from speckle-shearing inteferometry, in which the carrier frequency is modulated by deformation of a bending plate. Both the amount and the sign of the first derivative of the out-of-plane displacement can be obtained by these two transform techniques in the whole field. Phase distributions of the deflection slope are compared, which shows the wavelet analysis gives a better solution with noise reduction and without deficiency of filter window choice as for that in the Fourier transform. Meanwhile, the phase values in the path along the maximum WT amplitudes give a direct map of the second derivative patterns of the deflection, which presents the same image as that given by the shearing subtraction of the phase patterns from the inverse Fourier transformation but avoids the processing of unwrapping for the phase reconstruction.
24 citations
24 citations
TL;DR: In this paper, a general class of compressed sensing matrices is presented, which are then demonstrated to have associated sublinear-time sparse approximation algorithms, and methods for constructing specialized matrices from this class which are sparse when multiplied with a discrete Fourier transform matrix.
Abstract: We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are sparse when multiplied with a discrete Fourier transform matrix. Ultimately, these considerations improve previous sampling requirements for deterministic sparse Fourier transform methods.
23 citations
TL;DR: The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non- uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches.
23 citations
TL;DR: Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.
Abstract: An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.
23 citations