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.

A new chirp scaling algorithm based on the fractional Fourier transform

Abstract: The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has only recently started to appear in the field of signal processing. This has opened up the possibility of a new range of potentially promising and useful applications. In this letter, we develop a new FrFT-based chirp scaling algorithm (CSA) and compare its performance with the classical CSA based on the fast Fourier transform (FFT). Simulation results show that the FrFT-based CSA can offer significantly enhanced features compared to the classical FFT-based approach.

A Robust Sparse Fourier Transform in the Continuous Setting

Abstract: In recent years, a number of works have studied methods for computing the Fourier transform in sub linear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is continuous and naive discretization significantly worsens the sparsity level. We present an algorithm for robustly computing sparse Fourier transforms in the continuous setting. Let x(t) = x*(t) + g(t), where x* has a k-sparse Fourier transform and g is an arbitrary noise term. Given sample access to x(t) for some duration T, we show how to find a k-Fourier-sparse reconstruction x'(t) with [frac{1}{T}int0T abs{x(t) - x(t)}2 mathrm{d} t lesssim frac{1}{T}int0T abs{g(t)}2 mathrm{d}t. The sample complexity is linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution. Previous results with similar sample complexities could not tolerate an infinitesimal amount of i.i.d. Gaussian noise, and even algorithms with higher sample complexities increased the noise by a polynomial factor. We also give new results for how precisely the individual frequencies of x* can be recovered.

Nonnegative image reconstruction from sparse Fourier data: a new deconvolution algorithm

Abstract: This paper deals with image restoration problems where the data are nonuniform samples of the Fourier transform of the unknown object. We study the inverse problem in both semidiscrete and fully discrete formulations, and our analysis leads to an optimization problem involving the minimization of the data discrepancy under nonnegativity constraints. In particular, we show that such a problem is equivalent to a deconvolution problem in the image space. We propose a practical algorithm, based on the gradient projection method, to compute a regularized solution in the discrete case. The key point in our deconvolution-based approach is that the fast Fourier transform can be employed in the algorithm implementation without the need of preprocessing the data. A numerical experimentation on simulated and real data from the NASA RHESSI mission is also performed.

Analysis of Periodic and Aperiodic Coupled Nonuniform Transmission Lines Using the Fourier Series Expansion

Abstract: A general method is proposed to analyze periodic or aperiodic Coupled Nonuniform Transmission Lines (CNTLs). In this method, the per-unit-length matrices are expanded in the Fourier series. Then, the eigenvalues of periodic CNTLs and so the S parameters of aperiodic CNTLs are obtained. The validity of the method is studied using a comprehensive example.

Radiation from a finite cylindrical explosive source

Abstract: For an elastic material with an infinite circular cylindrical hole, the exact solution due to a pressure on a finite length of the cylinder is obtained as a function of the Laplace transform parameter on time and Fourier transform parameter on the z-coordinate (the axis of the cylinder). The applied pressure is a function of the time and the position z. Numerical inversion of the Laplace and Fourier transforms are required to determine the field quantities in the time and space parameters. In the far field, the inverse Fourier transform can be obtained by an asymptotic expansion. It remains to obtain the inverse Laplace transform numerically. We have found that for cylinders whose radius is small compared with the smallest wavelength of interest, an analytical solution can be obtained. Graphical results for the cases of instantaneous explosion and progression of the detonation with constant velocity are given. In both cases an exponential decay of the explosion pressure is assumed.