The DFT: An Owner's Manual for the Discrete Fourier Transform

Briggs, William L.; Henson, Van Emden

doi:10.1137/1.9781611971514

Cited by 324 publications

(267 citation statements)

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“…These results, based on the dns data of Hoyas & Jiménez (2008), suggest that, although p exhibits strong dependence on Re τw , the relative importance of the slow and rapid mechanisms in the creation of p does not. Therefore, despite the low † Notice that the spectra given by Moser et al (1999) are twice the dft of R + p p (in wall units), and have to be appropriately rescaled (Briggs & Henson 1995) …”

Section: Plane Channel Flow Configuration and Computational Methodsmentioning

confidence: 99%

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Wall effects on pressure fluctuations in turbulent channel flow

2013

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The purpose of the present paper is to study the influence of wall-echo on pressure fluctuations p , and on statistical correlations containing p , viz redistribution φ ij , pressure diffusion d (p) ij , and velocity/pressure-gradient Π ij . We extend the usual analysis of turbulent correlations containing pressure fluctuations in wall-bounded dns computations [Kim J.: J. Fluid Mech. 205 (1989) ) and surface (wall-echo; p (r;w) and p (s;w) ) terms. An algorithm, based on a Green's function approach, is developed to compute the above splittings for various correlations containing pressure fluctuations (redistribution, pressure diffusion, velocity/pressure-gradient), in fully developed turbulent plane channel flow. This exact analysis confirms previous results based on a method-of-images approximation [Manceau R., Wang M., Laurence D.: J. Fluid Mech. 438 (2001) 307-338] showing that, at the wall, p (V) and p (w) are usually of the same sign and approximately equal. The above results are then used to study the contribution of each mechanism on the pressure correlations in low Reynolds-number plane channel flow, and to discuss standard second-moment-closure modelling practices.

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Section: Plane Channel Flow Configuration and Computational Methodsmentioning

confidence: 99%

“…¶ The Fourier-transformsp (m) ,Q (m) ,B (m) ± ∈ C are computed using standard dft (discrete Fourier transform) techniques (Briggs & Henson 1995) in the periodic directions x and z, with maximum computable wavenumbers κx max = π(∆x) −1 and κz max = π(∆z) −1 . in the pde (2.3) to obtain the ode ‡…”

Section: Odes For the Fourier Transformsmentioning

confidence: 99%

Wall effects on pressure fluctuations in turbulent channel flow

2013

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“…l ) L l=0 corresponding to a singular value σ (2) ∈ (0, ε 2 ] (σ (1) σ (2) ) of the perturbed rectangular Hankel matrix (3.2). 4.…”

Section: Compute a Right Singular Vectorũmentioning

confidence: 99%

“…We can determine the zeros of the polynomialsP (1) andP (2) by computing the eigenvalues of the related companion matrices, see Remark 2.4. Note that by Corollary 4.6, the correct frequencies ω j can be approximately computed by any right singular vector corresponding to a small singular value of (3.2).…”

Section: Nmmentioning

confidence: 99%

Parameter estimation for exponential sums by approximate Prony method

2010

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The recovery of signal parameters from noisy sampled data is a fundamental problem in digital signal processing. In this paper, we consider the following spectral analysis problem: Let f be a real-valued sum of complex exponentials. Determine all parameters of f , i.e., all different frequencies, all coefficients, and the number of exponentials from finitely many equispaced sampled data of f . This is a nonlinear inverse problem. In this paper, we present new results on an approximate Prony method (APM) which is based on [1]. In contrast to [1], we apply matrix perturbation theory such that we can describe the properties and the numerical behavior of the APM in detail. The number of sampled data acts as regularization parameter. The first part of APM estimates the frequencies and the second part solves an overdetermined linear Vandermonde-type system in a stable way. We compare the first part of APM also with the known ESPRIT method. The second part is related to the nonequispaced fast Fourier transform (NFFT). Numerical experiments show the performance of our method.

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“…Here we will be concerned with arbitrary functions f ∈ C ∞ (IR), thus also with those for which f has a jump at X and −X. To diminish the impact of the jump, and in the spirit of Fourier series (see also [3], p. 95), we will replace the values f (±X) by the average values at the corresponding jumps, i.e., we will interpolate the following function, again denoted by f :…”

Section: Introductionmentioning

confidence: 99%