Nonequispaced discrete Fourier transformation (NDFT) is widely applied in all aspects of computational science and engineering. The efficiency accuracy NDFT has always been a critical issue hindering its comprehensive applications both intensive extensive scientific computing. In our previous work Yang et al. (2018), CUNFFT method was proposed it shown outstanding performance handling at interm...

We calculate the local Fourier transformations for a class of Ql-sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([15] 2.6.3). As an application, we calculate the local monodromy of l-adic hypergeometric sheaves introduced by Katz ([12]). We also discuss the characteristic p analogue of the Turrittin-Levelt Theorem for D-modules. The method used in this paper can be used ...

We determine the (arithmetic) local monodromy at 0 and at ∞ of the Kloosterman sheaf using local Fourier transformations and Laumon’s stationary phase principle. We then calculate -factors for symmetric products of the Kloosterman sheaf. Using Laumon’s product formula, we get functional equations of L-functions for these symmetric products and prove a conjecture of Evans on signs of constants o...

If Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded q-variation on dyadic coronas, we prove that the commutator [T, Tμ] = TTμ−TμT is bounded on the Besov space B p (R ), if T is any bounded linear operator on a couple of Besov spaces Bj ,rj p (R) (j = 0, 1, and 0 < σ1 < σ < σ0).

The properties of the Radon transform are used to derive the transformation invariant to translation, rotation and scaling. The invariant transformation involves translation compensation, angle representation and 1-D Fourier transform. The new object recognition method is studied experimentally in two domains, mammogram labels recognition and face recognition. For mammogram labels, the recognit...

The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other non-uniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable alg...

The pseudo-polar Fourier transform is a specialized nonequally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other nonuniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable algori...

The truncated Fourier series exhibits oscillation that does not disappear as the number of terms in the truncation is increased. This paper introduces 2-D fractional Fourier series (FrFS) according to the 1-D fractional Fourier series, and finds such a Gibbs oscillation also occurs in the partial sums of FrFS for bivariate functions at a jump discontinuity. In this study, the 2-D inverse polyno...