When n = 2, T is a Fourier multiplier, and it is well known that such operators are bounded on L, 1 < p < ∞, if m is a symbol of order 0. Coifman and Meyer [2]–[7], Kenig and Stein [14], and Grafakos and Torres [12] extended this result to the n > 2 case, showing that one had the mapping properties T : L1 × . . .× Ln−1 → Lpn (3) whenever 1 < pi ≤ ∞ (4) for i = 1, . . . , n− 1, 1/(n− 1) < pn <∞,...

Conversely, suppose all the low-order Fourier coe cients are 0. Since D̂(100 0) = Pr[x1 = 0] Pr[x1 = 1] = 0, x1 is equally likely to be 0 or 1, and similarly for the other xi's. Now let pa1a2 = Pr[x1x2 = a1a2]. Since x1, x2, and x1 x2 are all unbiased, we get the equations p00 + p01 = p00 + p10 = p00 + p11 = 1=2. Furthermore, p00 + p01 + p10 + p11 = 1. From these equations, we deduce that all of...

our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

Grazing X-ray reflectometry allows the analysis of thin layer stacks. The fitting of the reflectivity curve by a trial and error method can be used in order to determine the parameters of the films. Fourier analysis of the experimental reflectivity can directly give a rough determination of the profit index. Application to real examples shows the validity of the method.

In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...

It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shif...

In this paper, a transform based methodology is presented for compression of electrocardiogram (ECG) signal. The methodology employs different transforms such as Discrete Wavelet Transform (DWT), Fast Fourier Transform (FFT) and Discrete Cosine Transform (DCT). A comparative study of performance of different transforms for ECG signal is made in terms of Compression ratio (CR), Percent root mean...

We study a.e. convergence on L, and Lorentz spaces L, p > 2d d−1 , for variants of Riesz means at the critical index d( 1 2 − 1 p )− 1 2 . We derive more general results for (quasi-)radial Fourier multipliers and associated maximal functions, acting on L spaces with power weights, and their interpolation spaces. We also include a characterization of boundedness of such multiplier transformation...

This paper presents a novel method of combining global and local classifiers to form a more powerful classifier for lipreading. The global classifier uses Discrete Fourier Transform (DFT) to derive an image representation that captures global information. The local classifier uses block-based Gabor Wavelets Transform (BGWT) to extract local information of the input image. These two classifiers ...