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.

Reducing peak spectral error in inverse Fast Fourier Transform using MMX™ technology

Abstract: A method for computing a decimation-in-time Fast Fourier Transform of a sample is provided, the method including inputting first 2B-bit values representing the sample into a radix-4 first section of the decimation-in-time Fast Fourier Transform and performing first complex 2B-bit integer additions and subtractions on the first 2B-bit values to form second 2B-bit values, without performing a multiplication. The method also includes rounding the second 2B-bit values to form B-bit values output from the radix-4 first section of the decimation-in-time Fast Fourier Transform.

Determination of Relaxation Spectra from Damping Measurements

Abstract: A method is shown for the determination of the relaxation spectrum from the data furnished by dynamical experiments, and in particular from the damping (imaginary part of the complex modulus) as a function of frequency. The circular functions are eigenfunctions of the relevant integral equation, which can therefore be solved numerically by expansion. The spectrum is obtained by first making a Fourier analysis, multiplying every coefficient by the associated eigenvalue, and then synthesizing the new Fourier series. An estimate is given of the resolving power of the method, which is limited only by the error in the experimental data. As an illustration, the spectrum of polyisobutylene in the frequency domain corresponding to the rubber-glass transition is found from published data.

Simple and practical algorithm for sparse fourier transform

Abstract: We consider the sparse Fourier transform problem: given a complex vector x of length n, and a parameter k, estimate the k largest (in magnitude) coefficients of the Fourier transform of x. The problem is of key interest in several areas, including signal processing, audio/image/video compression, and learning theory.We propose a new algorithm for this problem. The algorithm leverages techniques from digital signal processing, notably Gaussian and Dolph-Chebyshev filters. Unlike the typical approach to this problem, our algorithm is not iterative. That is, instead of estimating "large" coefficients, subtracting them and recursing on the reminder, it identifies and estimates the k largest coefficients in "one shot", in a manner akin to sketching/streaming algorithms. The resulting algorithm is structurally simpler than its predecessors. As a consequence, we are able to extend considerably the range of sparsity, k, for which the algorithm is faster than FFT, both in theory and practice.

Short-space Fourier transform image processing

Abstract: The short-space Fourier transform (SSFT) is introduced as a means of describing discrete multi-dimensional signals of finite extent. It is an adaptation of the short-time Fourier transform developed for one-dimensional infinite-duration signals such as speech. By reflectively extending the finite signal segment, one can imagine an infinite duration signal which is "continuous." The proposed SSFT is the multidimensional generalization of the short-time Fourier transform operating upon the resulting infinite duration signal. Because boundary "discontinuities" are avoided, the proposed SSFT provides a transform representation free of extraneous spectral energy. An efficient algorithm for computing the SSET is described. SSFT image coding, an important application of the new transform method, provides localized spectral information without the undesirable phenomenon of "blocking effects."