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.

Susceptibilities for the brownian motion in a cosine potential with application to the rotation of a dipole in a constant external field

Abstract: The susceptibility for the brownian motion in a cosine potential is proportional to the one sided Fourier transform of the velocity autocorrelation function whereas the polarizability for the rotation of a dipole in a constant external field is proportional to the one sided Fourier transform of the time derivative of the sin- and cos-autocorrelation function. The one sided Fourier transform of these autocorrelation functions can be expressed by matrix continued fractions. They are evaluated for large, medium and even for very small damping constants, thus obtaining various susceptibilities practically in the whole region of friction constants. Furthermore the connection to the zero friction limit case is discussed.

Generalized Fourier transform for non-uniform sampled data.

Abstract: Fourier transform can be effectively used for processing of sparsely sampled multidimensional data sets. It provides the possibility to acquire NMR spectra of ultra-high dimensionality and/or resolution which allow easy resonance assignment and precise determination of spectral parameters, e.g., coupling constants. In this chapter, the development and applications of non-uniform Fourier transform is presented.

Computation of the One-Dimensional Unwrapped Phase

Abstract: In this paper, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 2 pi discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This paper compares existing algorithms for computing the unwrapped phase. Then, two composite algorithms are proposed that build upon the existing ones. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.

Fourier Analysis of Time Series

Abstract: Discrete-time wide-sense stationary stochastic processes, also called time series, arise from discrete-time measurements (sampling) of random functions. A particularly mathematically tractable class of such processes consists of the so-called moving averages and auto-regressive (and more generally, arma) time series. This chapter begins with the general theory of wss discrete-time stochastic processes (which essentially reproduces that of wss continuous-time stochastic processes) and then gives the representation theory of arma processes, together with their prediction theory. The last section is concerned with the realization problem: what models fit a given finite segment of autocorrelation function of a time series? The corresponding theory is the basis of parametric spectral analysis.