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.

The OFDM System Based on the Fractional Fourier Transform

Abstract: Transmission over wireless channels can lead to intersymbol interference (ISI) as well as interchannel (or intercarrier) interference (ICI). To decrease the results of ICI, this paper proposes an OFDM system based on the fractional Fourier transform (FrFT) in which traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the symbols. The multiplicative filter in fractional Fourier domain has been designed to equalize the received signal. Theoretical analysis and numerical simulation results show that the proposed equalizer in optimal fractional Fourier domain can significantly improve the performance of the system as compared to the Fourier domain equalizer.

Improved sparse fourier approximation results: faster implementations and stronger guarantees

Abstract: We study the problem of quickly estimating the best k-term Fourier representation for a given periodic function f: [0, 2?] ? ?. Solving this problem requires the identification of k of the largest magnitude Fourier series coefficients of f in worst case k 2 · log O(1) N time. Randomized sublinear-time Monte Carlo algorithms, which have a small probability of failing to output accurate answers for each input signal, have been developed for solving this problem (Gilbert et al. 2002, 2005). These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT) and empirically evaluated in Iwen et al. (Commun Math Sci 5(4):981---998, 2007). In this paper we present a new implementation, called the Gopher Fast Fourier Transform (GFFT), of more recently developed sparse Fourier transform techniques (Iwen, Found Comput Math 10(3):303---338, 2010, Appl Comput Harmon Anal, 2012). Experiments indicate that GFFT is faster than AAFFT. In addition to our empirical evaluation, we also consider the existence of sublinear-time Fourier approximation methods with deterministic approximation guarantees for functions whose sequences of Fourier series coefficents are compressible. In particular, we prove the existence of sublinear-time Las Vegas Fourier Transforms which improve on the recent deterministic Fourier approximation results of Iwen (Found Comput Math 10(3):303---338, 2010, Appl Comput Harmon Anal, 2012) for Fourier compressible functions by guaranteeing accurate answers while using an asymptotically near-optimal number of function evaluations.

Pricing Bermudan Options in Lévy Process Models

Abstract: This paper presents a Hilbert transform method for pricing Bermudan options in Levy process models. The corresponding optimal stopping problem can be solved using a backward induction, where a sequence of inverse Fourier and Hilbert transforms need to be evaluated. Using results from a sinc expansion based approximation theory for analytic functions, the inverse Fourier and Hilbert transforms can be approximated using very simple rules. The approximation errors decay exponentially with the number of terms used to evaluate the transforms for many popular Levy process models. The resulting discrete approximations can be efficiently implemented using the fast Fourier transform. The early exercise boundary is obtained at the same time as the price. Accurate American option prices can be obtained by using Richardson extrapolation.