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.

Adaptive weak signal identification system

Abstract: An adaptive weak signal identification system having a simple implementation which is capable of rapidly tracking weak signals with time varying frequencies in the presence of a strong interference signal. The system includes a first Fast Fourier Transform circuit for performing a Fast Fourier Transform on a discrete block of data points of an input data signal. A filter coefficient generator is coupled to the output of the Fast Fourier Transform circuit, and identifies the frequency of the strong interference signal, and then based thereon generates filter coefficients for a notch filter. A notch filter receives the generated filter coefficients, and further has the input data signal as an input, on which it performs a notch filtering operation to dramatically reduce the intensity of the interference signal. A second Fast Fourier Transform circuit then performs a Fast Fourier Transform on the output passed by the notch filter, and the output of the Fast Fourier Transform circuit is analyzed to identify the frequency of the weak signal of interest.

Generalized convolution theorem associated with fractional Fourier transform

Abstract: The fractional Fourier transform FRFT-a generalization of the well-known Fourier transform FT-is a comparatively new and powerful mathematical tool for signal processing. Many results in Fourier analysis have currently been extended to the FRFT, including the ordinary convolution theorem. However, the extension of the ordinary convolution theorem associated with the FRFT has been developed differently and is still not having a widely accepted closed-form expression. In this paper, a generalized convolution theorem for the FRFT is proposed, and the dual of it is also presented. The ordinary convolution theorem and some of its existing extensions related to the FRFT are shown to be special cases of the derived results. Moreover, some applications of the derived results are presented. Copyright © 2012 John Wiley & Sons, Ltd.

Convolution using the undecimated discrete wavelet transform

Abstract: Convolution is one of the most widely used digital signal processing operations. It can be implemented using the fast Fourier transform (FFT) with a computational complexity of O (N log N). The undecimated discrete wavelet transform (UDWT) is linear and shift invariant, so it can also be used to implement convolution. We propose a scheme to implement the convolution using the UDWT, and study its advantages and limitations.

An Exact and Fast Computation of Discrete Fourier Transform for Polar and Spherical Grid

Abstract: Numerous applied problems of two-dimensional (2-D) and 3-D imaging are formulated in continuous domain. They place great emphasis on obtaining and manipulating the Fourier transform in polar and spherical coordinates. However, the translation of continuum ideas with the discrete sampled data on a Cartesian grid is problematic. There exists no exact and fast solution to the problem of obtaining discrete Fourier transform for polar and spherical grids in the literature. In this paper, we develop exact algorithms to the above problem for 2-D and 3-D, which involve only 1-D equispaced fast Fourier transform with no interpolation or approximation at any stage. The result of the proposed approach leads to a fast solution with very high accuracy. We describe the computational procedure to obtain the solution in both 2-D and 3-D, which includes fast forward and inverse transforms. We find the nested multilevel matrix structure of the inverse process, and we propose a hybrid grid and use a preconditioned conjugate gradient method that exhibits a drastic improvement in the condition number.

Perspective projections in the space-frequency plane and fractional Fourier transforms

Abstract: Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can be approximately modeled in terms of the fractional Fourier transform. The region of validity of the approximation is examined. Numerical examples are presented.