Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.

Fast Fourier transform for discontinuous functions

Abstract: In computational electromagnetics and other areas of computational science and engineering, Fourier transforms of discontinuous functions are often required. We present a fast algorithm for the evaluation of the Fourier transform of piecewise smooth functions with uniformly or nonuniformly sampled data by using a double interpolation procedure combined with the fast Fourier transform (FFT) algorithm. We call this the discontinuous FFT algorithm. For N sample points, the complexity of the algorithm is O(/spl nu/Np+/spl nu/Nlog(N)) where p is the interpolation order and /spl nu/ is the oversampling factor. The method also provides a new nonuniform FFT algorithm for continuous functions. Numerical experiments demonstrate the high efficiency and accuracy of this discontinuous FFT algorithm.

Noise Analysis of Power System Frequency Estimated From Angle Difference of Discrete Fourier Transform Coefficient

Abstract: The frequency deviation of an electric power system is a reflection of its operating state. This frequency deviation can be estimated from angle variations of the discrete Fourier transform coefficient of the positive fundamental frequency. Most errors of the frequency estimate can arise from noise in the power system signal and the leakage effect of the negative fundamental frequency. This paper analyzes errors of the frequency estimates and the measured angle variations due to the noise. Their means and variances are derived theoretically with respect to signal-to-noise ratios and verified and analyzed through simulations.

The errors in FFT estimation of the Fourier transform

Abstract: The problem of determining the error in approximating the Fourier transform by the discrete Fourier transform is studied. Exact formulas for the relative error are established for classes of functions, called canonical-k (k/spl ges/0), and asymptotic error formulas are established for a much wider class of functions, called order-k. The formulas are dependent only on the class and not on the function in the class whose Fourier transform is being approximated, and this facilitates the application of the results.

Wavefront reconstruction using multiple directional derivatives and Fourier transform

Abstract: We present a Fourier-based regularized method for reconstructing the wavefront from multiple directional derivatives. This method is robust to noise, and is specially suited for deflectometry measurement.

On the use of symmetry in FFT computation

Abstract: It is well known that if a finite duration, N-point sequence x(n) possesses certain symmetries, the computation of its discrete Fourier transform (DFT) can be obtained from an FFT of size N/2 or smaller. This is accomplished by first preprocessing the sequence, taking the FFT of the processed sequence, and then postprocessing the results to give the desired transform. In this paper we show how a similar approach can be used for sequences which are known to have only odd harmonics. The approach is shown to be essentially the dual of the known method for time symmetry. Computer programs are included for implementing the special procedures discussed in this paper.