This paper presents some new results on numerical stability for various fast trigonometric transforms. In a worst case study, we consider the numerical stability of the classical fast Fourier transform (FFT) with respect to different precomputation methods for the involved twiddle factors and show the strong influence of precomputation errors on the numerical stability of the FFT. The examinati...

Abstract In this paper, it is shown that the performance of various frequency-domain estimators memory parameter can be boosted by inclusion non-Fourier frequencies in addition to regular Fourier frequencies. A fast two-stage algorithm for efficient computation amplitudes at these additional presented. first stage, naïve sine and cosine transforms are computed with a modified version Fast Trans...

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. In this paper, we extend the uncertainty principle for hypercomplex signals in the linear canonical transform domains, giving the tighter lower bound on ...

The classical signal processing technique known as Wiener filtering has been extended to the processing of oneand two-dimensional discrete data by digital operations with emphasis on reduction of the computational requirements. In the generalized Wiener filtering process a unitary transformation, such as the discrete Fourier, Hadamard, or Karhunen-Loeve transform is performed on the data that i...

The interaction of ferrocene-boronic acid with fructose is investigated in aqueous 0.1 m phosphate buffer at pH 7, 8 and 9. Two voltammetric methods, based on 1) a dual-plate generator-collector micro-trench electrode (steady state) and 2) a square-wave voltammetry (transient) method, are applied and compared in terms of mechanistic resolution. A combination of experimental data is employed to ...

Fast computation of two-dimensional (2-D) generalized discrete Fourier transforms (GDFTs) and generalized discrete Hartley transforms (GDHTs) are discussed in terms of a new method which is derived based on index permutation, linear congruences, and polynomial transforms. Further, the 2-D skew circular convolution computed by the proposed skew polynomial transform is also included. ( 2000 Elsev...

The DFT usually arises as an approximation to the continuous Fourier transform when functions are sampled at discrete intervals in space or time. The naive evaluation of the discrete Fourier transform is a matrix-vector multiplication W~g, and would take O(N) operations for N data-points. The general principle of the Fast Fourier Transform algorithms is to use a divide-and-conquer strategy to f...