منابع مشابه
Adaptive Fourier series - a variation of greedy algorithm
We study decomposition of functions in the Hardy space H2(D) into linear combinations of the basic functions (modified Blaschke products) in the system Bn(z) = √ 1 − |an|2 1 − anz n−1 ∏ k=1 z − ak 1 − akz , n = 1, 2, ..., (1) where the points an’s in the unit disc D are adaptively chosen in relation to the function to be decomposed. The chosen points an’s do not necessarily satisfy the usually ...
متن کاملDetermination of a jump by Fourier and Fourier-Chebyshev series
By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of ...
متن کاملFourier Transforms and the Fast Fourier Transform ( FFT ) Algorithm
and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...
متن کاملFractional-Fourier-transform calculation through the fast-Fourier-transform algorithm.
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...
متن کاملThe Cooley - Tukey Fast Fourier Transform Algorithm ∗
The publication by Cooley and Tukey [5] in 1965 of an e cient algorithm for the calculation of the DFT was a major turning point in the development of digital signal processing. During the ve or so years that followed, various extensions and modi cations were made to the original algorithm [6]. By the early 1970's the practical programs were basically in the form used today. The standard develo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2018
ISSN: 0170-4214,1099-1476
DOI: 10.1002/mma.4767