The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.
An Overview: From Fourier Analysis to Wavelet Analysis. The Integral Wavelet Transform and Time-Frequency Analysis. Inversion Formulas and Duals. Classification of Wavelets. Mul...
FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield ...
1. The Radix-2 Frameworks. Matrix Notation and Algorithms The FFT Idea The Cooley-Tukey Factorization Weight and Butterfly Computations Bit Reversal and Transposition The Cooley...
Abstract Partial Fourier reconstruction algorithms exploit the redundancy in magnetic resonance data sets so that half of the data is calculated during image reconstruction rath...
A generalized state realization of the Wiberg (1996) type is called normal if symbol variables have degree 1 and state variables have degree 2. A natural graphical model of such...
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