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The Discrete Fourier Transform: Part 4 The Spectral Leakage
 Journal of Object Technology
"... This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast ..."
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Cited by 4 (1 self)
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This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse
The Discrete Fourier Transform, Part 4: Spectral Leakage
"... This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast ..."
Abstract
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This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse
Efficient encoding via Gröbner bases and discrete Fourier transforms for several kinds of algebraic codes
 Submitted in 2007 IEEE Int. Symp. Information Theory, arXiv:cs.IT/0703104
"... Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2dimensional inverse discrete Fourier transform, which generalizes the Mattson–So ..."
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Cited by 4 (3 self)
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Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2dimensional inverse discrete Fourier transform, which generalizes the Mattson
The Discrete Fourier Transform, Part 5: Spectrogram
"... This paper is part 5 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on the spectrogram. The spectrogram performs a ShortTime Fourier Transform (STFT) in order to estimate the spectrum of a signal as a fu ..."
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This paper is part 5 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on the spectrogram. The spectrogram performs a ShortTime Fourier Transform (STFT) in order to estimate the spectrum of a signal as a
Developing And Comparing Numerical Methods For Computing The Inverse Fourier Transform
"... Computing the Fourier transform and its inverse is important in many applications of mathematics, such as frequency analysis, signal modulation, and filtering. Two methods will be derived for numerically computing the inverse Fourier transforms, and they will be compared to the standard inverse disc ..."
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discrete Fourier transform (IDFT) method. The first computes the inverse Fourier transform through direct use of the Laguerre expansion of a function. The second employs the Riesz projections, also known as Hilbert projections, to numerically compute the inverse Fourier transform. For some smooth functions
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 211 (52 self)
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by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error
Fast Discrete Curvelet Transforms
, 2005
"... This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform [12, 10] in two and three dimensions. The first digital transformation is based on unequallyspaced fast Fourier transforms (USFFT) while the second is based on the wrap ..."
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Cited by 175 (9 self)
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This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform [12, 10] in two and three dimensions. The first digital transformation is based on unequallyspaced fast Fourier transforms (USFFT) while the second is based
Comments on 'Sinc Interpolation of Discrete Periodic Signals'
, 1998
"... Recently, the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation. The expression obtained, however, is not numerically stable when evaluated at or near integer values of time. This correspondence presents a numerically stable formulat ..."
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Cited by 9 (0 self)
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formulation equivalent to the results reported in the above cited paper and which, when sampled, is also shown to be equivalent to the inverse discrete Fourier transform (IDFT).
An EM Algorithm for WaveletBased Image Restoration
, 2002
"... This paper introduces an expectationmaximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with lowcomplexity, expressed in terms of the wavelet coecients, taking a ..."
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Cited by 352 (22 self)
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the efficient image representation oered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. The algorithm alternates between an Estep based on the fast Fourier transform (FFT) and a DWTbased Mstep, resulting in an ecient iterative
Comments on "Sinc Interpolation of Discrete Periodic Signals"
"... : Recently, the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation. The expression obtained, however, is not numerically stable when evaluated at or near integer values of time. This correspondence presents a numerically stable formul ..."
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formulation equivalent to the results reported in the above cited paper and which, when sampled, is also shown to be equivalent to the inverse discrete Fourier transform (IDFT). To appear in the IEEE Transactions on Signal Processing 2 I.
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