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215,586
FOURIER SERIES
, 2003
"... • Windows are timedomain weighting functions that are used to reduce Gibbs ’ oscillations that are caused by the truncation of a Fourier series. • They are employed in a variety of traditional applications including power spectral estimation, beamforming, and digital filter design. • More recently, ..."
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• Windows are timedomain weighting functions that are used to reduce Gibbs ’ oscillations that are caused by the truncation of a Fourier series. • They are employed in a variety of traditional applications including power spectral estimation, beamforming, and digital filter design. • More recently
Fourier Series
"... t dt = # T/2form = n 0form #= n , (3) and # T 0 sin m#t cos n#t dt =0 (4) where # =2#/T , we have done all of the ground work for analytically describing any periodic signal. The concept of orthogonality is significant in power electronics, where we are often describing the conversion of ene ..."
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t dt = # T/2form = n 0form #= n , (3) and # T 0 sin m#t cos n#t dt =0 (4) where # =2#/T , we have done all of the ground work for analytically describing any periodic signal. The concept of orthogonality is significant in power electronics, where we are often describing the conversion of energy from one form to another. Our work generally involves dealing with signals that contain many frequency components. In terms of the average power represented by 1 these signals, Eq. 3 implies that if a particular frequency component is to contribute to average power flow, then that frequency must be present in both the voltage and the current. Exploitation of signal orthogonality can dramatically simplify circuit analysis in some cases. Thinking about the structure of the waveform before beginnin
Fourier series
, 2009
"... 2.8.3 The FourierPlancherel transformation............. 99 2.9 Fourier transformation of measures................... 104 Preface These notes are based on handwritten lecture notes in Danish from a graduate course in 1999. Parts of the Danish notes were written by Tage Gutmann Madsen for the second ..."
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2.8.3 The FourierPlancherel transformation............. 99 2.9 Fourier transformation of measures................... 104 Preface These notes are based on handwritten lecture notes in Danish from a graduate course in 1999. Parts of the Danish notes were written by Tage Gutmann Madsen for the second
Fourier Series and Their Applications
, 2006
"... Fourier series are of great importance in both theoretical and applied mathematics. For orthonormal families of complexvalued functions {φn}, Fourier Series are sums of the φn that can approximate periodic, complexvalued functions with arbitrary precision. This paper will focus on the Fourier Series ..."
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Fourier series are of great importance in both theoretical and applied mathematics. For orthonormal families of complexvalued functions {φn}, Fourier Series are sums of the φn that can approximate periodic, complexvalued functions with arbitrary precision. This paper will focus on the Fourier
Acceleration of Fourier Series
"... We discuss the effects of several sequence acceleration methods on the partial sums of Fourier series. For a large set of functions we show that these methods fail. ..."
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We discuss the effects of several sequence acceleration methods on the partial sums of Fourier series. For a large set of functions we show that these methods fail.
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 208 (52 self)
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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
CONVERGENCE OF RANDOM FOURIER SERIES
"... Abstract. This paper will study Fourier Series with random coefficients. We begin with an introduction to Fourier series on the torus and give some of the most important results. We then give some important results from probability theory, and build on these to prove a variety of theorems that deal ..."
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Abstract. This paper will study Fourier Series with random coefficients. We begin with an introduction to Fourier series on the torus and give some of the most important results. We then give some important results from probability theory, and build on these to prove a variety of theorems that deal
LOCALIZATION OF FACTORED FOURIER SERIES
"... Communicated by L. Leindler ABSTRACT. In this paper we deal with a main theorem on the local property of  ¯ N, pn  k summability of factored Fourier series, which generalizes some known results. ..."
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Communicated by L. Leindler ABSTRACT. In this paper we deal with a main theorem on the local property of  ¯ N, pn  k summability of factored Fourier series, which generalizes some known results.
Notes on Fourier Series
"... This notes on Fourier series complement the textbook. Besides the textbook, other introductions to Fourier series (deeper but still elementary) are Chapter 8 of CourantJohn [5] and Chapter 10 of Mardsen [6]. 1 Introduction and terminology We will be considering functions of a real variable with com ..."
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This notes on Fourier series complement the textbook. Besides the textbook, other introductions to Fourier series (deeper but still elementary) are Chapter 8 of CourantJohn [5] and Chapter 10 of Mardsen [6]. 1 Introduction and terminology We will be considering functions of a real variable
Essays on analysis Fourier series
, 2011
"... This essay is an introduction to analysis on a compact torus, including Fourier series, distributions, and Sobolev spaces, and a brief account of pseudodifferential operators. As an application, it will be shown that solutions of a smooth elliptic differential equation on any open subset of Rn are s ..."
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This essay is an introduction to analysis on a compact torus, including Fourier series, distributions, and Sobolev spaces, and a brief account of pseudodifferential operators. As an application, it will be shown that solutions of a smooth elliptic differential equation on any open subset of Rn
Results 1  10
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