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On the diagonalization of the discrete Fourier transform
, 2009
"... Dedicated to William Kahan and Beresford Parlett on the occasion of their 75th birthday Abstract. The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N = p is an odd prime number, we exhibit a c ..."
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Cited by 7 (4 self)
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Dedicated to William Kahan and Beresford Parlett on the occasion of their 75th birthday Abstract. The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N = p is an odd prime number, we exhibit a
ALTERNATIVES TO THE DISCRETE FOURIER TRANSFORM
"... It is wellknown that the discrete Fourier transform (DFT) of a finite length discretetime signal samples the discretetime Fourier transform of the same signal at equidistant points on the unit circle. Hence, as the signal length goes to infinity, the DFT approaches the DTFT. Associated with the D ..."
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Cited by 2 (2 self)
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It is wellknown that the discrete Fourier transform (DFT) of a finite length discretetime signal samples the discretetime Fourier transform of the same signal at equidistant points on the unit circle. Hence, as the signal length goes to infinity, the DFT approaches the DTFT. Associated
On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform
 Proc. IEEE
, 1978
"... AhmwThis Pw!r mak = available a concise review of data win compromise consists of applying windows to the sampled daws pad the ^ affect On the Of in the data set, or equivalently, smoothing the spectral samples. '7 of aoise9 m the ptesence of sdroag bar The two operations to which we subject ..."
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Cited by 645 (0 self)
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subject the data are momc mterference. We dm call attention to a number of common = in be rp~crh of windows den used with the fd F ~ sampling and windowing. These operations can be performed transform. This paper includes a comprehensive catdog of data win in either order. Sampling is well understood
The Discrete Fourier Transform, Part
"... 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
The Discrete Fourier Transform, Part
, 2010
"... This paper is part 6 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 correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a ShortTime Fourie ..."
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This paper is part 6 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 correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a Short
Eigenvectors and functions of the discrete Fourier transform
 IEEE Trans. Acoust., Speech, Signal Processing
, 1982
"... AbstractA method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be effi ..."
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Cited by 31 (0 self)
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AbstractA method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can
On the Parametrization of Algebraic Discrete Fourier Transforms
"... . Computing the Discrete Fourier Transform (DFT) of signals over some nite eld Fq often requires an extension to a large eld Fq n containing an appropriate primitive root of unity. The Algebraic Discrete Fourier Transforms (ADFTs) avoid the extension of the baseeld Fq and can be used to compute th ..."
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. Computing the Discrete Fourier Transform (DFT) of signals over some nite eld Fq often requires an extension to a large eld Fq n containing an appropriate primitive root of unity. The Algebraic Discrete Fourier Transforms (ADFTs) avoid the extension of the baseeld Fq and can be used to compute
The Fourier Series and the Discrete Fourier Transform
"... : The Fourier Series and its applications to the Discrete Fourier Transform are discussed The paper is written in a colloquial style to avoid intimidating readers who are of a lesser level of intelligence and ingenuity as the vastly brilliant authors. Introduction Deemed one of the crowning achiev ..."
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: The Fourier Series and its applications to the Discrete Fourier Transform are discussed The paper is written in a colloquial style to avoid intimidating readers who are of a lesser level of intelligence and ingenuity as the vastly brilliant authors. Introduction Deemed one of the crowning
Discrete Fourier Transformation (DFT):
, 2012
"... t = time (from 0,…,T1) T = total # samples f(t) is amplitude of wave at time t n = harmonic number (max possible harmonic is T/2, or Nyquist frequency) x[k] is sample at index k in wave table b) To reconstruct wave from the harmonics... You simply take the first equation above, and recompute the wa ..."
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t = time (from 0,…,T1) T = total # samples f(t) is amplitude of wave at time t n = harmonic number (max possible harmonic is T/2, or Nyquist frequency) x[k] is sample at index k in wave table b) To reconstruct wave from the harmonics... You simply take the first equation above, and recompute the wave at each moment of time: t = 0, 1, 2,..., T1. You compute what each harmonic value is at that time, and sum the results. The overall sum is the sample value at time t. Remember to add the a0 value to all values! (over)
The Discrete Fourier Transform in Coding and Cryptography
 IEEE Inform. Theory Workshop, ITW 98
, 1998
"... Some applications of the Discrete Fourier Transform #DFT# in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in gene ..."
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Cited by 8 (0 self)
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Some applications of the Discrete Fourier Transform #DFT# in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged
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