Fourier analysis and signal processing by use of the Mobius inversion formula

Reed, I. S.; Tufts, D.W.; Yu, Xiaoli; Truong, T. K.; Shih, M.T.; Yin, Xiang

doi:10.1109/29.106864

Cited by 63 publications

(48 citation statements)

References 6 publications

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“…Then, the arithmetic Hartley transform can be derived by the use of modified Möbius inversion formula for finite series [1].…”

Section: Lemma 1 (Fundamental Property)mentioning

confidence: 99%

“…Usual arithmetic theory deals with spectrum approximations via zero-or first-order interpolation [1,3,7]. The analysis presented in this work allows a more encompassing perception of the interpolation mechanisms and gives mathematical tools for establishing validation constraints to such interpolation process.…”

Section: Corollary 1 Inverse Discrete Hartley Transform Components Camentioning

confidence: 99%

“…In fact, as show by the set of Equations 14, zero-order interpolation is an (indeed good) approximation to the cosine asymptotic weighting function. Zero-order interpolation now formally justified was intuitively used in previous work by Tufts, Reed et al [1,2,3]. Hsu, in his Ph.D. dissertation, derives an analysis of first-order interpolation effect [7].…”

Section: Zero-order Interpolationmentioning

confidence: 99%

“…In 1990, Tufts-Sadasiv algorithm was revisited and its restrictions were removed by Irving Reed, Donald W. Tufts et al [1]. Now one could use arithmetic transform method to evaluate all Fourier coefficients (even and odd) of an arbitrary periodic function.…”

Section: Introductionmentioning

confidence: 99%

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How to interpolate in arithmetic transform algorithms

Cintra¹,

Oliveira²

2002

IIEEE International Conference on Acoustics Speech and Signal Processing

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In this paper, we propose a unified theory for arithmetic transforms of a variety of discrete trigonometric transforms. The main contribution of this work is the elucidation of the interpolation process required in arithmetic transforms. We show that the interpolation method determines the transform to be computed. Several kernels were examined and asymptotic interpolation formulae were derived. Using the arithmetic transform theory, we also introduce a new algorithm for computing the discrete Hartley transform.

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“…Then, the arithmetic Hartley transform can be derived by the use of modified Möbius inversion formula for finite series [1].…”

Section: Lemma 1 (Fundamental Property)mentioning

confidence: 99%

Section: Corollary 1 Inverse Discrete Hartley Transform Components Camentioning

confidence: 99%

Section: Zero-order Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

How to interpolate in arithmetic transform algorithms

Cintra¹,

Oliveira²

2002

IIEEE International Conference on Acoustics Speech and Signal Processing

View full text Add to dashboard Cite

show abstract

“…Similar, but different, algorithms were studied by Tufts and Sadasiv [2], Schiff and Walker [3] for the calculation of the Fourier coefficients of even periodic functions. This method was extended in [4] for the calculation of the Fourier coefficients of both the even and odd components of a periodic function. The Bruns approach was incorporated in [5] resulting in a more computationally balanced algorithm.…”

Section: Introductionmentioning

confidence: 99%