DFT spectrum filtering

Zarowski, C.J.; Yunik, M.; Martens, G.O.

doi:10.1109/29.1550

Cited by 7 publications

(2 citation statements)

References 8 publications

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“…The Walsh-Hadamard transform is used for such an application [5]. Also, it is well known from the literature that the fast Walsh-Hadamard transform can be efficiently used for the calculation of the DFT [28] for implementing adaptive filters [11] and for DFT spectrum filter realizations [34]. The usual frequency-domain FIR filtering problem can be easily converted into a Walsh frequencydomain filtering problem, and similar structure results in a possible alternative for infinite-impulse response filter implementations [17].…”

Section: Discussionmentioning

confidence: 99%

Family of unified complex Hadamard transforms

Rahardja¹,

Falkowski²

1999

IEEE Trans. Circuits Syst. II

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Novel discrete orthogonal transforms are introduced in this paper, namely the unified complex Hadamard transforms. These transforms have elements confined to four elementary complex integer numbers which are generated based on the Walsh-Hadamard transform, using a single unifying mathematical formula. The generation of higher dimension transformation matrices are discussed in detail.Index Terms-Digital signal processing, discrete transforms, fast algorithms, orthogonal transforms, unified complex Hadamard transforms.

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Section: Discussionmentioning

confidence: 99%

Family of unified complex Hadamard transforms

Rahardja¹,

Falkowski²

1999

IEEE Trans. Circuits Syst. II

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“…First, two-stage factorization of DFT where the preprocess is the Walsh-Hadamard Transform (WHT) was given in [18,19]. However, in that approach the postprocess does not consist of circular correlations, and there is no simple way to compute them.…”

Section: Computational Complexitymentioning

confidence: 99%

A novel correlation‐based FFT algorithm

Chin

1992

Journal of the Chinese Institute of Engineers

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Since the discovery of the fast Fourier transform (FFT), many new FFT algorithms have been developed. Conventionally, the convolution-based approach deals commonly with the prime length discrete Fourier transforms. In this paper, based on some theorems of Number Theory, a new algorithm for computing the FFT (with power of two length) is proposed. This novel recursive algorithm contains three stages, the first and the last stages contian only additions and substractions, and the second stage is of block diagonal form, with each block being a circular correlation/convolution matrix.The newly proposed convolution-based FFT algorithm has the following advantages:(1) In terms of computational counts, this algorithm can achieve the multiplicative lower bound derived by Winograd.(2) The proposed algorithm can easily be implemented in a parallel computing environment. (3) The proposed algorithm is recursive in nature, and thus the computation structure is rather regular.

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Walsh–Hadamard Transforms: A Review

Ashrafi¹

2017

Advances in Imaging and Electron Physics

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DFT spectrum filtering

Cited by 7 publications

References 8 publications

Family of unified complex Hadamard transforms

Family of unified complex Hadamard transforms

A novel correlation‐based FFT algorithm

Walsh–Hadamard Transforms: A Review

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