• Journal of Communications and Networks
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• 제13권5호
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• pp.449-455
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• 2011

Inspired by fast Jacket transforms, we propose simple factorization and construction algorithms for the M-dimensional discrete Fourier transform (DFT) matrices underlying generalized Chinese remainder theorem (CRT) index mappings. Based on successive coprime-order DFT matrices with respect to the CRT with recursive relations, the proposed algorithms are presented with simplicity and clarity on the basis of the yielded sparse matrices. The results indicate that our algorithms compare favorably with the direct-computation approach.

• The Journal of the Acoustical Society of Korea
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• 제15권4E호
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• pp.53-57
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• 1996

An extension of the well-known Fourier transform is developed in this paper. It is denoted as the generalized Fourier transform(GFT), since it encompasses the Fourier transform as its special case. The first idea of this extension can be found on [1]. In the definition of the N-point discrete GFT, it first construct a passband in time which functions as a window in the time domain. An appropriate interpretation of each variables are introduced during the definition of the GFT, followed by the formal derivation of the inverse GFT. This transform pair is similar to the windowing in the frequency domain such as the subband coding technique (or filter bank approach) and could be extended to the wavelet transform.

• 대한수학회보
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• 제53권3호
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• pp.733-749
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• 2016

We aim to compute discretely monitored geometric Asian option prices under the Heston model. This method involves explicit formula for multivariate generalized Fourier transform of volatility process and their integrals over different time intervals using a recursive method. As numerical results, we illustrate efficiency and accuracy of our method. In addition, we simulate scenarios which show evidently practical importance of our work.

• International Journal of Computer Science & Network Security
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• 제24권9호
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• pp.41-49
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• 2024

This paper proposes dual symbol superposition block carrier transmission with frequency domain equalization (DSS-FDE) system. This system is based upon χ-transform matrix, which is obtained by concatenation of discrete Hartley transform (DHT) matrix and discrete Fourier transform (DFT) matrices into single matrix that is remarkably sparse, so that, as it will be shown in this paper, it only has non-zero entries on its principal diagonal and one below the principle anti-diagonal, giving it shape of Latin alphabet χ. When multiplied with constellation mapped complex transmit vector, each entry of resultant vector is weighted superposition of only two entries of original vector, as opposed to all entries in conventional DFT based OFDM. Such a transmitter is close to single carrier block transmission with frequency domain equalization (SC-FDE), which is known to have no superposition. The DSS-FDE offers remarkable simplicity in transmitter design and yields great benefits in reduced complexity and low PAPR. At receiver-end, it offers the ability to harvest full diversity from multipath fading channel, full coding gain, with significant bit error rate (BER) improvement. These results will be demonstrated using both analytical expressions, as well as simulation results. As will be seen, this paper is Part III of three-paper series on alternative transforms for multicarrier communication (MC) systems.

• ETRI Journal
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• 제46권3호
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• pp.392-403
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• 2024

Even though generalized frequency division multiplexing is an alternative waveform method expected to replace the orthogonal frequency division multiplexing in the future, its implementation must alleviate channel effects. Least-squares (LS), a low-complexity channel estimation technique, could be improved by using the discrete Fourier transform (DFT) without increasing complexity. Unlike the usage of the LS method, the DFT-based method requires the receiver to know the channel impulse response (CIR) length, which is unknown. This study introduces a simple, yet effective, CIR length estimator by utilizing LS estimation. As the cyclic prefix (CP) length is commonly set to be longer than the CIR length, it is possible to search through the first samples if CP is larger than a threshold set using the remaining samples. An adaptive scale is also designed to lower the error probability of the estimation, and a simple signal-to-interference-noise ratio estimation is also proposed by utilizing a sparse preamble to support the use of the scale. A software simulation is used to show the ability of the proposed system to estimate the CIR length. Due to shorter CIR length of rural area, the performance is slightly poorer compared to urban environment. Nevertheless, satisfactory performance is shown for both environments.

• International Journal of Computer Science & Network Security
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• 제24권9호
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• pp.21-29
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• 2024

Precoding of the orthogonal frequency division multiplexing (OFDM) with Walsh Hadamard transform (WHT) is known in the literature. Instead of performing WHT precoding and inverse discrete Fourier transform separately, a product of two matrix can yield a new matrix that can be applied with lower complexity. This resultant transform, T-transform, results in T-OFDM. This paper extends the limited existing work on T-OFDM significantly by presenting detailed account of its computational complexity, a lower complexity receiver design, an expression for PAPR and its cumulative distribution function (cdf), sensitivity of T-OFDM to timing synchronization errors, and novel analytical expressions signal to noise ratio (SNR) for multiple equalization techniques. Simulation results are presented to show significant improvements in PAPR performance, as well improvement in bit error rate (BER) in Rayleigh fading channel. This paper is Part II of a three-paper series on alternative transforms and many of the concepts and result refer to and stem from results in generalized multicarrier communication (GMC) system presented in Part I of this series.

• 대한수학회지
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• 제59권2호
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.

• 융합신호처리학회논문지
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• 제9권4호
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• pp.295-303
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• 2008

변환영역 적응필터는 시간영역 적응필터보다 일반직으로 수렴속도가 빠르지만 필터의 차수가 증가함에 따라 계산량이 크게 증가한다. 이러한 문제점은 변환영역 적응필터를 서브밴드 분해구조로 변경함으로써 해결할 수 있다. 이 논문에서는 일반화된 서브밴드 분해 FIR 적응 필터의 수렴속도 향상을 위해 웨이블릿 변환영역에서 다이아딕 희소인자 서브필터를 가지는 일반화된 서브밴드 분해 FTR 적응 필터의 구조를 설계하였다. 그리고 이 적응필터에서 변환영역의 일반화된 등가입력을 유도하고 이 입력을 이용하여 LMS 일고리듬에 대한 수렴특성을 해석 및 평가하였다. 이 서브밴드 FIR 적응필터를 이용하여 역 모델링 시스템과 주기성 잡음제거기를 구성하고 LMS 알고리듬 대한 이 시스템들의 수련속도를 이산푸리에 변환을 이용한 서브밴드 적응필터의 것과 컴퓨터 모의실험으로 비교하였다.

• 한국통신학회논문지
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• 제24권8B호
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• pp.1558-1566
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• 1999

센서의 물리적인 한계에 의해서 저해상도의 영상밖에 얻을 수 없는 경우에도 고해상도의 영상이 필요할 때가 있다. 본 논문에서는 이러한 경우에 다중채널의 디컨벌루션 방법을 기반으로 다수의 저해상도 영상들로부터 하나의 고해상도 영상을 얻을 수 있는 영상 복원 알고리즘을 제안하고자 한다. 엘리어싱은 주파수 영역에서 해석하기 쉽기 때문에 DFT를 기반으로 한 방법이 일반적으로 사용되어졌다. 그러나 복원에 필요한 저해상도 영상이 충분하지 않거나, 저해상도 영상들이 가지는 정보가 적절하지 않을 경우에 대해서는 원하는 고해상도의 영상을 얻을 수 없었다. 그래서 이를 극복하기 위해 공간 영역으로 재해석하면 확장된 다중채널의 정규화를 사용할 수 있었으며, DFT대신에 DCT를 사용하여 연산량을 줄일 수 있었다. 이론적인 고찰과 실험을 통하여 우리가 제안한 알고리즘에 대한 유용성을 알아보았으며, 저해상도 영상의 움직임 정보가 올바르지 않을 경우에도 정규화를 사용하여 이를 극복할 수 있음을 실험을 통해서 알 수 있었다.