• Journal of Communications and Networks
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• v.13 no.5
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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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• v.15 no.4E
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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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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• v.24 no.9
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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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• v.46 no.3
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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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• v.24 no.9
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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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.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.4
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• pp.295-303
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• 2008

In general, transform domain adaptive filters show faster convergence speed than the time domain adaptive filters, but the amount of calculation increases dramatically as the filter order increases. This problem can be solved by making use of the subband structure in transform domain adaptive filters. In this paper, to increase the convergence speed on the generalized subband decomposition FIR adaptive filters, a structure of the adaptive filter with subfilter of dyadic sparsity factor in wavelet transform domain is designed. And, in this adaptive filter, the equivalent input in transform domain is derived and, by using the input, the convergence properties for the LMS algorithm is analyzed and evaluated. By using this sub band adaptive filter, the inverse system modeling and the periodic noise canceller were designed, and, by computer simulation, the convergence speeds of the systems on LMS algorithm were compared with that of the subband adaptive filter using DFT(discrete Fourier transform).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.8B
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• pp.1558-1566
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• 1999

While high resolution images are required for various applications, aliased low-resolution images are only available due to the physical limitations of sensors. In this paper, we propose an algorithm to reconstruct a high resolution image from multiple aliased low-resolution images, which is based on the generalized multichannel deconvolution technique. The conventional approaches are based on the discrete Fourier transform (DFT) since the aliasing effect is easily analyzed in the frequency domain. However, the useful solution may not be available in many cases, i.e., the underdetermined cases or the insufficient subpixel information cases. In order to compensate for such ill-posedness, the generalized multichannel regularization was adopted in the spatial domain. Furthermore, the usage of the discrete cosine transform instead of the DFT leads to the computationally efficient reconstruction algorithm. The validity of the proposed algorithm is both theoretically and experimentally demonstrated in this paper. It is also shown that the effect of inaccurate motion information is reduced by regularization.