• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.498-503
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• 2009

As for Hadamard Transform, because the calculation time of this transform is slower than Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT), the effectiveness and the practicality are insufficient. Then, the computational complexity can be decreased by using the butterfly operation as well as FFT. We composed calculation time of FFT with that of Fast Complex Hadamard Transform by constructing the algorithm of Fast Complex Hadamard Transform. They are indirect conversions using program of complex number calculation, and immediate calculations. We compared calculation time of them with that of FFT. As a result, the reducing the calculation time of the Complex Hadamard Transform is achieved. As for the computational complexity and calculation time, the result that quadrinomial Fast Complex Hadamard Transform that don't use program of complex number calculation decrease more than FFT was obtained.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.10
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• pp.1617-1623
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• 1989

The introduction of the fast Fourier transform(FFT),an efficient computational algorithm for the discrete Fourier transform(DFT) by Cooley and Tukey(1965), has brought to the limelight various other discrete transforms. Some of the analog functions from which these transforms have been derived date back to the early 1920's, for example, Walsh functions (Walsh, 1923) and Hadamard Transform(Enomoto et al, 1965). Fast algorithms developed for the forward transform are equally applicable, exept for minor changes, to the inverse transform. In this paper, we present a simple pipelined Hadamard matrix(HM) which is used to develop a fast algorithm for the Hadamard Processor (HP). The Fast Hadamard Transform(FHT) can be derived using matrix partitioning techniques. The HP system is incorporated through a modular design which permits tailoring to meet a wide range of video data link applications. Emphasis has been placed on a low cost, a low power design suitable for airbone system and video codec.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1379-1382
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• 1997

We introduce a fast implementation of the adaptive transversal filter which uses least-mean-square(LMS) algorithm. The fast Hadamard transform(FHT) is used for the implementation of the filter. By using the proposed filter we can get the significant time reduction in computatioin over the conventional time domain LMS filter at the cost of a little performance. By computer simulation, we show the comparison of the propsed Hadamard-domain filter and the time domain filter in the view of multiplication time, mean-square error and robustness for noise.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.2
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• pp.301-308
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• 1987

In this paper, we have defined the Weighted Hadamard Transform (WHT) and developed efficient algorithms for the fast computation of the WHT. The WHT is applied to digital image processing and compared with Hadamard Transform (HT). We have weighted at the center spatial frequency domains of the Hadamard Transform and transmitted a image and then center high frequencies are neglected at the receiving. The WHT of signal to noise ratio(SNR) and image quality are enhanced than the HT.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.616-619
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• 1997

The spectrum-recovery scheme in Hadamard transform spectroscopy is commonly implemented with a fast Hadamard transform (FHT). When the Hadamard or simplex matrix corresponding to the mask does not have the same ordering as the Hadamard matrix corresponding to the FHT, a modification is required. When the two Hadamard matrices are in the same equivalence class, this modification can be implemented as a permutation scheme. This paper investigates permutation schemes for this application. This paper is to relieve the confusion about the applicability of existing techniques, reveals a new, more efficient method: and leads to an extension that allows a permutation scheme to be applied to any Hadamard or simplex matrix in the appropriate equivalence class.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.173-176
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• 1987

This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.769-772
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• 2001

Waish-Hadamard Transform은 압축, 필터링, 코드 디자인 등 다양한 이미지처리 분야에 응용되어왔다. 이러한 Hadamard Transform을 기본으로 확장한 Jacket Transform은 행렬의 원소에 가중치를 부여함으로써 Weighted Hadamard Matrix라고 한다. Jacket Matrix의 cocyclic한 특성은 암호화, 정보이론, TCM 등 더욱 다양한 응용분야를 가질 수 있고, Space Time Code에서 대역효율, 전력면에서도 효율적인 특성을 나타낸다 [6],[7]. 본 논문에서는 Distributed Arithmetic(DA) 구조를 이용하여 Fast Jacket Transform(FJT)을 구현한다. Distributed Arithmetic은 ROM과 어큐뮬레이터를 이용하고, Jacket Watrix의 행렬을 분할하고 간략화하여 구현함으로써 하드웨어의 복잡도를 줄이고 기존의 시스톨릭한 구조보다 면적의 이득을 얻을 수 있다. 이 방법은 수학적으로 간단할 뿐 만 아니라 행렬의 곱의 형태를 단지 덧셈과 뺄셈의 형태로 나타냄으로써 하드웨어로 쉽게 구현할 수 있다. 이 구조는 입력데이타의 워드길이가 n일 때, O(2n)의 계산 복잡도를 가지므로 기존의 시스톨릭한 구조와 비교하여 더 적은 면적을 필요로 하고 FPGA로의 구현에도 적절하다.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.242-242
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• 2000

Comparing to the conventional adaptive filters using LMS algorithm, the proposed adaptive filters can reduce the amounts of computation and have robustness to variance of characteristics of input signals. LMS algorithm is performed in the domain of Hadamard transform after a reference signal and input signal are transformed by fast Hadamard transformation. As a transformation from time domain to Hadamard transformed domain, the proposed filter not only maintains the performance of estimating an input signal but also greatly reduces the number of multiplication. Moreover, the effect of characteristic changes of input signal is decreased. Computer simulation shows the stability and robustness of the proposed filter.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.571-579
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• 1999

In this paper, a Hadamard transform imaging spectrometer(HTIS) is proposed by using a grill spectrometer. And we reconfigure the system by using the grill sectrometer which uses a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the Hadamard transform imaging spectrometer and apply the mask characteristics compensation method, i.e. $ {T}^{-1}$ method, to complete fast algorithm. Also, through computer simulations the superiority of the proposed system in this paper to the conventional Hadamard transform spectrometer(HTS) is proved and the performance of the two systems are compared by introducing average mean square error(AMSE) as the algebraic criterion.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.1A
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• pp.43-50
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• 2012

The use of an error-correcting code is essential in digital communication systems where the channel is noisy. Unless a receiver has accurate channel coding parameters, it becomes difficult to decode the digitized encoding bits correctly. In this paper, estimation algorithm for RM(Reed-Muller) codes using FHT (Fast Hadamard algorithm) is proposed. The proposed algorithm estimates the channel coding parameters of RM codes and then decodes the codes using the characteristic of FHT. And we also verify the algorithm by performing intensive computer simulation in additive white gaussian noise (AWGN) channel.