• 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.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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.4
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• pp.251-258
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• 1986

There is much redundancy in image data such as TV signals and many techniques to redice it have been studied. In this paper, Hadamard transform is studied through computer simulation and experimental model. Each element of hadamard matrix is either +1 or -1, and the row vectors are orthogonal to another. Its hardware implementation is the simplest of the usual orthogonal transforms because addition and sulbraction are necessary to calculate transformed signals, while not only addition but multiplication are necessary in digital Fourier transform, etc. Linclon data (64$ imes$64) are simulated using 8th-order and 16th-order Hadamard transform, and 8th-order is implemented to hardware. Theoretical calculation and experimental result of 8th-order show that 2.0 bits/sample are required for good quality.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.9
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• pp.30-40
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• 2014

As the Hadamard transform can be generalized into the Jacket transform, in this paper, we generalize the Haar transform into the Jacket-Haar transform. The entries of the Jacket-Haar transform are 0 and ${\pm}2^k$. Compared with the original Haar transform, the basis of the Jacket-Haar transform is general and more suitable for signal processing. As an application, we present the DCT-II(discrete cosine transform-II) based on $2{\times}2$ Hadamard matrix and HWT(Haar Wavelete transform) based on $2{\times}2$ Haar matrix, analysis the performances of them and estimate them via the Lenna image simulation.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1125-1128
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• 1993

We propose the new method about the neural-based pattern recognition by using Hadamard transform for the improvement of learning speed, stability and flexibility of network. We can obtain the spatial feature of pattern by Hadamard transformed pattern. We carried out an experiment to estimate the effect of Hadamard transform. We tried the learning of numeric patterns, and tried the pattern recognition with noisy pattern. As a result, the learning times of the network for the 'Hadamard' case is smaller than that of usual case. And the recognition rate of the network for the 'Hadamard' case is higher than that of usual case, too.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.1
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• pp.132-137
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• 2007

Jacket transforms are a class of transforms which are simple to calculate, easily inverted and are size-flexible. Previously reported jacket transforms were generalizations of the well-known Walsh-Hadamard transform (WHT) and the center-weighted Hadamard transform (CWHT). In this paper we present a new class of jacket transform not derived from either the WHT or the CWHT. This class of transform can be applied to any even length vector, and is applicable to finite fields and is useful for constructing error control codes.

• 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 Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.5
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• pp.205-215
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• 2006

In this paper an optical power meter using Hadamard transform, which can be used in multiple channel optical elements alignment system, is proposed. A traditional optical power meter in multiple channel optical elements alignment system is able to judge how well the elements are aligned each other by measuring optical power of the first and the last two channels with at least two detectors. It has critical drawback that the alignment accuracy per channel is dependent on the number of detectors. The proposed optical power meter can get noise reduction by the Hadamard transform based multiplexing technique. The Hadamard transform based multiplexing technique using spatial light modulators is distinguished by the best enhancement of signal-to-noise ratio (SNR) for the reconstructed signals. Moreover, the noise reduction increases with increasing the order of multiplexing, namely the number of optical element channels. The proposed system is implemented by PDLC (Polymer Dispersed Liquid Crystal) mask which is operated by electric filed and generates optimal multiplexing patterns based on the Hadamard transform and single detector. It means that we obtain not only the each channel's optical power of multiple channel elements at once but also the best enhancement of SNR with single detector. Experimental results show that the proposed optical power meter is suitable for an active optical alignment system for multiple channel optical elements.

• 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.