• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.28-34
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• 2007

In this paper, we present a quasi-Jacket block matrices over binary matrices which all are belong to a class of cocyclic matrices is the same as the Hadamard case and are useful in digital signal processing, CDMA, and coded modulation. Based on circular permutation matrix(CPM) cocyclic quasi block low-density matrix is introduced in this paper which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.889-896
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• 2006

The crest factor distribution of orthogonal frequency division multiplexing (OFDM) symbol sequences is evaluated and it is shown that OFDM symbol sequences with a short period are expected to have a high crest factor. The crest factor relationship between two input symbol sequences, Hamming distance D apart is also derived. Using these two results, we propose two criteria for a phase sequence set of the selected mapping (SLM) scheme and suggest the rows of the cyclic Hadamard matrix constructed from an m-sequence as the near optimal phase sequence set of the SLM scheme.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.575-584
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• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.601-603
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• 1998

In this paper, Hadamard transform imaging spectrometers utilizing Grill spectrometers are proposed. General Hadamard Transform Spectrometers (HTS) carry out one-encoding through input masks, but Grill spectrometers carry out double-encoding through entrance and exit masks. Thus Grill spectrometers increase the signal-to-noise ratio by double-encoding. we reconfigure the system by using the Grill spectrometers which use a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the system and apply the mask characteristics method, i.e. $T^{I}$ method, to complete fast algorithm. Through computer simulations, we want to prove the superiority of the proposed system by comparing with the conventional HTS. From Observations concerning the average mean square error(AMSE) associated with estimates from the $T^{I}$ spectrum-recovery method, the relative performances of the two systems are compared.

• The Journal of the Acoustical Society of Korea
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• v.20 no.1
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• pp.13-20
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• 2001

Adaptive digital filters with long impulse response such as acoustic echo canceller and active noise controller suffer from slow convergence and computational burden. Subband techniques and multirate signal processing have been recently developed to improve the problem of computational complexity and slow convergence in conventional adaptive filter. Any FIR transfer function can be realized as a serial connection of interpolators followed by subfilters with a sparse impulse response. In this case, each interpolator which is related to the column vector of Hadamard matrix has band-pass magnitude response characteristics shifted uniformly. Subband technique using Hadamard transform and decimation of subband signal to reduce sampling rate are adapted to system modeling and acoustic noise cancellation In this paper, delayless subband structure with nonuniform bandwidth has been proposed to improve the performance of the convergence speed without aliasing due to decimation, where input signal is split into subband one using tree-structured filter bank, and the subband signal is decimated by a decimator to reduce the sampling rate in each channel, then subfilter with sparse impulse response is transformed to full band adaptive filter coefficient using Hadamard transform. It is shown by computer simulations that the proposed method can be adapted to general adaptive filtering.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.8
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• pp.1452-1459
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• 2016

Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing in and under Nyquist rate representation. Generally, the measurement prediction usually works well with a small block while the quality of recovery is known to be better with a large block. In order to overcome this dilemma, conventional research works use a structural measurement matrix with which compressed sensing is done in a small block size but recovery is performed in a large block size. In this way, both prediction and recovery are made to be improved at same time. However, the conventional researches did not compare the performances of the structural measurement matrix, affected by the block size. In this paper, by expanding a structural measurement matrix of conventional works, their performances are compared with different block sizes. Experimental results show that a structural measurement matrix with $4{\times}4$ Hadamard transform matrix provides superior performance in block size 4.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.19-26
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• 2013

In this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of $4{\times}4$ and $8{\times}8$ Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.7
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• pp.17-21
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• 2008

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.343-352
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• 2006

A real matrix A is called a sign-central matrix if for, every matrix $\tilde{A}$ with the same sign pattern as A, the convex hull of columns of $\tilde{A}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $(x_1,{\ldots},x_n)^T$ is called stable if $\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|$. A tight sign-central matrix is called a $tight^*$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($tight^*$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $tight^*$ sign-central.

• Journal of Internet Computing and Services
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• v.8 no.3
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• pp.33-43
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• 2007

In this proper, we proposes a robust watermarking against the lossy compression in the Hadamard domain. The Hadamard matrix consists of only 1 or -1 and can be computed veru fast. The Hadamrd transform has the inverse transform therefore it is able to be applied into the watermarking technology. In embedding process, we select 10 coefficients from intermediate frequency domain and create two watermark patterns. In extraction process, we use the watermark patterns and compare them to detect the watermark information. When we use the standard image ($512{\times}512$) and binary watermark image ($64{\times}64$), the results of these examines are PSNR for $38{\sim}42dB$ and BER for $3.9{\sim}12.5%$. The JPEG QF between 30 and100, naked human eyes can detect to watermark image easily. The experimental results show that performance of Hadamard domain is better than those of DCT, FFT, and DWT.