• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.307-315
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• 2019

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.

• The Journal of the Korea Contents Association
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• v.8 no.4
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• pp.79-85
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• 2008

These days, orthogonal frequency division multiplexing (OFDM) transmission method is widely used for broadband communication systems. The OFDM, which uses sine waves as orthogonal basis functions, is one of the orthogonal waveform modulation techniques. In this paper, we investigate a wavelet packet modulation method which uses wavelet packets instead of sine waves as the basis functions. The wavelet packets may have different patterns in two dimensional time-frequency domain, and we can design the packets appropriate for the channel environments with much flexibility. In this paper, we investigate the characteristics of the wavelet packet modulation as one of the multicarrier modulation methods, And we illustrate by simulations that narrowband interference can be reduced effectively by control the bandwidth of the wavelet packets.

• Spatial Information Research
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• v.17 no.4
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• pp.455-462
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• 2009

A method to find the nearly optimal PSNR values for compression was tried to remotely sensed images. There is no rule to find the best wavelet pairs for image processing. The expected wavelet pairs following the suggested algorithm showed the optimal result for various kinds of images. Firstly, the PSNR variations with three wavelet families were analyzed. In many cases the longer wavelet filter shows the higher PSNR value, but the rate is getting less in orthogonal wavelet families. Wavelets with moderate filter length are suggested at the point of computational cost. For biorthogonal families it was hard to predict from the length of filters. Multiresolution wavelet analysis was used up to level 3 with three kinds of wavelet families. Biorthogonal wavelet family showed irregular pattern to get the maximum PSNR values, while orthogonal wavelet families showed regular pattern. In orthogonal wavelet families the nearly optimal wavelet pair can be predicted from the level 1.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.639-647
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• 1996

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.9
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• pp.1188-1197
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• 1995

This paper describes an algorithm that reduces computational requirement of the Kalman filter and estimates the signal efficiently. The reference signals are mapped onto the orthogonal wavelet transform domain so that the eigenvalue spread of its autocorrelation matrix could be smaller than that in the time domain. In the wavelet transform domain the autocorrelation matrix is nearly diagonal. Therefore, the transformed signal can be decomposed each orthogonal elements. The Kalman filter can be applied to each orthogonal elements and computational requirement is reduced. The possibility of applying the parallel Kalman filter was verified through the theory and simulation. The eigenvalue spread in the wavelet transform domain is smaller 8.35 times than that in the time domain and the computational requirement is reduced from 1.4 times to 2. 93 times than that of the conventional Kalman filter.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.5
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• pp.853-860
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• 2001

This paper presents the new two denoising methods using wavelet. One is new spatially selective noise filtration(NSSNF) using spatial correlation and the other is undecimated discrete wavelet transform (UDWT) threshold-based. NSSNF got the flexible gain special property of SNR adding new parameter at the existing SSNF and UDWT had superior denosing effect than orthogonal wavelet transform(OWT) applied soft-threshold by applied hard-threshold. We selected additive white gaussian noise(AWGN) in this test environment. Also we analyzed and compared ousting denoising method using SNR as standard of judgement of improvemental effect.

• Journal of IKEEE
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• v.21 no.1
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• pp.39-45
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• 2017

Image compression is now essential for applications such as transmission and storage in data bases. For video and digital image applications the use of long tap filters, while not providing any significant coding gain, may increase the hardware complexity. We use a wavelet transform in order to obtain a set of bi-orthogonal sub-classes of images; First, the design of short kernel symmetric analysis is presented in 1-dimensional case. Second, the original image is decomposed at different scales using a subband filter banks. Third, this paper is presented a technique for obtaining 2-dimensional bi-orthogonal filters using McClellan transform. It is shown that suggested wavelet bases is well used on wavelet transform for image compression. From performance comparison of bi-orthogonal filter, we actually use filters close to ortho-normal filters on application of wavelet bases to image analysis.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.181-189
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• 2017

A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.