• MALSORI
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• no.47
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• pp.85-96
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• 2003

It is difficult to implement sound field effect on real time using linear convolution in time domain because linear convolution needs much multiply operations. In this paper three ways is introduced to reduce multiplication operations. Firstly, linear convolution in time domain is replaced with circular convolution in frequency domain. It means that it operates multiplication in place of convolution. Secondly, one frame will be divided into several frames. It will reduce the multiplication operation in processing that transforms time domain into frequency domain. Finally, QFT will be used in place of FFT. Three ways result much reduction in multiplication operations. The reduction of the multiplication operation makes the real time implementation possible.

• MALSORI
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• no.51
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• pp.85-98
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• 2004

It is almost impossible to generate the sound field effect in real time with the time-domain linear convolution because of its large multiplication operation requirement. To solve this, three methods are introduced to reduce the number of multiplication operations in this paper. Firstly, the time-domain linear convolution is replaced with the frequency-domain circular convolution. In other words, the linear convolution result can be derived from that of the circular convolution. This technique reduces the number of multiplication operations remarkably, Secondly, a subframe concept is introduced, i.e., one original frame is divided into several subframes. Then the FFT is executed for each subframe and, as a result, the number of multiplication operations can be reduced. Finally, the QFT is used in stead of the FFT. By combining all the above three methods into our final the SFE generation algorithm, the number of computations are reduced sufficiently and the real-time SFE generation becomes possible with a general PC.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.3
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• pp.112-118
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• 2014

As higher quality of image is required for digital image scaling, longer processing time is required. Therefore the technology that can make higher quality image quickly is needed. We propose the double linear-cubic convolution interpolation which creates the high quality image with low complexity and hardware resources. The proposed interpolation methods which are made up of four one-dimensional linear interpolations and one one-dimensional cubic convolution perform linear-cubic convolution interpolation in horizontal and vertical direction. When compared in aspects of peak signal-to-noise ratio(PSNR), performance time and amount of hardware resources, the proposed interpolation provided better PSNR, low complexity and less hardware resources than bicubic convolution interpolation.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.505-514
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• 2019

In this paper, some results are obtained from studying convolution on the spectrum of full transformation semigroup and some of its subsemigroups using Cayley's table. The shift of ${\alpha}$ determines its eigenvalues and one-dimensional linear convolution is complex in Symmetric group.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1037-1041
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• 2007

With the advent of sound field simulator, many sound fields have been reproduced by obtaining the impulse responses of specific acoustic spaces like famous concert hall, opera house. This sound field reproduction has been done by the linear convolution operation between the sound input signal and the impulse response of certain acoustic space. However, the conventional finite impulse response based linear convolution operation always makes real-time implementation of sound field generator impossible due to the large amount of computational burden. This paper introduces the fast convolution method using perceptual redundancy in the processed signals, input audio signal and room impulse response. Temporal and spectral psycho-acoustic filters considering masking effects are implemented in the proposed convolution structure. It reduces the computational burden of convolution methods for realtime implementation of a sound field generator. The conventional convolutions are compared with the proposed one in views of computational burden and sound quality. In the proposed method, a considerable reduction in the computational burden was realized with acceptable changes in sound quality.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.231-237
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• 2008

With the advent of sound field simulator, many sound fields have been reproduced by obtaining the impulse responses of specific acoustic spaces like famous concert hall, opera house. This sound field reproduction has been done by the linear convolution operation between the sound input signal and the impulse response of certain acoustic space. However, the conventional finite impulse response based linear convolution operation always makes real-time implementation of sound field generator impossible due to the large amount of computational burden. This paper introduces the fast convolution method using perceptual redundancy in the processed signals, input audio signal and room impulse response. Temporal and spectral real-time masking blocks are implemented in the proposed convolution structure. It reduces the computational burden of convolution methods for real-time implementation of a sound field generator. The conventional convolutions are compared with the proposed one in views of computational burden and sound quality. In the proposed method, a considerable reduction in the computational burden was realized with acceptable changes in sound quality.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.537-565
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• 2015

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.3
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• pp.265-270
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• 2004

This paper addresses the effect of group delay in satellite communication system. Phase of signal is distorted by the non-constant group delay. Group delay can be modeled as linear, parabolic and cubic type according to the polynomial characteristic. We investigate BER performance of satellite communication system with each 3 kinds of group delay. As signal bandwidth becomes wider, group delay makes more influence on the signal. BNR performance of satellite communication system is found when data rates are 1Mbps, 4Mbps and 8Mbps. Convolution coding with the code rate of 1/2 or 7/8 is used. At BER =10$\^$-5/, system with group delay needs more SNR of minimum 0.3㏈ to maximum 4.4㏈ than system without group delay. The worst case of BER performance happens in the linear group delay, 7/8 punctured convolution coding and 8 Mbps. The required SNR is increased by 4.4㏈ at this worst case.

• Steel and Composite Structures
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• v.11 no.5
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• pp.403-421
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• 2011

In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.