• 전자공학회논문지B
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• 제30B권9호
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• pp.54-63
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• 1993

Quantization error, generated by the quantization process of an image, is inherent in computer vision. Because, especially in stereo vision, the quantization error in a 2-D image results in position errors in the reconstructed 3-D scene, it is necessary to analyze it mathematically. In this paper, the analysis of the probability density function (pdf) of quantization error for a line-based stereo matching scheme is presented. We show that the theoretical pdf of quantization error in the reconstructed 3-D position information has more general form than the conventional analysis for pixel-based stereo matching schemes. Computer simulation is observed to surpport the theoretical distribution.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.313-316
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• 1999

In this paper, a quantization algorithm by which the accumulative error can be prevented is presented. In digital control systems, the quantization cannot be avoided because of the finite word length of digital computers. The error due to quantization of the computed values may be tolerable in case of directly using them. In case of using the accumulated values, the error between sum of the original values and that of the quantized values becomes larger as the number of the values to be summed increases. Such an increasing accumulative error is critical for the control of precise NC machines, robots and autonomous vehicles. To solve this problem, a quantization algorithm without the accumulative error is presented. Basically, the algorithm is based on the feedback loop by which the accumulationive of the quantization error can be prevented. The error boundness of the proposed algorithm is proven and a computer simulation is performed to show the validity of the algorithm.

• 한국통신학회논문지
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• 제29권6C호
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• pp.857-864
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• 2004

MPEG이나 JPEG 영상 압축 표준에서는 영상을 블록 단위로 나누어서 DCT를 하고 양자화 시킨다. 그리고 역양자화 값으로 양자화 구간의 중앙값을 사용한다. DCT 평균제곱 오차를 줄이려면 평균값을 사용하는 것이 최적이나 현재에는 uniform 분포를 가정하고 중앙값을 사용한다. 따라서 본 논문에서는 DCT 계수의 확률 분포함수가 Laplacian 분포를 따른다고 가정하고 역양자화 값으로 평균값을 사용했을 때 PSNR 개선 정도를 살펴왔다. 그리고 보정전의 양자화 오차와 보정 후의 양자화 오차를 이론적인 수식으로 나타내 보았다. 보정으로 인한 양자화잡음의 감소치의 이론적인 최대 값은 1.66 ㏈이다. 실험결과 제안된 대표값을 취했을 경우 기존의 방법보다 PSNR이 0.2∼0.4 ㏈정도 향상된다.

• 대한전기학회논문지
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• 제43권2호
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• pp.318-329
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• 1994

This paper deals with the finite wordlength effect on the performance of digital PID controllers. The finite wordlength, one of the major limitation factors in digital controllers, results on two kinds of quantization error : the signal quantization error and the coefficient quantization error. This paper derives the variance of the plant output due to the signal quantization error. Using stability margins as performance criterion, the statistical wordlength concept is adopted for coefficient wordlength selection. Finally, the experimental results exhibit satisfactory performance of the digital PID controller with statistical coefficient wordlength.

• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2000년도 추계종합학술대회논문집
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• pp.85-88
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• 2000

Signal splitting and perfect reconstruction in subband coding is based on the assumption that quantization errors are negligible. But if subband signal is quantized, 4 types of errors occurs thus it is not impossible to do perfect reconstruction. These errors are QMF design error, aliasing error, signal error and random error. By using the QMF for subband splitting, the QMF error does not present. and by using the Lloyd-Max quantizer for the quantization and by using an appropriate synthesis filter, all signal dependent errors can be cancelled and the remaining error is random error which is uncorrelated with the original image〔1〕. In this thesis, Lenna and Camera-Man image are devided into 10 subbands by using the D4 and D20 wavelet And the subband signals are quantized by using the Lloyd-Max quantizer and the quantization errors are compared. and evaluated.

• ETRI Journal
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• 제45권1호
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• The Journal of the Acoustical Society of Korea
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• 제16권1E호
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• pp.41-48
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• 1997

The very purpose of subband codec is the attainment of data rate compression through the use of quantizer and optimum bit allocation for each decimated signal. Yet the question of floating-point quantization effects in subband codec has received scant attention. There has been no direct focus on the analysis of quantization errors, nor on design with quantization errors embedded explicitly in the criterion. This paper provides a rigorous theory for the modelling, analysis and optimum design of the general M-band subband codec in the presence of the floating-point quantization noise. The floating-point quantizers are embedded into the codec structure by its equivalent multiplicative noise model. We then decompose the analysis and synthesis subband filter banks of the codec into the polyphase form and construct an equivalent time-invariant structure to compute exact expression for the mean square quantization error in the reconstructed an equivalent time-invariant structure to compute exact expression for the mean square quantization error in the reconstructed output. The optimum design criteria of the subband codec is given to the design of the analysis/synthesis filter bank and the floating-point quantizer to minimize the output mean square error. Specific optimum design examples are developed with two types of filter of filter banks-orthonormal and biorthogonal filter bank, along with their perpormance analysis.

• 대한자기공명의과학회:학술대회논문집
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• 대한자기공명의과학회 2002년도 제7차 학술대회 초록집
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• pp.75-75
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• 2002

목적： 고자장 자기공명영상 시스템 등으로 신호대잡음비가 향상됨에 따라 데이터 측정에서 analog-to-digital converter (ADC)의 quantization noise 가 중요한 시스템 사양으로 부각되고 있다. 특히 자기공명영상은 공간주파수 영역에서 데이터를 측정하기 때문에 dc와 ac간의 신호 차이가 매우 크며, 이러한 dynmic range는 3-D 영상에서 더욱 커진다. 본 연구에서는 다양한 자기총명 영상기법 및 실험 파라미터에 따른 신호의 dynamic range와 ADC의 bit 수에 따른 quantization noise를 살펴봄으로써, 주어진 시스템에 적합한 ADC의 bit 수를 분석하고자 한다. 대상 및 방법： 펄스 시퀀스의 종류, 파라미터, 2D/3D 등에 따른 각 신호의 크기를 수학적으로 모델링하여 신호의 크기를 예측하였다. 또한 whole body MRI 시스템에서 실험을 통하여 신호의 크기를 비교하였다. ADC의 quantization noise를 실험과 시뮬레이션을 통하여 살펴보았다. 시뮬레이션은 test 영상을 Inverse FFT 하여 spatial frequency domain data를 만든 후, 다양한 bit 수의 ADC로 quantization을 한 후 다시 영상을 재구성하였다. 재구성된 영상과 원영상 간의 error가 quantization noise가 된다. 또한 이러한 error가 주파수 영역에서의 error 값과 일치하는지를 확인하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.131-135
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• 1991

A quantization error model is suggested for analog to frequency(A/F) converter in strapdown inertial navigation system(SDINS),which is characterized by some white noise exciting the state variables. Also, effects on the performance of SDINS by analog to digital(A/D) converter and A/F converter are analyzed and compared via covariance simulation. As a result, A/F converter turns out to be superior to the A/D converter with respect to the induced navigation error and the difficulty in circuit realization. The quantization error model developed in this paper appears to be useful for optimal filter design.

• 한국통신학회논문지
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• 제29권2C호
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• pp.298-305
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• 2004

본 논문은 워드길이가 W 비트인 입력으로부터 W 비트를 출력하는 고정길이 modified Booth 곱셈기에 대한 오차보상 방법을 설명한다. 효율적으로 양자화 오차를 보상하기 위해 Booth 인코더의 출력정보를 이용하여 오차보상 바이어스를 생성한다. 절단된 부분이 양자화 오차에 미치는 영향에 따라 두 그룹(major or minor group)으로 나누고, 각 그룹에 서로 다른 오차보상 방법을 적용한다. 기존 방법과 비교하여 제안한 방법이 오차보상 바이어스를 생성하는 회로의 하드웨어 오버헤드는 비슷하면서 약 50％ 정도 양자화 오차가 적음을 시뮬레이션을 통해 보인다. 또한, 면적과 전력소모 면에서 제안한 고정길이 곱셈기가 이상적인 곱셈기 보다 약 40％ 정도 적게 나타났다.