• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.12a
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.2
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• pp.155-165
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• 1990

The problem of quantization errors in digital filter design arises because of the practical necessity due to finite wordlength implementation. These errors are classified into coefficient quantization error and roung off error. In this paper, in order to analyze and reduce these errors, minimum ceefficient quantization realization is directly derived form impulse responese design specification. And using the equivalent transform relation between minimum coefficient quantization error and minimum roundoff error realizations, we synthesize an optimal realization state-space digital filter. This technique is analyzed by the simulation of an approximated 3rd model, which shows that it is superior to direct or cascade state-space digital filter in quantization errors.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.7A
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• pp.794-806
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• 2004

This paper deals with correction of frequency offset and analysis of quantization angle noise in the IEEE 802.1la OFDM system. The rotation phase per symbol due to the carrier frequency offset is estimated from auto-correlation of the short Preambles, which are over-sampled for the reduction of noise in OFDM signals. The pilot signals are introduced to estimate the rotation phase per OFDM symbol due to estimation error of the carrier frequency offset and the sampling frequency onset. During the estimation and correction of the frequency onsets, a CORDIC processor and a look-up table are used for the conversion between a rotation phase and its complex number. Being calculated by a limited number of bits in the CORDIC processor and the look-up table, the rotation phase and its complex number have quantization angle errors. The quantization errors are analyzed as SNR (signal to noise ratio) due to the quantization bit numbers. The minimum bit number is suggested to meet the specification of IEEE 802.1la properly. Finally, the quantization errors are evaluated through simulations on number of quantization bits and SNR of received signals.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.9
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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.

• The Journal of the Acoustical Society of Korea
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• v.16 no.1E
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.3
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• pp.155-157
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• 2014

In this paper, a novel codebook generation strategy is proposed. With the given codebooks, two codeword selection procedures are proposed and analyzed for generating the quantized multiple-input multiple-output (MIMO) channel state information (CSI). Furthermore, three different quantization and normalization strategies are analyzed. The simulation results suggest that the proposed 'quantized channel generation method 2' is the best strategy to reduce the quantization and normalization errors to generate the final quantized MIMO CSI.

• Journal of Advanced Navigation Technology
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• v.15 no.5
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• pp.850-856
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• 2011

The error diffusion method is one of the digital halftoning methods that diffuses quantization errors of current processing pixel to neighboring pixels and get a high-quality black-white image. This method has the problematic case which partially increase or decrease summation of diffused errors in the process of diffusing the quantization error. In this paper, we analyze Floyd-Steinberg method, Jarvis-Judice-Ninke method, Stucki method, and Shiau-Fan method as a representative case of error diffusion methods and propose a solution method of this problem.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.4
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• pp.50-56
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• 1997

In this paper, efficient quantization methods of line spectrum pairs (LSP) which has good performances and low complexity and memory are proosed for vocoder of mobile communication system. The adaptive quantization method utilizing the ordering property of LSP parameters is used in a scalar quantizer and a vector-scalar hybrid quantizer. The proposed scalar quantization algorithm needs 31 bits/frame to maintain the transparent quality of speech. The improved vector-scalar quantizer achieves an average spectral distortion of 1dB using 26 bits/frame. The proposed methods are evaluated in the channel errors and changed the predictor structure to maintain the robustness to channel errors.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.4
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• pp.387-397
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• 1992

The spatial domain design of 2-dimensional separable denominator digital filters(SDDF) based on the reduced dimensional decomposition can be realized when the given 2-D impulse response specifications are decomposed into a pair of 1-D specifications via singular value decompositions(SVD). Because of use of the balaned approximation and equivalent transform as 1-D design algorithm, 2-D design algorithm retains the advantage that is numerically stable and can minimize quantization errors. In this paper in order to analyze and reduce these errors, minimum comfficient quantization realization is directly derived from impulse response specification. And using the equivalent trans form relation between mininum coefficient quantization error and minimum roundoff error realizations, we optimally realize a SDDF. This algorithm is analyzed by the simulation, which shows that it is superior to direct or balanced realization in quantization errors.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.