The mid-rise time-to-digital converter (TDC), e.g., a binary (bang-bang) phase detector and other few-bit TDCs, is commonly used as the phase detector (PD) in a digital phase locked loop (DPLL) because of the design s...
详细信息
The mid-rise time-to-digital converter (TDC), e.g., a binary (bang-bang) phase detector and other few-bit TDCs, is commonly used as the phase detector (PD) in a digital phase locked loop (DPLL) because of the design simplicity and ultra-low consumption in terms of area and power. However, its hard quantization nonlinearity makes it nontrivial to estimate its linearized gain and the power of the quantization error (QE) that it introduces, and hence can make the linearized analysis at the DPLL-system level inaccurate. This tutorial paper formulates a minimum-mean-square-error estimator that is used to provide an accurate linearized analysis of the TDC;it takes into account the interaction between the quantization characteristic of the TDC and the statistical properties of the input jitter of a frequency synthesizer in both integer-N and fractional-N modes. A strategy for minimizing the TDC's QE is provided;so-designed TDCs with equidistant quantization thresholds are able to achieve optimum jitter minimization at both the TDC and DPLL levels. Finally, the effective linear operating region of such TDCs is derived, which explains when the "hard quantizer" can be regarded as an almost linear PD and when not. Behavioral simulations at the TDC-block and DPLL-system levels underpin our analysis.
The exact analysis of second order bandpass Delta-Sigma modulator with sinusoidal inputs is performed. The results indicate that quantization error is neither uniformly distributed nor white. The quantization error sp...
详细信息
The exact analysis of second order bandpass Delta-Sigma modulator with sinusoidal inputs is performed. The results indicate that quantization error is neither uniformly distributed nor white. The quantization error spectrum is purely discrete and symmetric with one forth of sampling frequency, and the locations of these discrete frequency components are strongly dependent on input amplitudes. Similar results are also observed for passband communication signals, such as quadrature amplitude modulation. From the analysis, crosscorrelation between quantization error and sinusoidal input was shown to exist but can be cancelled out by proper design of the noise shaping function. Crosscorrelation can degrade the performance of the delta-sigma system. Hence, the exact analysis is another method to enable design for high performance.
In this paper a stochastic analysis of the quantization error in a stereo imaging system has been presented. Further the probability density function of the range estimation error and the expected value of the range e...
详细信息
In this paper a stochastic analysis of the quantization error in a stereo imaging system has been presented. Further the probability density function of the range estimation error and the expected value of the range error magnitude are derived in terms of various design parameters. Further the relative range error is proposed.
作者：
Kamgar-Parsi, BKamgar-Parsi, BUSN
Res Lab Navy Ctr Appl Res Artificial Intelligence Washington DC 20375 USA USN
Res Lab Div Informat Technol Washington DC 20375 USA
quantization of the image plane into pixels results in the loss of the trite location of features within pixels and introduces an error in ang quantity computed from feature positions in the image. Here, we derive clo...
详细信息
quantization of the image plane into pixels results in the loss of the trite location of features within pixels and introduces an error in ang quantity computed from feature positions in the image. Here, we derive closed-form, analytic expressions for the error distribution function, thr mean absolute error (MAE), and the mean square error (MSE) due to triangular tessellation, for differentiable functions of an arbitrary number of independently quantized points, using a linear approximation of the function. These quantities are essential in examining the intrinsic sensitivity of image professing algorithms. Square and hexagonal pixels were treated in previous papers. An interesting result is that for all possible cases 0.99 < (D) over bar(T)/(D) over bar(S) < 1.13, where (D) over bar(T) and (D) over bar(S) are the MAE in triangular and square tessellations.
Due to the special nature of the acquisition domain, the quantization process of magnetic resonance imaging (MRI) data presents challenges that are not present in other medical imaging techniques. In this article, we ...
详细信息
Due to the special nature of the acquisition domain, the quantization process of magnetic resonance imaging (MRI) data presents challenges that are not present in other medical imaging techniques. In this article, we demonstrate that the quantization error in MRI cannot be assumed to be a random variable with uniform distribution across the entire acquisition domain. Furthermore, the introduced error is not statistically independent of the input signal. On the contrary, we show that this error is correlated with the object that is being scanned, producing perceptually unpleasant artifacts in the image domain. Although the quantization error is not generally a critical issue in two-dimensional (2D) MRI acquisition, it could be in the case of 3D acquisitions and in noise estimation measurements. (C) 2014 Wiley Periodicals, Inc.
Hexagonal spatial sampling is used widely in image and signal processing. However, no rigorous treatment of the quantization error due to hexagonal sampling has appeared in the literature. In this paper, we develop ma...
详细信息
Hexagonal spatial sampling is used widely in image and signal processing. However, no rigorous treatment of the quantization error due to hexagonal sampling has appeared in the literature. In this paper, we develop mathematical tools for estimating quantization error in hexagonal sensory configurations. These include analytic expressions for the average error and the error distribution of a function of an arbitrary number of independently quantized variables. These two quantities are essential for assessing the reliability of a given algorithm. They can also be used to compare the relative sensitivity of a particular algorithm to quantization error for hexagonal and other spatial samplings, e.g., square, and can have an impact on sensor design. Furthermore, we show that the ratio of hexagonal error to square error is bounded between 0.90 and 1.05.
The problem of estimating quantization error in 2D images is an inherent problem in computer *** outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an *** estimation o...
详细信息
The problem of estimating quantization error in 2D images is an inherent problem in computer *** outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an *** estimation of quantization error has its own importance in stereo *** the quantization error cannot be controlled fully,still statistical error analysis helps us to measure the performance of stereo systems that relies on the imaging ***,it is assumed that the quantization error in 2D images is distributed uniformly that need not to be true from a practical *** this paper,we have incorporated noise distributions(Triangular and Trapezoidal)for the stochastic error analysis of the quantization error in stereo imaging *** the validation of the theoretical analysis,the detailed simulation study is carried out by considering different cases.
The quantization error in the measurement of Fourier intensity for phase retrieval is discussed and a multispectra method is proposed to reduce this error. The Fourier modulus used for phase retrieval is usually obtai...
详细信息
The quantization error in the measurement of Fourier intensity for phase retrieval is discussed and a multispectra method is proposed to reduce this error. The Fourier modulus used for phase retrieval is usually obtained by measuring Fourier intensity with a digital device. Therefore, quantization error in the measurement of Fourier intensity leads to an error in the reconstructed object when iterative Fourier transform algorithms are used. The multispectra method uses several Fourier intensity distributions for a number of measurement ranges to generate a Fourier intensity distribution with a low quantization error. Simulations show that the multispectra method is effective in retrieving objects with real or complex distributions when the iterative hybrid input-output algorithm (HIO) is used.
Since most depth maps are quantized to 8-bit numbers in current 3D video systems, the induced cardboard effects can disturb human perception. Moreover, depth maps with larger resolution suffer more from the quantizati...
详细信息
ISBN:
(纸本)9781479903566
Since most depth maps are quantized to 8-bit numbers in current 3D video systems, the induced cardboard effects can disturb human perception. Moreover, depth maps with larger resolution suffer more from the quantization error. Therefore, this paper proposes an optimization approach to reduce the depth quantization error with well-preserved structure of the depth maps. The experimental results demonstrate that the proposed approach can successfully recover the structure characteristics from the quantized depth maps. Evaluation in mean square error (MSE) and mean structural similarity index (MSSIM) also strongly support our theory and algorithm. Through enhancing the quality of the depth maps from the very beginning, this work can benefit most 3D processing applications, such as 3D modeling, shape registration, and view synthesis.
In this paper, we analyze how neighborhood size and number of weights in the self-organizing map (SOM) effect quantization error. A sequence of i.i.d. one-dimensional random variable with uniform distribution is consi...
详细信息
In this paper, we analyze how neighborhood size and number of weights in the self-organizing map (SOM) effect quantization error. A sequence of i.i.d. one-dimensional random variable with uniform distribution is considered as input of the SOM. First obtained is the linear equation that an equilibrium state of the SOM satisfies with any neighborhood size and number of weights. Then it is shown that the SOM converges to the unique minimum point of quantization error if and only if the neighborhood size is one, the smallest. If the neighborhood size increases with the increasing number of weights at the same ratio, the asymptotic quantization error does not converge to zero and the asymptotic distribution of weights differs from the distribution of input samples. This suggests that in order to achieve a small quantization error and good approximation of input distribution, a small neighborhood size must be used. Weight distributions in numerical evaluation confirm the result. (C) 2000 Elsevier Science B.V. All rights reserved.
暂无评论