The effects of quantization noise and sensor nonideality on digital differentiator-based rate measurement

The fact that VCO-ADCs produce noise-shaped quantization noise suggests that a link between frequency modulation and Sigma-Delta modulation should exist. The connection between a VCO-ADC and a first-order Sigma-Delta modulator has been already explained using Pulse Frequency Modulation. In this article, we attempt to extend this explanation to a generic Sigma-Delta modulator. We show that the link between Sigma-Delta modulation and Pulse Frequency Modulation relies in a sampling invariance property that defines the equivalence between both entities. This equivalence property, allows to go beyond the white quantization noise model of a Sigma-Delta modulator, revealing the origin of some nonlinear phenomena. We first predict spurious tones which cannot be explained by circuit non linearity. Multi-bit and single-bit modulators are shown to belong to a same generic class of systems. Finally, quantizer overload is analyzed using our model. The results are applied to Continuous-Time Sigma-Delta modulators of orders one, two and three and then extended to a generic case.

This paper analyzes the effect of digital differentiation on the measurement of flicker emission from grid-connected wind turbines (WTs). The flicker measurement procedure is defined in the IEC 61400-21 standard, which includes the estimation of a fictitious grid for the measurement of voltage fluctuations exclusively generated by a WT. The study focuses on two aspects of the implementation of the derivative of the line current that affect the estimation of the fictitious grid, namely the bandwidth and the phase response of the digital differentiator. The experiments were performed under two different frameworks, by using simulated simple waveforms and voltage and current recordings from an actual WT. The work cautions about the adverse effect of the phase response of the even-length finite impulse-response differentiators. It also recommends implementing digital differentiators with an accurate bandwidth to derive potential spectral components in the current in the whole bandwidth required by the procedure. This aim can be achieved by increasing either the length of the filter or the sampling rate of the processing. The conclusions should help in accurately implementing the procedure and reducing the deviations found in the flicker emission measurements for grid-connected WTs.

With improving optical device technology it is now possible to consider constructing very large optoelectronic neural networks containing of the order of 1000 fully interconnected neurons. Whether such systems will work, though, depends on the quality of the optical devices and the network architecture. A recent study has indicated that a 200 neuron single layer polarization logic network can operate under the constraints of presently available spatial light modulators.1 In this paper we will extend this study to examine the effect of device limitations on the performance of single- and multilayer networks containing up to 1000 fully interconnected neurons. We consider the effect of nonlinearities, contrast ratio, and quantization noise in the weight matrix and the effect of noise at the inputs and outputs on the convergence rate and number of patterns that can be classified.

Coherent average technique — a tutorial review

The envelope pulse-width modulation (EPWM) transmitter has been studied to address the power efficiency issue on the linear amplification of OFDM signals. However, the delta- sigma (Delta-Sigma) modulator in the EPWM transmitter generates quantization noise that degrades signal quality. In this paper, OFDM in-band noise characteristics of EPWM transmitters are analyzed for first and second order Delta-Sigma modulators. Distortion noise power due to envelope clipping of OFDM signals is also analyzed. The combined effects of noise and distortion on the error vector magnitude (EVM) and adjacent channel leakage power ratio (ACLR) are examined. Simulations to validate the total performance were performed using the IEEE 802.11a OFDM signal. Results showed good agreement with analytical results considering a linear-approximation gain for the 1-bit quantizer in Delta-Sigma modulators. The first order EPWM transmitter provides slightly better EVM and ACLR values than second order EPWM transmitters, since the effective quantizer gain of second order Delta-Sigma modulators is smaller, that limits the noise- shaping capability of Delta-Sigma modulators. A 0.1% clipping probability for a first order EPWM transmitter with an oversampling ratio of 32 and a three-pole Butterworth bandpass filter gives an EVM of 1.8% and ACLR of-37.9 dB.

In this article, a global output feedback control scheme is developed for a class of uncertain nonlinear systems subject to input quantization and unknown output function. By employing a time-varying gain and a time-invariant gain, we address the challenges posed by quantization errors and nonlinear functions with an unknown linear growth rate. Additionally, we determine an allowable measurement sensitivity error by solving a straightforward inequality. We demonstrate that the proposed scheme ensures global asymptotic stability for the system and guarantees that all signals of the closed-loop system remain bounded. Finally, we validate the proposed approach through a mathematical example and an experiment conducted on the QUBE-Servo 2 equipped with an inertial disc module.

Extensions of the limiting qnanfizafion error formula of Bennet are proved. These are of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_{s,k}(N,F)=N^{-\beta}B</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the number of output levels, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_{s,k}(N,F)</tex> is the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> th moment of the metric distance between quantizer input and output, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta,B&gt;0,k=s/\beta</tex> is the signal space dimension, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</tex> is the signal distribution. If a suitably well-behaved <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -dimensional signal density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(x)</tex> exists, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B=b_{s,k}[\int f^{\rho}(x)dx]^{1/ \rho},\rho=k/(s+k)</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b_{s,k}</tex> does not depend on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> . For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k=1,s=2</tex> this reduces to Bennett's formula. If <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</tex> is the Cantor distribution on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[0,1],0&lt;k=s/ \beta=\log 2/ \log 3&lt;1</tex> and this <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> equals the fractal dimension of the Cantor set <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[12,13]</tex> . Random quantization, optimal quantization in the presence of an output information constraint, and quantization noise in high dimensional spaces are also investigated.

A fully dynamic third-order EF-CIFF noise-shaping SAR ADC with NTF zeros optimization and passive integration

This work considers the problem of remote estimation of Wiener processes and proposes a sample preprocessing method to ensure the convergence of the estimation distortion. Specifically, the autocorrelation of the Wiener process is exploited to counteract the effect of strong quantization noise arising from the linearly increasing variance over time. We first derive the exact expression for the convergent mean squared error (MSE) without considering transmission outages to explain the proposed preprocessing method. Then, the analysis is extended to more complex and general scenarios with outages. Based on the derived MSE, the quantization precision, the sampling interval, and the transmission time of a single piece of update information are optimized individually. We further give two algorithms to obtain two global suboptimal MSEs for practical cases considering low thresholds of quantization precision and sampling interval, following a demonstration of the unsolvability of the joint optimization. The numerical results reveal that dynamic distortion plays a greater role than static distortion due to the fast-varying nature of the Wiener process, which also verifies the effectiveness of the proposed preprocessing method in controlling the quantization error.

This paper presents an application of the [Formula: see text] modulation technique to the on-chip dynamic test for analog-to-digital converters (ADCs). The required stimulus such as a single- or two-tone signal is encoded into one-bit [Formula: see text] sequence, which is applied to an ADC under test through a driving buffer and a simple low-pass reconstruction filter. By a systematic approach, we select the order and type of a [Formula: see text] modulator and develop a frequency plan suitable for the spectral measurement. In this way, we achieve a high dynamic range suitable for spectral harmonic and intermodulation distortion tests for ADCs. For high frequency measurements (up to the Nyquist frequency), we propose a novel low-pass/band-pass modulation scheme that allows to avoid harmful effects of the low-frequency quantization noise. Also we address the distortion components which originate from the buffer imperfections for a nonreturn-to-zero waveform representing the encoded stimulus. We show that the low-frequency distortion components can be cancelled by using a simple iterative predistortion technique supported by measurements with a DC-calibrated ADC. By correlation between low- and high-frequency components also the high frequency distortions can be largely reduced. The presented techniques are illustrated by simulation results of an ADC under test.

This paper describes a low-voltage fractional-N hybrid phase-locked loop (HPLL) architecture that does not require current biasing. A hybrid loop control with a digital integral path and an analog proportional-gain path offers technology scalability as well as linear phase detection. The analog control path consists of a flip-flop phase detector (PD) and passive loop filters including a programmable notch filter. To mitigate ΔΣ quantization noise and PD nonlinearity effects, an FIR-filtered ΔΣ modulation is employed for fractional division. The proposed bias-free fractional-N HPLL is implemented in 65nm CMOS. At 1.2GHz output, the phase noise of -97dBc/Hz at 1MHz offset frequency and the reference spur of -76dBc with the programmable notch filter are measured. When 14nm FinFET technology is used, simulation results show that a 1.2GHz bias-free PLL can be designed with a 0.4V supply.

We address the problem of text super-resolution: given a single image of text scanned in at low resolution from a piece of paper, return the image that is mostly likely to be generated from a noiseless high-resolution scan of the same piece of paper. In doing so, we wish to: (1) avoid introducing artifacts in the high-resolution image such as blurry edges and rounded corners, (2) recover from quantization noise and grid-alignment effects that introduce errors in the low-resolution image, and (3) handle documents with very large glyph sets such as Japanese's Kanji. Applications for this technology include improving the display of: fax documents, low-resolution scans of archival documents, and low-resolution bitmapped fonts on high-resolution output devices.

Quantization noise due to interface devices of finite wordlength and the effects of this noise on the performance of a control system are analyzed. A digital filtering scheme for minimizing the effect of quantization noise along the derivative path of the control algorithm is developed and implemented. Results obtained by digital simulation are verified experimentally.

A novel system to image and reconstruct a 3-dimensional map of the refractive index based on the diffraction of light through a transparent sample is presented. This method is tested and validated on computer-generated data sets. The proposed system is an advanced variation of an imaging technique used in engineering for the study of aerodynamics. This method, which is termed Reference Image Topography, is used to reconstruct the water/air interface of the free surface in fluid dynamics studies. This surface profile is reconstructed by comparing an image of a random pattern viewed through the transparent free surface against a reference image, to determine the change in the refractive index caused by changes in the height. The proposed system is highly sensitive and capable of imaging intricate features in the transparent sample that are of low contrast when imaged with other imaging methods. For each projection, the change in direction of the light passing through the sample when placed in between the light source and the imaging system, can be related to the line integral for the change in refractive index across the sample. Utilizing multiple projections, a 3- dimensional map of the refractive index of the sample is reconstructed with computed tomography.

The performance of continuous-time (CT) delta-sigma modulators (/spl Delta//spl Sigma/M's) suffers more severely from time jitter in the quantizer clock than discrete-time designs. Clock jitter adds a random phase modulation to the modulator feedback signal, which whitens the quantization noise in the band of interest and hence degrades converter resolution. Even with a perfectly uniform sampling clock, a similar whitening can be caused by metastability in the quantizer: a real quantizer has finite regeneration gain, and thus, quantizer inputs near zero take longer to resolve. This paper quantifies the performance lost due to clock jitter in a practical integrated CT /spl Delta//spl Sigma/M clocked with an on-chip voltage-controlled oscillator. It also characterizes metastability in a practical integrated quantizer using the quantizer output zero-crossing time and rise time as a function of both quantizer input voltage and the slope of the input voltage at the sampling instant, and predicts the maximum-achievable performance of a practical CT /spl Delta//spl Sigma/M given jitter and metastability constraints.