Small Quantization Research Articles

DC Coefficient Distributions for P-Frames in H.264/AVC

In this letter, the distributions of direct current (DC) coefficients for P-frames in H.264/AVC are analyzed, and the distortion model of the Gaussian source under the quantization of the dead-zone plus-uniform threshold quantization with uniform reconstruction quantizer is derived. Experimental results show that the DC coefficients of P-frames are best approximated by the Laplacian distribution and the Gaussian distribution at small quantization step sizes and at large quantization step sizes, respectively.

A Quantization Error Minimization Method Using DDS-DAC for Wideband Fractional-N Frequency Synthesizer

This paper presents a technique to reduce the quantization error in fractional division for a wideband fractional-N frequency synthesizer. By using a direct digital synthesis phase accumulator as the fractional divider and a DAC as the phase-to-pulse converter, the quantization error can be much smaller than the one by conventional sigma-delta modulated multi-modulus divider. With small quantization error, a dedicated compensation mechanism is no longer necessary for wide loop bandwidth applications. To demonstrate this concept, a prototype chip was implemented with 0.18-μm CMOS. The synthesizer consumes 19 mA from a 1.8 V supply. With 1 MHz closed-loop bandwidth, the in-band noise is -98 dBc/Hz and the 3 MHz offset noise is -122 dBc/Hz for a 1.8 GHz output. The output exhibited 27 dB phase noise reduction compared to the generic sigma-delta structure. The settling time is 2 μs under a 35 MHz frequency step.

A Mixed-Signal Synchronous/Asynchronous Control for High-Frequency DC-DC Boost Converters

This paper investigates the application of a mixed-signal synchronous/asynchronous digital controller to DC-DC boost converters. The digital control synchronously generates current and voltage ramps by using two low-resolution digital-to-analog converters. The switch turn-on and turn-off are determined asynchronously by comparing the converter-state variables and the digitally generated current and voltage ramps. The control features high dynamic performance, frequency modulation during transients, small quantization effects, and low complexity. In order to evaluate the dynamic performance and compare the proposed solution with conventional analog peak-current-mode control, a small-signal model of the synchronous/asynchronous modulation is derived. Even if aimed to an integrated digital controller, experimental investigation has been performed by using discrete components, implementing the digital control in a field-programmable gate array by using a VHDL. The simulation and experimental results on 100-W DC-DC boost converter confirm the proposed analysis and show that the proposed solution enables a dynamic performance that is comparable with that of analog peak-current- mode control.

Noise-proofing the doubly SH-projected coefficients for synthesizing images under environment lighting

The brute-force way to synthesize images of an object under various lighting environments is very time consuming. To speed up the synthesizing process, we can model the bidirectional reflectance distribution function (BRDF) of each surface element as a spherical harmonic (SH) coefficient matrix based on the double SH projection. With the SH coefficient matrices of all surface elements, we can relight an object under the global illumination. However, applying the classical least square method for the double SH projection, the returned SH coefficients are prohibitively large in magnitude because samples are available on the upper hemisphere only. Hence, the synthesizing process is very sensitive to small quantization noise introduced by the compression process. Existing methods to this noise-sensitivity problem mainly focus on the single SH projection. It should be noticed that the double SH projection further amplifies the artifacts. Straightforwardly extending existing methods to the double SH projection may not be theoretically nor practically feasible. In this paper, we present a robust estimation method for the double SH projection. With the proposed method, severe artifacts in synthesized images can be significantly reduced. Comparison with the existing Sloan's method is performed to support the effectiveness of the proposed method.

High efficient ECG compression based on reversible round-off non-recursive 1-D discrete periodized wavelet transform

Error propagation and word-length-growth are two intrinsic effects influencing the performance of wavelet-based ECG data compression methods. To overcome these influences, a non-recursive 1-D discrete periodized wavelet transform (1-D NRDPWT) and a reversible round-off linear transformation (RROLT) theorem are developed. The 1-D NRDPWT can resist truncation error propagation in decomposition processes. By suppressing the word- length-growth effect, RROLT theorem enables the 1-D NRDPWT process to obtain reversible octave coefficients with minimum dynamic range (MDR). A non-linear quantization algorithm with high compression ratio (CR) is also developed. This algorithm supplies high and low octave coefficients with small and large decimal quantization scales, respectively. Evaluation is based on the percentage root-mean-square difference (PRD) performance measure, the maximum amplitude error (MAE), and visual inspection of the reconstructed signals. By using the MIT-BIH arrhythmia database, the experimental results show that this new approach can obtain a superior compression performance, particularly in high CR situations.

A Novel ECG Data Compression Method Based on Nonrecursive Discrete Periodized Wavelet Transform

In this paper, a novel electrocardiogram (ECG) data compression method with full wavelet coefficients is proposed. Full wavelet coefficients involve a mean value in the termination level and the wavelet coefficients of all octaves. This new approach is based on the reversible round-off nonrecursive one-dimensional (1-D) discrete periodized wavelet transform (1-D NRDPWT), which performs overall stages decomposition with minimum register word length and resists truncation error propagation. A nonlinear word length reduction algorithm with high compression ratio (CR) is also developed. This algorithm supplies high and low octave coefficients with small and large decimal quantization scales, respectively. This quantization process can be performed without an extra divider. The two performance parameters, CR and percentage root mean square difference (PRD), are evaluated using the MIT-BIH arrhythmia database. Compared with the SPIHT scheme, the PRD is improved by 14.95% for 4 < or = CR < or = 12 and 17.6% for 14 < or = CR < or = 20.

Space Division Multiple Access With a Sum Feedback Rate Constraint

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.

Transform domain transcoding from MPEG-2 to H.264 with interpolation drift-error compensation

With the increasingly extensive applications of the new emerging video coding standard H.264, it inspires an urgent need to transcode the widely available MPEG-2 compressed video to H.264 format. In this paper, we investigate the issues on transcoding MPEG-2 into H.264 in transform domain with consideration of drift error due to the mismatch of motion compensation, and propose a transform domain solution to transcode MPEG-2 into H.264. We first analyze two major kinds of drifting error resulting from the mismatch of motion compensation: interpolation error and quantization error. The former is caused by the difference between the interpolation filters adopted in these two standards, thus very unique to the transform domain transcoding from MPEG-2 to H.264. Furthermore, it is identified as the dominant factor of the video quality degradation, especially in the case of small quantization parameter at high bit-rate, by extensive experimental results. As a major contribution of this paper, the close form of interpolation error is derived from transform domain. We then proposed the transcoding scheme based on quantization error drifting compensation and Interpolation error drifting compensation. Experimental results show that the proposed transform domain transcoding scheme achieves very promising performance in terms of low computational complexity and high transcoded video quality. Most importantly, its peak signal-to-noise ratio is very close to the cascaded transcoding architecture with time-consuming decoding and recoding process in pixel domain.

Probabilities of randomly centered small balls and quantization in Banach spaces

We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.

Quantization loss for convolutional decoding in Rayleigh-fading channels

This article presents a theoretical analysis (based on tight upper bounds on the error probability) of quantization loss with integer metrics used for convolutional decoding in the Rayleigh-fading channel. Optimum configurations with respect to the generalized cutoff rate criterion are established for 2-bit, 3-bit and 4-bit quantizers, and corresponding losses with both de facto industry-standard 1/2-rate and associated punctured 3/4-rate codes are evaluated. Assuming optimized thresholds, 4-bit metrics are shown to incur only a small quantization loss. However, results also indicate that the loss is sensitive to suboptimum threshold spacing.

On quantization error of self-organizing map network

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.

Application of the bilinear compression function to calorimetry

The energy dynamic range required by a calorimeter may exceed, if high speed is also required, the technical limitations of available ADCs. In this case the use of a dynamic compressor matching the energy range to the ADC range may be an adequate solution. The requirement for the compression function is to add an appropriately small quantization error to the calorimeter resolution. The bilinear compression function is easy to realize, it is therefore interesting to study the conditions under which it is adequate and which are the parameters of the compression curve, the slope ratio and the break point, minimizing the additional error due to quantization.

Design of multiplierless elliptic IIR filters with a small quantization error

We present a new technique for the design of multiplierless IIR elliptic filters. The multiplierless filter has all multiplication constants implemented with a small number of shifters and adders. The proposed technique is based on sensitivity analysis. An analytical expression for amplitude response sensitivity is derived for the filter structures consisting of two allpass subfilters in parallel. It is shown that the amplitude response sensitivity to some constant x can be expressed as a product of the filter reflectance function and the phase sensitivity of the allpass section that implements the constant. The closed-form expressions for the phase sensitivities of the first- and second-order allpass sections are also developed. It is shown in the paper that the (n+1)/2 most sensitive constants can be directly controlled by the transfer function parameters if the transfer function is derived by the bilinear transformation from an elliptic minimal Q-factors (EMQF) analog prototype. This way, (n+1)/2 multiplication constants can be implemented without quantization, leaving the filter characteristic strictly elliptic. This is achieved for a class of low-noise allpass sections and for the wave lattice digital filter as well. The quantization of the remaining (n-1)/2 less-sensitive constants is performed using the phase-tolerance scheme and phase-sensitivity functions. The proposed design technique is straight-forward and, consequently, very fast. The application is demonstrated on the examples of narrowband, wideband, and halfband filters.

Optimal Chebychev interpolation filters for accurate beam steering

This work addresses the problem of the implementation of fractional sample delays necessary for accurate digital beamforming with small steering delay quantization. Past work in this area has employed techniques which upsample by an integer factor, providing an intermediate higher sampling rate at which more accurate delays can be implemented. The signal is then downsampled to the original rate. This results in a minimum delay resolution equal to the original sampling interval divided by the integer valued upsampling factor. The approach presented herein uses existing signal processing techniques to perform resampling without requiring a conversion to an intermediate higher sampling rate [J. O. Smith and P. Gossett, Proc. Intl. Conf. on ASSP (March 1984), Vol. 2, pp. 19.4.1–19.4.2]. This method allows for continuously variable delay values. This technique is extended by the inclusion of interpolation filters which are optimal in a Chebychev or min–max sense. It is shown that the design of fractional delay filters is a complex-valued optimization problem. Specifically, the design of Chebychev optimal filters can be posed as a quadratically constrained quadratic program. Techniques for designing Chebychev optimal fractional delay filters, as well as several examples, will be presented.

Coding scheme and hardware structure of a high-rate digital HDTV codec with partly error-free encoding

For contributing HDTV signals inside a studio and between different studios the and cability for multiple encoding and decoding of signals without visible errors is demanded. Ideally there would be no errors at all. For that reason a rather high bit-rate of 560 Mbit/s for transmission is under discussion. To start out from an active range of 1152 lines, 1920 pels/line and a field frequency of 50 Hz, a data rate of 885 Mbit/s and a compression factor of about 1.6 is needed. The paper describes an intraframe HDTV coder which meets this condition with a simple one-dimensional DPCM and a subsequent entropy coder. Only in the cases where pure entropy coding is not sufficient, a small quantization with 6 bits for the luminance component signal and 5 or 4 bits for the chrominance component is performed. The resulting quality after coding and reconstruction is excellent for different test sequences with a signal-to-noise ratio of about 60 dB. A discussion of the hardware implementation of the proposed codec structure shows that using gate arrays makes it possible to realize nearly all of the codec components in fast CMOS technology. The critical part of the scheme, the VLC decoder, will be discussed in detail. The system frequency for coding and decoding was limited to 72 MHz.

Computer holography: Object dependent deterministic diffusers

When computer-generated holograms are utilized to handle intensity information in data storage, display, and incoherent image processing it is important to ensure high diffraction efficiency and small quantization errors. Diffusers are introduced to achieve these goals. An object dependent deterministic diffuser is presented.

量子化出力誤差が小さいDDCアルゴリズム

量子化出力誤差が小さいDDCアルゴリズム

Photochemistry of semiconductor colloids. Preparation of extremely small ZnO particles, fluorescence phenomena and size quantization effects

Extremely small ZnO particles (< 2.5 nm) are formed in the precipitation of Zn 2+ by OH − in alcoholic solution. The absorption threshold and fluorescence band shift towards longer wavelengths upon growth of the colloidal particles. These shifts are typical for the transition from molecular to semiconductor material. The colloidal ZnO could be separated in the form of a powder with a specific surface of 108 m 2/g. A Cu 2+-doped colloid was also prepared. Colloidal ZnO has a strong fluorescence, λ max = 540 nm, which decays with τ = 10 ns, and a weak one, λ mun = 370 nm, τ < 1 ns. Intense illumination in the absence of O 2 results in the disappearance of the 540 nm fluorescence and a blue-shift of the absorption spectrum. Both changes are immediately reversed upon admission of air. The results are explained on the basis of the Hauffe mechanism for the dissolution of ZnO, in which intermediate Zn + plays a role. Prolonged illumination of a propanolic sol leads to precipitation of zinc metal. In the presence of 1 × 10 −1 M methylviologen. MV + is formed with a quantum yield of 60%.

A wave-packet formulation of multiparticle production at high energies

Starting from a free boson gas in a box, we formulate a statistical approach to multi-particle production. The specific feature of the small box quantization is the fact that one-particle wave functions are wave packets instead of plane waves. In this context we investigate the jet model with Bose-Einstein (BE) statistics. The transverse cut-off function is naturally related to the size of the box (production region). We compare our results with experimental data.

Detecting the Presence of Speech Using ADPCM Coding

When speech is coded using a differential pulse-code modulation system with an adaptive quantizer, the digital code words exhibit considerable variation among all quantization levels during both voiced and unvoiced speech intervals. However, because of limits on the range of step sizes, during silent intervals the code words vary only slightly among the smallest quantization steps. Based on this principle, a simple algorithm for locating the beginning and end of a speech utterance has been developed. This algorithm has been tested in computer simulations and has been constructed with standard integrated circuit technology.