Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “quantization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Quantization effects in Viterbi decoding rate 1/n convolutional codes

A Viterbi decoder's performance loss due to quantizing data from the additive white Gaussian noise (AWGN) channel is studied. An optimal quantization scheme and branch metric calculation method are presented. The uniformly quantized channel capacity C(sub u)(q) is used to determine the smallest number of quantization bits q that does not cause a significant loss. The quantizer stepsize which maximizes C(sub u)(q) almost minimizes the decoder bit error rate (BER). However, a slightly larger stepsize is better, like the value that minimizes the Bhattacharyya bound. The range and renormalization of state metrics is analyzed, in particular for K = 15 decoders such as the Big Viterbi Decoder (BVD) for the Galileo mission. These results are required to design reduced hardware complexity Viterbi decoders with a negligible quantization loss.

Onyszchuk, I. M.↗
NASA NTRS1993

Visual optimization of DCT quantization matrices for individual images

Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coefficient as an approximation to the local response of a visual 'channel'. For a given quantization matrix, the DCT quantization errors are adjusted by contrast sensitivity, light adaptation, and contrast masking, and are pooled non-linearly over the blocks of the image. This yields an 8x8 'perceptual error matrix'. A second non-linear pooling over the perceptual error matrix yields total perceptual error. With this model we may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.

Watson, Andrew B.↗
NASA NTRS1993

A visual detection model for DCT coefficient quantization

The discrete cosine transform (DCT) is widely used in image compression, and is part of the JPEG and MPEG compression standards. The degree of compression, and the amount of distortion in the decompressed image are determined by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. Our approach is to set the quantization level for each coefficient so that the quantization error is at the threshold of visibility. Here we combine results from our previous work to form our current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color.

Ahumada, Albert J., Jr.↗
NASA NTRS1995

Visibility of Wavelet Quantization Noise

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗
NASA NTRS1997

Visibility of wavelet quantization noise

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

NASA Center ARC↗
DOE OSTI2014

Flat minimal quantizations of Stäckel systems and quantum separability

In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, natural Hamiltonian systems from a given Riemann space are expressed by some flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations. - Highlights: • Using Stäckel transform, separable Hamiltonians are expressed by flat coordinates. • The concept of admissible flat minimal quantizations is developed. • The class of Stäckel systems, separable after minimal flat quantization is established. • Separability of related stationary Schrödinger equations is presented in explicit form.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Two quantization approaches to the Bateman oscillator model

We consider two quantization approaches to the Bateman oscillator model. One is Feshbach–Tikochinsky’s quantization approach reformulated concisely without invoking the SU(1,1) Lie algebra, and the other is the imaginary-scaling quantization approach developed originally for the Pais–Uhlenbeck oscillator model. The latter approach overcomes the problem of unbounded-below energy spectrum that is encountered in the former approach. In both the approaches, the positive-definiteness of the squared-norms of the Hamiltonian eigenvectors is ensured. Unlike Feshbach–Tikochinsky’s quantization approach, the imaginary-scaling quantization approach allows to have stable states in addition to decaying and growing states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum simulation of second-quantized Hamiltonians in compact encoding

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. Here, we show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the φ 4 -theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quantization of the Thermal Hall Conductivity at Small Hall Angles

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev’s non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ x x due to phonons is much larger than the expected quantized thermal Hall conductance $κ$ $^{q}_{xy}$ = (πT/12)($k$ $^{2}_{B}$/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L >> ℓ, where ℓ is a thermalization length. We obtain ℓ ~ T –5 for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Furthermore, our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ xy /κ xx ~ 10 –3 , in α–RuCl 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Bit Grooming: statistically accurate precision-preserving quantization with compression, evaluated in the netCDF Operators (NCO, v4.4.8+)

Abstract. Geoscientific models and measurements generate false precision (scientifically meaningless data bits) that wastes storage space. False precision can mislead (by implying noise is signal) and be scientifically pointless, especially for measurements. By contrast, lossy compression can be both economical (save space) and heuristic (clarify data limitations) without compromising the scientific integrity of data. Data quantization can thus be appropriate regardless of whether space limitations are a concern. We introduce, implement, and characterize a new lossy compression scheme suitable for IEEE floating-point data. Our new Bit Grooming algorithm alternately shaves (to zero) and sets (to one) the least significant bits of consecutive values to preserve a desired precision. This is a symmetric, two-sided variant of an algorithm sometimes called Bit Shaving that quantizes values solely by zeroing bits. Our variation eliminates the artificial low bias produced by always zeroing bits, and makes Bit Grooming more suitable for arrays and multi-dimensional fields whose mean statistics are important. Bit Grooming relies on standard lossless compression to achieve the actual reduction in storage space, so we tested Bit Grooming by applying the DEFLATE compression algorithm to bit-groomed and full-precision climate data stored in netCDF3, netCDF4, HDF4, and HDF5 formats. Bit Grooming reduces the storage space required by initially uncompressed and compressed climate data by 25–80 and 5–65 %, respectively, for single-precision values (the most common case for climate data) quantized to retain 1–5 decimal digits of precision. The potential reduction is greater for double-precision datasets. When used aggressively (i.e., preserving only 1–2 digits), Bit Grooming produces storage reductions comparable to other quantization techniques such as Linear Packing. Unlike Linear Packing, whose guaranteed precision rapidly degrades within the relatively narrow dynamic range of values that it can compress, Bit Grooming guarantees the specified precision throughout the full floating-point range. Data quantization by Bit Grooming is irreversible (i.e., lossy) yet transparent, meaning that no extra processing is required by data users/readers. Hence Bit Grooming can easily reduce data storage volume without sacrificing scientific precision or imposing extra burdens on users.

58 GEOSCIENCES↗
NASA NTRS1972

Quantization noise in digital speech

The amount of quantization noise generated in a digital-to-analog converter is dependent on the number of bits or quantization levels used to digitize the analog signal in the analog-to-digital converter. The minimum number of quantization levels and the minimum sample rate were derived for a digital voice channel. A sample rate of 6000 samples per second and lowpass filters with a 3 db cutoff of 2400 Hz are required for 100 percent sentence intelligibility. Consonant sounds are the first speech components to be degraded by quantization noise. A compression amplifier can be used to increase the weighting of the consonant sound amplitudes in the analog-to-digital converter. An expansion network must be installed at the output of the digital-to-analog converter to restore the original weighting of the consonant sounds. This technique results in 100 percent sentence intelligibility for a sample rate of 5000 samples per second, eight quantization levels, and lowpass filters with a 3 db cutoff of 2000 Hz.

Schmidt, O. L.↗
NASA NTRS1977

Minimum distortion quantizers

The well-known algorithm of Max is used to determine the minimum distortion quantizers for normal, two-sided exponential, and specialized two-sided gamma input distributions and for mean-square, magnitude, and relative magnitude error distortion criteria. The optimum equally-spaced and unequally-spaced quantizers are found, with the resulting quantizer distortion and entropy. The quantizers, and the quantizers with entropy coding, are compared to the rate distortion bounds for mean-square and magnitude error.

Jones, H. W., Jr.↗
NASA NTRS1991

Video data compression using artificial neural network differential vector quantization

An artificial neural network vector quantizer is developed for use in data compression applications such as Digital Video. Differential Vector Quantization is used to preserve edge features, and a new adaptive algorithm, known as Frequency-Sensitive Competitive Learning, is used to develop the vector quantizer codebook. To develop real time performance, a custom Very Large Scale Integration Application Specific Integrated Circuit (VLSI ASIC) is being developed to realize the associative memory functions needed in the vector quantization algorithm. By using vector quantization, the need for Huffman coding can be eliminated, resulting in superior performance against channel bit errors than methods that use variable length codes.

Krishnamurthy, Ashok K.↗
NASA NTRS1991

An all digital implementation of a modified Hamming net for video compression with prediction and quantization circuits

The hardware and algorithms used to vector quantize (VQ) predicted pixel intensity differences for real-time video compression are described. The hardware is designed for rapid vector quantization performance, which entails the development of application-specific associative memory circuits. A modified DPCM algorithm is originally examined to determine how neural circuitry could enhance its operation. It was determined that quantization and encoding could be improved by consolidating these two functions into one, and by increasing the amount of information (i.e. number of pixels) quantized at a time. The result is a predictive scheme that vector quantizes differential values. Some of the disadvantages of VQ algorithms are solved using associative memories. The video compression algorithm and the associative memory design are described.

Kaul, Richard↗
NASA NTRS1999

Weighted MinMax Algorithm for Color Image Quantization

The maximum intercluster distance and the maximum quantization error that are minimized by the MinMax algorithm are shown to be inappropriate error measures for color image quantization. A fast and effective (improves image quality) method for generalizing activity weighting to any histogram-based color quantization algorithm is presented. A new non-hierarchical color quantization technique called weighted MinMax that is a hybrid between the MinMax and Linde-Buzo-Gray (LBG) algorithms is also described. The weighted MinMax algorithm incorporates activity weighting and seeks to minimize WRMSE, whereby obtaining high quality quantized images with significantly less visual distortion than the MinMax algorithm.

Reitan, Paula J.↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗