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Generalizations of Nyquist-Shannon sampling theorem for reconstructing signals
Nonuniform sampling is a branch of sampling theory involving results related to the Nyquist–Shannon sampling theorem. Nonuniform sampling is based on
Nonuniform_sampling
Sufficiency theorem for reconstructing signals from samples
most likely be lost. The sampling theory of Shannon can be generalized for the case of nonuniform sampling, that is, samples not taken equally spaced
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Concept in applied mathematics
many signals have their energy distributed nonuniformly in the frequency domain. Therefore, a nonuniform sampling scheme could be more convenient and useful
Non-uniform discrete Fourier transform
Non-uniform_discrete_Fourier_transform
Computational problem
pairs. Nonuniform sampling distributions attempt to place more milestones in areas that improve the connectivity of the roadmap. Quasirandom samples typically
Motion_planning
Array that replaces runtime computation with a simpler array indexing operation
table can be reduced by using nonuniform sampling, which means that where the function is close to straight, we use few sample points, while where it changes
Lookup_table
Generating pseudo-random numbers that follow a probability distribution
methods for generating independent samples: Rejection sampling for arbitrary density functions Inverse transform sampling for distributions whose CDF is known
Non-uniform random variate generation
Non-uniform_random_variate_generation
Formula in probability theory
Application to Estimation Detection". In Marvasti, Farokh A. (ed.). Nonuniform Sampling: Theory and Practice. Springer. ISBN 0306464454. Ylvisaker, N. D
Rice's_formula
Method for numerical integration
b]} needs to be divided into uneven intervals – perhaps due to uneven sampling of data, or missing or corrupted data points. Suppose we divide the interval
Simpson's_rule
Computer technology
; Wong, C.M. (1996). "A digital audio processing system based on nonuniform sampling delta modulation". IEEE Transactions on Consumer Electronics. 42:
Silence_compression
but it is not necessary. The use of nonuniform sampling is often used in stereological work. The point sampled intercept method selects cells using a
Proportionator
Statistical property of a test item
DIF, where one group consistently has an advantage over the other, and nonuniform DIF, where the advantage varies based on the individual's ability level
Differential_item_functioning
Method of representing curves and surfaces in computer graphics
1016/0010-4485(89)90059-6. Clear explanation of NURBS for non-experts About Nonuniform Rational B-Splines – NURBS TinySpline: Opensource C-library with bindings
Non-uniform_rational_B-spline
Accuracy of light source in showing color of objects
space in which the color distance is calculated (CIEUVW) is obsolete and nonuniform. Use CIELAB or CIELUV instead. The chromatic adaptation transform used
Color_rendering_index
difficult due to variations in the atomization efficiency from the sample matrix, and nonuniformity of concentration and path length of analyte atoms (in graphite
Graphite furnace atomic absorption
Graphite_furnace_atomic_absorption
Algorithm to find Euclidean shortest paths
"Incremental Sampling-based Algorithms for Optimal Motion Planning". arXiv:1005.0416 [cs.RO]. Karaman, Sertac; Frazzoli, Emilio (5 May 2011). "Sampling-based
Any-angle_path_planning
Mathematical function defined piecewise by polynomials
often use an extended concept of a spline known as a Nonuniform rational B-spline (NURBS). If sampled data from a function or a physical object is available
Spline_(mathematics)
Description of the physical characteristics of a rock unit
(euhedral) to irregular crystals (anhedral), whether the rock shows highly nonuniform crystal sizes (is porphyritic), or whether grains are aligned (which is
Lithology
Intelligence test
manual to convert the ratio IQs with means varying between age ranges and nonuniform standard deviations to IQs with a mean of 100 and a uniform standard deviation
Stanford–Binet Intelligence Scales
Stanford–Binet_Intelligence_Scales
Measure of unpredictability of outcomes
equal for a uniform distribution, but measure the unpredictability of a nonuniform distribution in different ways. The min-entropy is never greater than
Min-entropy
Power spectrum of a noise signal
following meanings: In facsimile or display systems, such as television, a nonuniformity in the white area of the image, i.e., document or picture, caused by
Colors_of_noise
Algorithm that generates an approximation of a random number sequence
Springer. Hörmann W., Leydold J., Derflinger G. (2004, 2011), Automatic Nonuniform Random Variate Generation, Springer-Verlag. Knuth D.E. The Art of Computer
Pseudorandom_number_generator
Sedimentary process of rivers
Ranga Raju, Kittur G. (August 2010). "Suspended Wash Load Transport of Nonuniform Sediments". Journal of Hydraulic Engineering. 136 (8): 534–543. doi:10
Wash_load
Theorem in probability theory
location missing publisher (link) Michel, R. (1981). "On the constant in the nonuniform version of the Berry-Esséen theorem". Zeitschrift für Wahrscheinlichkeitstheorie
Berry–Esseen_theorem
Color rendering score
(CIE Ra, 1974). The color space used in CIE Ra (CRI) is outdated and nonuniform, and CQS uses CIELAB as a replacement. The Von Kries chromatic adaptation
Color_quality_scale
Methods of estimating differential entropy given some observations
fairly similar, whereas in a strongly nonuniform distribution they may vary a lot more.) When in under-sampled regime, having a prior on the distribution
Entropy_estimation
Self-reinforcing single wave packet
; Zhukov, A. I.; Voronov, V. P. (1998). "Magnetic soliton motion in a nonuniform magnetic field". Journal of Experimental and Theoretical Physics. 87 (2):
Soliton
Distance over which a wave's shape repeats
time-scale methods: adaptive decompositions, uncertainty principles, and sampling. Birkhäuser. p. 348. ISBN 978-0-8176-4276-1. See Figure 4.20 in A. Putnis
Wavelength
Image processing technique
magnitudes. For example, the motivation for anisotropic diffusion (also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is
Edge-preserving_smoothing
Lithography using 13.5 nm UV light
tolerance for illumination can be ±15°, or even less. Annular illumination nonuniformity and asymmetry also significantly impact the imaging. Newer systems have
Extreme ultraviolet lithography
Extreme_ultraviolet_lithography
Lossy audio compression format
temporal noise shaping (TNS), the Kaiser window (described below), a nonuniform quantizer, and a reworking of the bitstream format to handle up to 16
Advanced_Audio_Coding
1954 U.S. thermonuclear weapon test in the Marshall Islands
interstage to smooth the spatial profile (i.e. reduce coherence and nonuniformities) of the primary's irradiance are of utmost importance. This was done
Castle_Bravo
Discrete Fourier transform algorithm
FFTs For applications such as MRI, it is necessary to compute DFTs for nonuniformly spaced grid points and/or frequencies. Multipole-based approaches can
Fast_Fourier_transform
Light technique
imaging. Its nonuniform variant, warped-stretch transform, realized with nonlinear group delay, offers variable-rate spectral domain sampling, as well as
Time stretch dispersive Fourier transform
Time_stretch_dispersive_Fourier_transform
Matrix representing a Euclidean rotation
distributed over the unit sphere of directions, S2, while the angle has the nonuniform distribution over [0,π] noted previously (Miles 1965). Euler–Rodrigues
Rotation_matrix
Mechanism with bendable rotation axis
Robert Hooke analysed the joint and found that its speed of rotation was nonuniform, but that property could be used to track the motion of the shadow on
Universal_joint
Stress test with different levels of stress in each perpendicular direction
Triaxial tests of classical construction had been criticized for their nonuniform stress and strain field imposed within the specimen during larger deformation
Triaxial_shear_test
Metal heat treatment process
However careful consideration should be given to materials that contain nonuniform or non-symmetric sections. Different cross sections may have different
Carburizing
r r o r ( h ) ≤ ε {\displaystyle error(h)\leq \varepsilon } . In the nonuniform random attribute noise model the algorithm is learning a Boolean function
Error tolerance (PAC learning)
Error_tolerance_(PAC_learning)
Act providing national standards for cigarette packaging in the US
extent consistent with this declared policy. (B) Not impeded by diverse, nonuniform, and confusing cigarette labeling and advertising regulations with respect
Cigarette Labeling and Advertising Act
Cigarette_Labeling_and_Advertising_Act
Problem in probability theory
e^{-e^{-c}/(m-1)!},{\text{ as }}n\to \infty .} In the general case of a nonuniform probability distribution, according to Philippe Flajolet et al. E (
Coupon_collector's_problem
features on the planet (plains, volcanoes, rifts, etc.) is decidedly more nonuniform than the crater population. This means that while the nature of resurfacing
Geodynamics_of_Venus
Subclass of liquid crystal
property underpinning all liquid crystals is anisotropy (directional nonuniformity, typically manifested by an elongated rodlike shape), which under appropriate
Cholesteric_liquid_crystal
Proposed quantum computer implementation
transported between regions in an interconnected trap and is subjected to a nonuniform magnetic field, decoherence can occur in the form of the equation below
Trapped-ion_quantum_computer
Karp, Richard M.; Lipton, Richard J. (1980). "Some connections between nonuniform and uniform complexity classes". In Miller, Raymond E.; Ginsburg, Seymour;
Sparse_language
Optical imaging method
is well preserved while maintaining the same sampling rates compared to uniform case without down-sampling. Image compression was demonstrated at 36 million
Serial time-encoded amplified microscopy
Serial_time-encoded_amplified_microscopy
Separation technique to characterize the size of colloidal particles
New Separation Concept Based on a Coupling of Concentration and Flow Nonuniformities". Separation Science. 1: 123–125. doi:10.1080/01496396608049439. Giddings
Field_flow_fractionation
Informatics of nanomaterials
It differs from cheminformatics in that nanomaterials usually involve nonuniform collections of particles that have distributions of physical properties
Nanoinformatics
Hypothetical Solar System planet
predicted orbital distribution of the longest lived of these objects is nonuniform. Most would have orbits with perihelia ranging from 5 AU to 35 AU and
Planet_Nine
Particle motion in a non-uniform electric field due to dipole-field interactions
difference between dielectrophoretic forces exerted on different particles in nonuniform electric fields is known as DEP separation. The exploitation of DEP forces
Dielectrophoresis
Medical imaging procedure
Wayback Machine "It is a single dose parameter that reflects the risk of a nonuniform exposure in terms of an equivalent whole-body exposure." Hill B, Venning
CT_scan
Technique used in optical systems
the Shack–Hartmann. Ocular aberrations are caused by spatial phase nonuniformities in the wavefront exiting the eye. In a Shack-Hartmann wavefront sensor
Adaptive_optics
Discrete analog of a derivative
{(x-1)(x-2)}{2}}\\\\&=2+(x-1)(x-2)\\\end{aligned}}\end{matrix}}} For the case of nonuniform steps in the values of x, Newton computes the divided differences, Δ j
Finite_difference
Property of space that quantifies the magnetic influence at a given location
opposite poles. If, however, the magnetic field of the first magnet is nonuniform (such as the H near one of its poles), each pole of the second magnet
Magnetic_field
MRI procedure that measures brain activity by detecting associated changes in blood flow
inserted, say into the subject's mouth, to patch the magnetic field. The nonuniformities are often near brain sinuses such as the ear and plugging the cavity
Functional magnetic resonance imaging
Functional_magnetic_resonance_imaging
NASA satellite of the Explorer program
chamber and an Anton 302 Geiger–Müller tube (GM). Due to the complex nonuniform shielding of the detectors, only approximate energy threshold values were
Explorer_6
Material deformation mechanism
stress, because of variations in the filament, causes the filament to sag nonuniformly, which ultimately introduces further torque on the filament. It is this
Grain_boundary_sliding
Computer output device
the primary elements of the display, typically averaged across it in nonuniform displays. A related unit is pixel pitch, In LCDs, pixel pitch is the distance
Computer_monitor
American convicted murderer (born 1979)
for penalty other than death and its omission from the trial record, "nonuniform 'application of the law'" during trial and sentencing, and admission at
Thomas_Bartlett_Whitaker
Brain stimulation using magnetic fields
shaped with variable internal density and water content, leading to a nonuniform magnetic field strength and conduction throughout its tissues. The effects
Transcranial magnetic stimulation
Transcranial_magnetic_stimulation
Higher-level programming standard for heterogeneous computing
2024-07-11. Jin, Zheming; Vetter, Jeffrey S. (November 2022). "Evaluating Nonuniform Reduction in HIP and SYCL on GPUs". 2022 IEEE/ACM 8th International Workshop
SYCL
Chinese historical period
Frachetti, Michael (2012). "Multiregional Emergence of Mobile Pastoralism and Nonuniform Institutional Complexity across Eurasia". Current Anthropology. 53 (1):
Neolithic_in_China
Making devices resist ionizing radiation
Yavandhassani, J. (2025). "Modeling of total ionizing dose (TID) effects on the nonuniform distribution of Si/SiO2 interface trap energy states in MOS devices".
Radiation_hardening
Stellar core remnant
limiting mass increases only slightly. If the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in
White_dwarf
Mechanism for regulating the speed of clocks
suspended by a thread; the bob could be reversed to eliminate the effects of nonuniform density. He calculated the length to the center of oscillation of thread
Pendulum
multidirectional radius sampling to more accurately represent non-circular branch cross-sections and non-spherical spine heads. The Rayburst Sampling Algorithm uses
NeuronStudio
State of matter
introduction of the weaker secondary optical lattice. Studies of vortices in nonuniform Bose–Einstein condensates as well as excitations of these systems by the
Bose–Einstein_condensate
Innermost Galilean moon of Jupiter
Tackley, P. J. (2001). "Convection in Io's asthenosphere: Redistribution of nonuniform tidal heating by mean flows". J. Geophys. Res. 106 (E12): 32971–32981
Io_(moon)
Global climate cycles
will gradually start earlier in the year. Precession means the Earth's nonuniform motion (see above) will affect different seasons. Winter, for instance
Milankovitch_cycles
Human research factorization and quantification system
based on discrete sampling. This relies on the mathematical Nyquist theorem stating that a signal at W Hz can be reconstructed by sampling every 1/W seconds
Human_performance_modeling
Tendency of a liquid surface to shrink to reduce surface area
1007/BF01011513. Cahn, J.W.; Hilliard, J.E. (1958), "Free energy of a nonuniform system. I. Interfacial free energy", J. Chem. Phys., 28 (2): 258–266,
Surface_tension
Different forms of boron
adjacent atoms. The isolated B 12 icosahedra are not stable, due to the nonuniformity of the honeycomb; thus boron is not a molecular solid, but the icosahedra
Allotropes_of_boron
Dust floating in space
emitting or absorbing dust particles. Dust particles can scatter light nonuniformly. Forward scattered light is light that is redirected slightly off its
Cosmic_dust
another element (the base metal), forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation
Glossary_of_engineering:_M–Z
J. J. Riley (1983). "Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow". Phys. Fluids. 26 (4): 883–889. Bibcode:1983PhFl...26..883M. doi:10
Particle-laden_flow
Quantum computing implementation
oscillators for which energy levels are discretized (or quantized) with nonuniform spacing between energy levels, denoted Δ E {\displaystyle \Delta E} .
Superconducting quantum computing
Superconducting_quantum_computing
Family of probability distributions
WS (1999). "Clustering of murine lung metastases reflects fractal nonuniformity in regional lung blood flow". Invasion and Metastasis. 18 (5–6): 285–296
Tweedie_distribution
Sensor which measures heat transfer
construction of the sensor. In particular, some designs have a strongly nonuniform sensitivity. Others even exhibit a sensitivity to lateral fluxes. The
Heat_flux_sensor
Method that extracts features from radiographic medical images
Lee LY, Chang JT, Tsan DL, Ng SH, et al. (March 2015). "Zone-size nonuniformity of 18F-FDG PET regional textural features predicts survival in patients
Radiomics
Algorithm
illustrated with the reconstruction of a bandlimited function from its nonuniformly spaced sampling values. However, it has been pointed out that the reported success
Kaczmarz_method
Indian-American Physicist
properties of BiFeO3 due to stabilization of crystal structure and nonuniformity in spin cycloid structure by La substitution. Seehra investigated the
Mohindar_Singh_Seehra
Model of chemical adsorption
adsorption of carbon nanoparticles. Historically, the theory was used to model nonuniform adsorbates and multi-components solutes. For certain pairs of adsorbates
Polanyi_potential_theory
Type of visual artifact
Frequency-encoding sampling in all the rows of the matrix (128, 256 or 512) takes place during a single echo (milliseconds). Phase-encoded sampling takes several
MRI_artifact
Microtechnology
is the motion of uncharged particles due to induced polarization from nonuniform electric fields. Dielectrophoresis can be used in bio-MEMS for dielectrophoresis
Bio-MEMS
Uniformity of handedness
(e.g., magnetite sediments) this initial ee would be small due to nonuniformities in the magnetization of the surface. This occurs because Earth's geomagnetic
Homochirality
limited resolution, and a lower accuracy of the evaluation in the case of nonuniform stresses or inhomogeneous material properties. The so-called calibration
Hole_drilling_method
Sediment
types apart from post-settlement alluvium, and (3) respects the spatial (nonuniform) and temporal (time-transgressive) variability of LS: "Legacy sediment:
Legacy_sediment
warped in a context-aware manner, such that it results in nonuniform Fourier domain sampling. The transformation is defined as: A S T { E ~ i n ( ω ) }
Anamorphic_stretch_transform
American fluid dynamicist
Uzol, J. Katz, Turbulence Within a Turbomachine Rotor Wake Subject to Nonuniform Contraction, Aiaa Journal 46(11) (2008) 2687–2702. M.R. Snyder, O.M. Knio
Joseph_Katz_(professor)
Power generation technology
result, oxygen will be impeded to diffuse into catalyst layer, leading to nonuniform power generation in the FC. This new design enabled the first FC stack
Proton-exchange membrane fuel cell
Proton-exchange_membrane_fuel_cell
points towards strong regions of the nonuniform electric field while nDEP points towards weak regions of the nonuniform electric field. Live cells can quickly
Electromanipulation
Motion of a curve based on its curvature
curvature scale space is less computationally intensive, more robust against nonuniform noise, and less strongly influenced by small-scale shape differences.
Curve-shortening_flow
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
Boy/Male
Tamil
Lord of the Sun, The Sun, Sun God
Girl/Female
American, Arabic, Australian, Latin
Dedicated to God Mars; Lady; Feminine of Martin; Warlike
Boy/Male
German, Swedish
Bluish; Lead Colored
Biblical
who is like to God?
Girl/Female
Japanese
Child with a collar. The suffix -ko means child.
Boy/Male
Australian, Chinese, Dutch, Portuguese
Silver Voice; Hell's Door; Slanting Surface
Boy/Male
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Handsome
Girl/Female
German, Greek
Light
Boy/Male
Arabic, Muslim
From the Battlefield
Female
Danish
, sword spirit.
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
NONUNIFORM SAMPLING
n.
An implement for sampling butter; a butter trier.