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Theory about lossy data compression
rate–distortion functions. Rate–distortion theory was created by Claude Shannon in his foundational work on information theory. In rate–distortion theory
Rate–distortion_theory
A distortion function in mathematics and statistics, for example, g : [ 0 , 1 ] → [ 0 , 1 ] {\displaystyle g:[0,1]\to [0,1]} , is a non-decreasing function
Distortion_function
Alteration of the original shape of a signal
output is undistorted. Distortion occurs when the transfer function F is more complicated than this. If F is a linear function, for instance a filter
Distortion
Concept in financial economics
the variance of the portfolio's return. The Wang transform function (distortion function) for the Value at Risk is g ( x ) = 1 x ≥ 1 − α {\displaystyle
Coherent_risk_measure
Risk measure derived by applying a distortion function to a loss distribution
mathematics and economics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial
Distortion_risk_measure
Class of algorithms in information theory
either the information theoretic capacity of a channel, the rate-distortion function of a source or a source encoding (i.e. compression to remove the
Blahut–Arimoto_algorithm
Topics referred to by the same term
economics Distortion function, used to define distortion risk measures In mathematics, distortion has several meanings, including: Distortion (mathematics)
Distortion_(disambiguation)
Scientific study of digital information
specified fidelity level measured by a distortion function. This subset of information theory is called rate–distortion theory. Error-correcting codes (channel
Information_theory
Process of mapping a continuous set to a countable set
error) is referred to as quantization error, noise or distortion. A device or algorithmic function that performs quantization is called a quantizer. An
Quantization (signal processing)
Quantization_(signal_processing)
Deviation from rectilinear projection (optics)
In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image
Distortion_(optics)
Measurement of the harmonic distortion present in a signal
The total harmonic distortion (THD or THDi) is a measurement of the harmonic distortion present in a signal; THD is defined as the ratio of the sum of
Total_harmonic_distortion
Electronic test equipment used to generate electrical waveforms
Although function generators cover both audio and radio frequencies, they are usually not suitable for applications that need low distortion or stable
Function_generator
established earlier by Oohama in the course of determining the rate–distortion function of the quadratic Gaussian CEO problem. In this case it follows from
Entropy_power_inequality
Statement in complex analysis
{\displaystyle |w|\geq {1 \over 4}.} The Koebe distortion theorem gives a series of bounds for a univalent function and its derivative. It is a direct consequence
Koebe_quarter_theorem
Generalized version of classical Green's function
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations
Multiscale_Green's_function
Estimated potential loss for an investment under a given set of conditions
other. Value at risk can also be written as a distortion risk measure given by the distortion function g ( x ) = { 0 if 0 ≤ x < 1 − α 1 if 1 − α ≤ x
Value_at_risk
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Technique in information theory
information bottleneck can also be viewed as a rate distortion problem, with a distortion function that measures how well Y is predicted from a compressed
Information_bottleneck_method
the distortion is a measure of the amount by which a function from the Euclidean plane to itself distorts circles to ellipses. If the distortion of a
Distortion_(mathematics)
Reconstruction of a filtered signal
that we wish to recover, but has been convolved with a filter or distortion function g, before we recorded it. Usually, h is a distorted version of f
Deconvolution
Distortion pedals are a type of effects unit designed to add distortion to an audio signal to create a warm, gritty, or fuzzy character. Depending on
List_of_distortion_pedals
Mathematical relation assigning a probability event to a cost
information theory, this loss function is known as Hamming distortion. In many applications, objective functions, including loss functions as a particular case
Loss_function
Amplitude distortion is distortion occurring in a system, subsystem, or device when the output amplitude is not a linear function of the input amplitude
Amplitude_distortion
Electronic sound synthesis method
Phase distortion (PD) synthesis is a synthesis method introduced in 1984 by Casio in its CZ range of synthesizers. In outline, it is similar to phase modulation
Phase_distortion_synthesis
Inclination to skew perceptions of others based on fantasy
Parataxic distortion is a psychiatric term first used by Harry S. Sullivan to describe the inclination to skew perceptions of others based on fantasy.
Parataxic_distortion
Characterization of distortion in map projections
distortion, is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 to characterize local distortions
Tissot's_indicatrix
Technique for reducing low-resolution image distortion
signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower
Spatial_anti-aliasing
Risk measure estimating the average loss in the worst tail of the distribution
loss". Expected shortfall can also be written as a distortion risk measure given by the distortion function g ( x ) = { x 1 − α if 0 ≤ x < 1 − α , 1 if 1
Expected_shortfall
Non-linear effect in amplitude modulation
Intermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies, caused by
Intermodulation
Stochastic process generalizing Brownian motion
with respect to the squared error distance, i.e. its quadratic rate-distortion function, is given by R ( D ) = 2 π 2 D ln 2 ≈ 0.29 D − 1 . {\displaystyle
Wiener_process
Empirical relationship between actual and perceived changed intensity of stimulus
distortion function and the psychophysical functions could be separated, formulated a behavioral condition equivalent to the psychophysical function being
Stevens's_power_law
FM synthesis sound chip by Yamaha
model Mega Drive/Genesis) or by implementing a function in the emulated chip to apply a crossover distortion effect to simulate a YM2612. Used in conjunction
Yamaha_YM2612
Overview of finance and finance-related topics
returns around their expected value Distortion risk measure – Risk measure derived by applying a distortion function to a loss distribution Spectral risk
Outline_of_finance
Process forming a path from many random steps
with respect to the squared error distance, i.e. its quadratic rate distortion function, is given parametrically by R ( D θ ) = 1 2 ∫ 0 1 max { 0 , log 2
Random_walk
Hungarian mathematician (1941–2019)
rate distortion function of discrete stationary processes". Problemy Peredachi Informatsii. VII (2): 3–14. Marton, K. (1975). "On the rate distortion function
Katalin_Marton
Response of an optical system to a point source of light
spread function may be independent of position in the object plane, in which case it is called shift invariant. In addition, if there is no distortion in
Point_spread_function
Distributed source coding concept
ISSN 0018-9448. Wyner, Aaron D.; Ziv, Jacob (January 1976). "The rate-distortion function for source coding with side information at the decoder". IEEE Transactions
Slepian–Wolf_coding
Term in information theory
D)}{\log D}},} where R ( X , D ) {\displaystyle R(X,D)} is the rate-distortion function that is defined as R ( X , D ) = min ‖ X − X ^ ‖ 2 ≤ D I ( X , X
Information_dimension
Concept in geometric group theory
metric on the corresponding group; the distortion of H in G is the asymptotic equivalence class of the function R ↦ diam H ( B G ( 0 , R ) ∩ H ) diam
Subgroup_distortion
Signal with properties that vary cyclically with time
spectral density. For a Gaussian cyclostationary process, its rate distortion function can be expressed in terms of its cyclic spectrum. The reason S x
Cyclostationary_process
Audio process
In electronic music, waveshaping is a type of distortion synthesis in which complex spectra are produced from simple tones by altering the shape of the
Waveshaper
Classical quantization technique from signal processing
quantization Related topics Speech coding Ogg Vorbis Voronoi diagram Rate-distortion function Data clustering Centroidal Voronoi tessellation Image segmentation
Vector_quantization
On tangency patterns of circles
maps from a specified domain to the unit disk, having a specified distortion function. Several applications of the circle packing theorem use it to study
Circle_packing_theorem
Delays experienced through a linear time-invariant system
a result, the signal's waveform experiences distortion as it passes through the system. This distortion can cause problems such as poor fidelity in analog
Group_delay_and_phase_delay
Integral expressing the amount of overlap of one function as it is shifted over another
mathematical operation on two functions f and g that produces a third function f∗g, as the integral of the product of the two functions after one is reflected
Convolution
Leakage of fluid surrounding the brain and spinal cord through tears in the dura mater
as personality changes, altered behaviors and impairment of executive functions, similar to behavioral-variant frontotemporal dementia as the frontal
Cerebrospinal_fluid_leak
Functions such that f(–x) equals f(x) or –f(x)
real-valued odd function is imaginary and odd. (see Fourier analysis § Symmetry properties) In signal processing, harmonic distortion occurs when a sine
Even_and_odd_functions
Problem in information theory and communication
subsets are still needed. The effective cost function that needs to be minimized is a weighted sum of distortion and decoder storage J=D+λC The system design
Distributed_source_coding
Swiss mathematician
1952 a function (now called the Hersch-Pfluger distortion function) useful in estimating the distortion of quasiconformal mappings. Entire functions with
Albert_Pfluger
Image distortion caused by projection
keystone effect is the apparent distortion of an image caused by projecting it onto an angled surface. It is the distortion of the image dimensions, such
Keystone_effect
Formula that visually represents itself when graphed
Carries between binary positions can alter additional bits, creating distortions or other changes in the resulting bitmap. Nevertheless, the example demonstrates
Tupper's self-referential formula
Tupper's_self-referential_formula
Characteristic of an optical system
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector is a scale-dependent description of their
Optical_transfer_function
Spatial distortion in cosmology
Redshift-space distortions are an effect in observational cosmology where the spatial distribution of galaxies appears squashed and distorted when their
Redshift-space_distortions
AM/FM radio receiver introduced in 1978
clipping headroom equals 0.46 dB). The dynamic headroom was 0.63 dB. ... The distortion at 1,000 Hz was nearly unmeasurable at any power level. It was no more
Pioneer_SX-1980
Cylindrical conformal map projection
large-scale sheets in the equirectangular projection as a way to minimize distortion of directions. If these sheets were brought to the same scale and assembled
Mercator_projection
Israeli computer scientist
bound. They proved the convergence to Shannon bound known as "rate-distortion function". But their algorithm is far from being useful and assumes a-priori
Ilan_Sadeh
Coherent risk measure using weighted outcomes based on risk aversion
trivially a spectral measure of risk. Distortion risk measure – Risk measure derived by applying a distortion function to a loss distribution Cotter, John;
Spectral_risk_measure
Signal processing effect
sampling result in the identical sample. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different
Aliasing
Temperature at which a material deforms
Heat deflection temperature or heat distortion temperature (DTUL, HDT, or HDTUL) is the temperature at which a polymer or plastic sample deforms under
Heat_deflection_temperature
In functional analysis, a branch of mathematics, the distortion problem is to determine by how much one can distort the unit sphere in a given Banach space
Distortion_problem
Guitar distortion pedal
The ProCo RAT is a distortion pedal produced by ProCo Sound for use with electric guitar. The RAT has become one of the industry's most popular effects
Pro_Co_RAT
Electronic devices that generate electronic signals
distortion can be measured using a very-low-distortion audio generator as the signal source, with appropriate equipment to measure output distortion
Signal_generator
Information-theoretic measure
modeled using the logistic function g(z)=1/(1+e−z) where z is some function of the input vector x, commonly just a linear function. The probability of the
Cross-entropy
Ratio of the fundamental signal to the output's strongest spurious signal
output of DAC to the RMS value of the next largest noise or harmonic distortion component (which is referred to as “spurious” or a “spur”) at its output
Spurious-free_dynamic_range
Type of malicious software
noticeable. UNIWARD (Universal Wavelet Relative Distortion) (2014): Uses a universal distortion function applicable to multiple image formats, balancing
Stegomalware
Organ central to the nervous system
brains, some branches of vertebrate evolution have led to substantial distortions of brain geometry, especially in the forebrain area. The brain of a shark
Brain
Equal-area pseudocylindrical global map projection
cannot be mapped onto a plane without distortion, all (planar) maps distort shapes in one way or another. The distortion can be visualized using an index called
Equal_Earth_projection
Systematic representation of the surface of a sphere or ellipsoid onto a plane
symmetry in the scales and hence in the distortions: map distances from the central point are computed by a function r(d) of the true distance d, independent
Map_projection
Mechanism of spontaneous symmetry breaking
degeneracy of the wave function cannot correspond to a stable structure. In mathematical terms, the APESs characterising the JT distortion arise as the eigenvalues
Jahn–Teller_effect
Electronic circuit which counteracts non-linear behavior of an amplifier
including pre- and post-distortion and feedback linearization. Most commonly used is pre-distortion linearization. The function performed by the linearizer
Linearizer
Audio signal processing technique
results by applying a cubic distortion function (whereas Cook and Paolillo's technique may be termed "square-law modulation distortion"). This new characteristic
Chirp_compression
Test and measurement instrument
parameters, including level, gain, noise, harmonic and intermodulation distortion, frequency response, relative phase of signals, interchannel crosstalk
Audio_analyzer
Average uncertainty in variable's states
the function log(1p(E)), where log is the logarithm, which gives 0 surprise when the probability of the event is 1. In fact, log is the only function that
Entropy_(information_theory)
Camera lens with a very short focal length
distortion that is characteristic of a fisheye lens. Neither denotes a particular range of focal lengths, the difference is only whether distortion is
Ultra_wide_angle_lens
Topics referred to by the same term
store brand used by Metro Inc. Adverse selection Selection effect, a distortion of data arising from the way that the data are collected Selection-based
Selection
Output of a dynamic system when given a brief input
processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input
Impulse_response
Function of propagation delay and Doppler frequency
{\displaystyle f} , χ ( τ , f ) {\displaystyle \chi (\tau ,f)} . It represents the distortion of a returned pulse due to the receiver matched filter (commonly, but
Ambiguity_function
Ratio of active power to apparent power
...and voltage-time relationship deviates from the pure sine function. The distortion at the point of generation is very small (about 1% to 2%), but
Power_factor
Species of virus
Symptoms are typical of viral diseases. Papaya exhibits yellowing, leaf distortion, and severe mosaic. Oily or water-soaked spots and streaks appear on the
Papaya_ringspot_virus
Minimum sampling rate to avoid aliasing
reconstructed function that has less bandwidth. In most cases, the differences are viewed as distortion. Figure 3 depicts a type of function called baseband
Nyquist_rate
Geometric transformation that preserves lines but not angles nor the origin
affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension
Affine_transformation
Adaptive optics optimization freuqency
definitions attempt to represent the frequency at which the turbulence distortion of the image is changing. The reciprocal of the Greenwood frequency is
Greenwood_frequency
Cluster analysis problem
high-dimensional data, causing the distortion to increase without limit. If, as described above, K is made an increasing function of p, namely, K = ⌊ α p ⌋ {\displaystyle
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Measured time difference as explained by relativity theory
the integral can be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function τ ( t ) = c g ln ( g t c + 1 + ( g t c ) 2
Time_dilation
Measurement of a signal at discrete time intervals
theoretically perfect reconstruction, collectively referred to as distortion. Various types of distortion can occur, including: Aliasing. Some amount of aliasing
Sampling_(signal_processing)
Instrument for displaying time-varying signals
for properties such as amplitude, frequency, rise time, time interval, distortion, and others. Originally, calculation of these values required manually
Oscilloscope
Mechanism of spontaneous symmetry breaking
degenerate electronic term does not necessarily remove the instability and distortion of a polyatomic system induced by the Jahn–Teller effect (JTE), provided
Pseudo_Jahn–Teller_effect
Mathematical space with a notion of distance
distance between its points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for studying many
Metric_space
Maximum frequency of non-aliased component upon sampling
sampler, the resulting discrete-time sequence is said to be free of the distortion known as aliasing, and the corresponding sample rate is said to be above
Nyquist_frequency
Correlation as a function of distance
Rate distortion theory – Theory about lossy data compressionPages displaying short descriptions of redirect targets Radial distribution function – Description
Correlation_function
API plugins for graphics editor software
interactive perspective warp effects. To a large extent, with its draggable distortion handles and its moving, scaling and rotating options, this simply duplicates
Kai's_Power_Tools
Analytic function in mathematics
In analysis, a lacunary function or series is an analytic function containing many zero coefficients in its basis decomposition. A series can be lacunary
Lacunary_function
Group theory function
mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which
Dehn_function
Digital image distortion
been significantly distorted. Warping may be used for correcting image distortion as well as for creative purposes (e.g., morphing). The same techniques
Image_warping
System of identifying electrical power devices
in ANSI/IEEE Standard C37.2 Standard for Electrical Power System Device Function Numbers, Acronyms, and Contact Designations. Many of these devices protect
ANSI_device_numbers
Recall of fabricated, misinterpreted or distorted memories
subtle inaccuracies to surreal fabrications, and may include confusion or distortion in the temporal framing (timing, sequence or duration) of memories. In
Confabulation
Inclusion of one mathematical structure in another, preserving properties of interest
directed. A mapping ϕ:X→Y of metric spaces is called an embedding (with distortion C>0) if LdX(x,y)≤dY(ϕ(x),ϕ(y))≤CLdX(x,y) for every x,y∈X and some constant
Embedding
Manufacturer of innovative photographic lenses
Traditional and anamorphic. Laowa 15 mm f/4 Wide Angle Macro with shift function by Venus Optics Laowa 9 mm f/2.8 super wide angle lens for APS-C, introduced
Venus_Optics
Non-sinusoidal waveform
infinite harmonics are sampled and the resulting tone contains aliasing distortion. An audio demonstration of a sawtooth played at 440 Hz (A4) and 880 Hz
Sawtooth_wave
Pseudoazimuthal compromise map projection
(German for 'triple') refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance. x = 1 2 ( λ cos φ 1 + 2 cos φ sin
Winkel_tripel_projection
travel, tourism, insurance
DISTORTION FUNCTION
DISTORTION FUNCTION
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, Functionary of the Interior.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, a great functionary.
Biblical
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Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
DISTORTION FUNCTION
DISTORTION FUNCTION
DISTORTION FUNCTION
DISTORTION FUNCTION
DISTORTION FUNCTION
DISTORTION FUNCTION
DISTORTION FUNCTION
travel, tourism, insurance