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In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform ... | Wikipedia/Continuous_Fourier_transform |
In signal processing, the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal
x
[
n
]
{\displaystyle x[n]}
with a finite impulse response (FIR) filter
h
[
n
]... | Wikipedia/Overlap-add_method |
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x).
For example, for floor: ⌊2.4... | Wikipedia/Ceiling_function |
In applied mathematics, the Joukowsky transform (sometimes transliterated Joukovsky, Joukowski or Zhukovsky) is a conformal map historically used to understand some principles of airfoil design. It is named after Nikolai Zhukovsky, who published it in 1910.
The transform is
z
=
ζ... | Wikipedia/Joukowsky_transform |
In mathematics the finite Fourier transform may refer to either
another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g., F.J.Harris (pp. 52–53) describes the finite Fourier transform as a "continuous periodic function" and the discrete Fourier transform (DFT) as "a set of samples of th... | Wikipedia/Finite_Fourier_transform_(disambiguation) |
In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal
x
[
n
]
{\displaystyle x[n]}
and a finite impulse response (FIR) filter
h
[
... | Wikipedia/Overlap-save_method |
A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently... | Wikipedia/Function_of_time |
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.
The polynomials arise in:
signal processing as Hermitian wavelets for wavelet transform analysis
probability, such as the Edgeworth series, as well as in connection with Brownian motion;
combinatorics, as an example of an Appell se... | Wikipedia/Hermite_function |
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic.
The oldest and simplest method, known since antiquity as long multipli... | Wikipedia/Multiplication_algorithms |
In time series analysis, Bartlett's method (also known as the method of averaged periodograms), is used for estimating power spectra. It provides a way to reduce the variance of the periodogram in exchange for a reduction of resolution, compared to standard periodograms. A final estimate of the spectrum at a given freq... | Wikipedia/Bartlett_method |
In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group G that is constant on the conjugacy classes of G. In other words, it is invariant under the conjugation map on G. Such functions play a basic role in representation theory.
== Chara... | Wikipedia/Class_function |
Welch's method, named after Peter D. Welch, is an approach for spectral density estimation.
It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.
The method is based on the concept of using periodogram spectrum estimates, which are the result of conv... | Wikipedia/Welch_method |
In applied mathematics, the sliding discrete Fourier transform is a recursive algorithm to compute successive STFTs of input data frames that are a single sample apart (hopsize − 1). The calculation for the sliding DFT is closely related to Goertzel algorithm.
== Definition ==
Assuming that the hopsize between two co... | Wikipedia/Sliding_discrete_Fourier_transform |
In mathematical analysis, a bump function (also called a test function) is a function
f
:
R
n
→
R
{\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} }
... | Wikipedia/Bump_function |
This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be in... | Wikipedia/Fourier-related_transform |
In a Fourier transformation (FT), the Fourier transformed function
f
^
(
s
)
{\displaystyle {\hat {f}}(s)}
is obtained from
f
(
... | Wikipedia/Indirect_Fourier_transform |
Time stretch dispersive Fourier transform (TS-DFT), otherwise known as time-stretch transform (TST), temporal Fourier transform or photonic time-stretch (PTS) is a spectroscopy technique that uses optical dispersion instead of a grating or prism to separate the light wavelengths and analyze the optical spectrum in real... | Wikipedia/Time_stretch_dispersive_Fourier_transform |
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things:
a way of representing commutative Banach algebras as algebras of continuous functions;
the fact that for commutative C*-algebras, this representation is an isometric isomorphism.
In the former case, o... | Wikipedia/Gelfand_transform |
In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type.
T... | Wikipedia/Fourier–Mukai_transform |
In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously.
== Definition ==
The continuous wavelet transform of a function
... | Wikipedia/Continuous_wavelet_transform |
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as
rect
(
t
a
... | Wikipedia/Rectangular_function |
In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign:
f
∗
(
x
)
=
f
... | Wikipedia/Hermitian_function |
In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory and functional analysis. It was introduced by Ralph Fox in 1945.
If the co... | Wikipedia/Compact-open_topology |
In Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has 4 parameters and 1 constraint, so it is a 3-dimensional family, and can be visualized as the action of the special linear group SL2(C) on the time–frequency plane (do... | Wikipedia/Linear_canonical_transform |
In signal 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 signal, called an impulse (δ(t)). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both ... | Wikipedia/Impulse_response_function |
In mathematical physics and harmonic analysis, the quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn generalizes the Fourier transform.
Roughly speaking, the Fourier transform corresponds to a change of variables from time to frequency (in the context ... | Wikipedia/Quadratic_Fourier_transform |
In mathematics, Schwartz space
S
{\displaystyle {\mathcal {S}}}
is the function space of all functions whose derivatives are rapidly decreasing. This space has the important property that the Fourier transform is an automorphism on... | Wikipedia/Schwartz_functions |
A pitch detection algorithm (PDA) is an algorithm designed to estimate the pitch or fundamental frequency of a quasiperiodic or oscillating signal, usually a digital recording of speech or a musical note or tone. This can be done in the time domain, the frequency domain, or both.
PDAs are used in various contexts (e.g.... | Wikipedia/Pitch_detection_algorithm |
In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing the odd component of the function plus cosine waves representing the even component of the function. The modern Fourier transform concisely contains both the sine and co... | Wikipedia/Sine_and_cosine_transforms |
In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.
Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wav... | Wikipedia/Chirplet_transform |
In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29, 1976 in a letter to David Kazhdan as an analogue of the usu... | Wikipedia/Fourier–Deligne_transform |
The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution
... | Wikipedia/Lorentzian_function |
In mathematics, an absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite.
For a real-valued function, since
∫
|
f
(
x
)
... | Wikipedia/Absolutely_integrable_function |
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an isosceles triangle of height 1 and base 2 in which case it is referred to as the triangular function. Triangular functions are useful in signal processing a... | Wikipedia/Triangular_function |
QuickTime Graphics is a lossy video compression and decompression algorithm (codec) developed by Apple Inc. and first released as part of QuickTime 1.x in the early 1990s. The codec is also known by the name Apple Graphics and its FourCC SMC. The codec operates on 8-bit palettized RGB data. The bit-stream format of Qui... | Wikipedia/QuickTime_Graphics |
Multiple-image Network Graphics (MNG) is a graphics file format published in 2001 for animated images. Its specification is publicly documented and there are free software reference implementations available.
MNG is closely related to the PNG image format. When PNG development started in early 1995, developers decided ... | Wikipedia/Multiple-image_Network_Graphics |
The Adaptive Multi-Rate (AMR, AMR-NB or GSM-AMR) audio codec is an audio compression format optimized for speech coding. AMR is a multi-rate narrowband speech codec that encodes narrowband (200–3400 Hz) signals at variable bit rates ranging from 4.75 to 12.2 kbit/s with toll quality speech starting at 7.4 kbit/s.
AMR w... | Wikipedia/Adaptive_Multi-Rate_audio_codec |
Variable-Rate Multimode Wideband (VMR-WB) is a source-controlled variable-rate multimode codec designed for robust encoding/decoding of wideband/narrowband speech. The operation of VMR-WB is controlled by speech signal characteristics (i.e., source-controlled) and by traffic condition of the network (i.e., network-cont... | Wikipedia/Variable-Rate_Multimode_Wideband |
Adaptive Multi-Rate Wideband (AMR-WB) is a patented wideband speech audio coding standard developed based on Adaptive Multi-Rate encoding, using a similar methodology to algebraic code-excited linear prediction (ACELP). AMR-WB provides improved speech quality due to a wider speech bandwidth of 50–7000 Hz compared to na... | Wikipedia/Adaptive_Multi-Rate_Wideband |
In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing the odd component of the function plus cosine waves representing the even component of the function. The modern Fourier transform concisely contains both the sine and co... | Wikipedia/Cosine_transform |
Enhanced Variable Rate Codec B (EVRC-B) is a speech codec used by CDMA networks. EVRC-B is an enhancement to EVRC and compresses each 20 milliseconds of 8000 Hz, 16-bit sampled speech
input into output frames of one of the four different sizes:
Rate 1 - 171 bits,
Rate 1/2 - 80 bits,
Rate 1/4 - 40 bits,
Rate 1/8 ... | Wikipedia/Enhanced_Variable_Rate_Codec_B |
Better Portable Graphics (BPG) is a file format for coding digital images, which was created by programmer Fabrice Bellard in 2014. He has proposed it as a replacement for the JPEG image format as the more compression-efficient alternative in terms of image quality or file size. It is based on the intra-frame encoding ... | Wikipedia/Better_Portable_Graphics |
PGF (Progressive Graphics File) is a wavelet-based bitmapped image format that employs lossless and lossy data compression. PGF was created to improve upon and replace the JPEG format. It was developed at the same time as JPEG 2000 but with a focus on speed over compression ratio.
PGF can operate at higher compression ... | Wikipedia/Progressive_Graphics_File |
Variable bitrate (VBR) is a term used in telecommunications and computing that relates to the bitrate used in sound or video encoding. As opposed to constant bitrate (CBR), VBR files vary the amount of output data per time segment. VBR allows a higher bitrate (and therefore more storage space) to be allocated to the ... | Wikipedia/Variable_bitrate_encoding |
Extended Adaptive Multi-Rate – Wideband (AMR-WB+) is an audio codec that extends AMR-WB. It adds support for stereo signals and higher sampling rates. Another main improvement is the use of transform coding (transform coded excitation – TCX) additionally to ACELP. This greatly improves the generic audio coding. Automat... | Wikipedia/Extended_Adaptive_Multi-Rate_–_Wideband |
Full Rate (FR), also known as GSM-FR or GSM 06.10 (sometimes simply GSM), was the first digital speech coding standard used in the GSM digital mobile phone system. It uses linear predictive coding (LPC). The bit rate of the codec is 13 kbit/s, or 1.625 bits/audio sample (often padded out to 33 bytes/20 ms or 13.2 kbit... | Wikipedia/Full_Rate |
In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in ... | Wikipedia/Butterfly_(FFT_algorithm) |
Enhanced Full Rate or EFR or GSM-EFR or GSM 06.60 is a speech coding standard that was developed in order to improve the quality of GSM.
Enhanced Full Rate was developed by Nokia and the Université de Sherbrooke (Canada). In 1995, ETSI selected the Enhanced Full Rate voice codec as the industry standard codec for GSM/D... | Wikipedia/Enhanced_full_rate |
Half Rate (HR or GSM-HR or GSM 06.20) is a speech coding system for GSM, developed in the early 1990s.
Since the codec, operating at 5.6 kbit/s, requires half the bandwidth of the Full Rate codec, network capacity for voice traffic is doubled, at the expense of audio quality. The sampling rate is 8 kHz with resolution ... | Wikipedia/Half_Rate |
Engineering is the practice of using natural science, mathematics, and the engineering design process to solve problems within technology, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, ele... | Wikipedia/Science_and_engineering |
In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem states that a stochastic process can be represented as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of... | Wikipedia/Karhunen-Loève_transform |
Adaptive Transform Acoustic Coding (ATRAC) is a family of proprietary audio compression algorithms developed by Sony. MiniDisc was the first commercial product to incorporate ATRAC, in 1992. ATRAC allowed a relatively small disc like MiniDisc to have the same running time as CD while storing audio information with mini... | Wikipedia/Adaptive_Transform_Acoustic_Coding |
The Joint Photographic Experts Group (JPEG) is the joint committee between ISO/IEC JTC 1/SC 29 and ITU-T Study Group 16 that created and maintains the JPEG, JPEG 2000, JPEG XR, JPEG XT, JPEG XS, JPEG XL, and related digital image standards. It also has the responsibility for maintenance of the JBIG and JBIG2 standards ... | Wikipedia/Joint_Photographic_Experts_Group |
Enhanced Variable Rate CODEC (EVRC) is a speech codec used in CDMA networks. It was developed in 1995 to replace the QCELP vocoder which used more bandwidth on the carrier's network, thus EVRC's primary goal was to offer the mobile carriers more capacity on their networks while not increasing the amount of bandwidth or... | Wikipedia/Enhanced_Variable_Rate_Codec |
Dynamic Resolution Adaptation (DRA) was an audio encoding specification developed by DigiRise Technology. It had been selected as the Chinese national audio coding standard, and declared suitable for China Multimedia Mobile Broadcasting and DVB-H as addressed in the International Journal of Digital Multimedia Broadcas... | Wikipedia/Dynamic_Resolution_Adaptation |
Advanced Systems Format (formerly Advanced Streaming Format, Active Streaming Format) is Microsoft's proprietary digital audio/digital video container format, especially meant for streaming media. ASF is part of the Media Foundation framework.
== Overview and features ==
ASF is based on serialized objects which are e... | Wikipedia/Advanced_Systems_Format |
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and the... | Wikipedia/Spectral_methods |
A facial recognition system is a technology potentially capable of matching a human face from a digital image or a video frame against a database of faces. Such a system is typically employed to authenticate users through ID verification services, and works by pinpointing and measuring facial features from a given imag... | Wikipedia/Facial_recognition_systems |
In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator. A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.
The difference between the deg... | Wikipedia/Proper_transfer_function |
In the IEEE 802 reference model of computer networking, the logical link control (LLC) data communication protocol layer is the upper sublayer of the data link layer (layer 2) of the seven-layer OSI model. The LLC sublayer acts as an interface between the medium access control (MAC) sublayer and the network layer.
The... | Wikipedia/Logical_Link_Control |
The Radio Resource Control (RRC) protocol is used in UMTS, LTE and 5G on the Air interface. It is a layer 3 (Network Layer) protocol used between UE and Base Station. This protocol is specified by 3GPP in TS 25.331 for UMTS, in TS 36.331 for LTE and in TS 38.331 for 5G New Radio. RRC messages are transported via the P... | Wikipedia/Radio_Resource_Control |
The Signalling Connection Control Part (SCCP) is a network layer protocol that provides extended routing, flow control, segmentation, connection-orientation, and error correction facilities in Signaling System 7 telecommunications networks. SCCP relies on the services of MTP for basic routing and error detection.
== ... | Wikipedia/Signalling_Connection_Control_Part |
The Mobile Application Part (MAP) is an SS7 protocol that provides an application layer for the various nodes in GSM and UMTS mobile core networks and GPRS core networks to communicate with each other in order to provide services to users. The Mobile Application Part is the application-layer protocol used to access the... | Wikipedia/Mobile_Application_Part |
In data networking, telecommunications, and computer buses, an acknowledgement (ACK) is a signal that is passed between communicating processes, computers, or devices to signify acknowledgment, or receipt of message, as part of a communications protocol. Correspondingly a negative-acknowledgement (NAK or NACK) is a sig... | Wikipedia/Acknowledgement_(data_networks) |
The Broadcast/Multicast control (BMC) is a sublayer of layer 2 protocol of Radio Interface Protocol Architecture as per BMC-STD. It exists in the user plane only. It is located above the Radio Link Control (RLC), a layer 2 responsible for mapping logical channels. It is similar to 802.11's LLC layer which supports mult... | Wikipedia/Broadcast/Multicast_Control |
Network planning and design is an iterative process, encompassing
topological design, network-synthesis, and network-realization, and is aimed at ensuring that a new telecommunications network or service meets the needs of the subscriber and operator.
The process can be tailored according to each new network or servic... | Wikipedia/Network_design |
The Open Systems Interconnection (OSI) model is a reference model developed by the International Organization for Standardization (ISO) that "provides a common basis for the coordination of standards development for the purpose of systems interconnection."
In the OSI reference model, the components of a communication s... | Wikipedia/Open_Systems_Interconnection |
Systems Network Architecture (SNA) is IBM's proprietary networking architecture, created in 1974. It is a complete protocol stack for interconnecting computers and their resources. SNA describes formats and protocols but, in itself, is not a piece of software. The implementation of SNA takes the form of various communi... | Wikipedia/Systems_Network_Architecture |
In a digitally modulated signal or a line code, symbol rate, modulation rate or baud is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in baud (Bd) or symbols per second. In the case of a line code, the symbol rate is the ... | Wikipedia/Symbol_rate |
Peer-to-peer (P2P) computing or networking is a distributed application architecture that partitions tasks or workloads between peers. Peers are equally privileged, equipotent participants in the network, forming a peer-to-peer network of nodes. In addition, a personal area network (PAN) is also in nature a type of dec... | Wikipedia/Peer-to-peer_networking |
In the OSI networking model, Data Link Control (DLC) is the service provided by the data link layer. Network interface cards have a DLC address that identifies each card; for instance, Ethernet and other types of cards have a 48-bit MAC address built into the cards' firmware when they are manufactured.
There is also a... | Wikipedia/Data_Link_Control |
The Recursive InterNetwork Architecture (RINA) is a new computer network architecture proposed as an alternative to the architecture of the currently mainstream Internet protocol suite. The principles behind RINA were first presented by John Day in his 2008 book Patterns in Network Architecture: A return to Fundamental... | Wikipedia/Recursive_Internetwork_Architecture |
The Hierarchical internetworking model is a three-layer model for network design first proposed by Cisco in 1998. The hierarchical design model divides enterprise networks into three layers: core, distribution, and access.
== Access layer ==
End-stations and servers connect to the enterprise at the access layer. Acce... | Wikipedia/Hierarchical_internetworking_model |
The Network Driver Interface Specification (NDIS) is an application programming interface (API) for network interface controllers (NICs).
== Specification ==
It was jointly developed by Microsoft and 3Com Corporation and is mostly used in Microsoft Windows. However, the open-source NDISwrapper and Project Evil driver... | Wikipedia/Network_Driver_Interface_Specification |
The Address Resolution Protocol (ARP) is a communication protocol for discovering the link layer address, such as a MAC address, associated with a internet layer address, typically an IPv4 address. The protocol, part of the Internet protocol suite, was defined in 1982 by RFC 826, which is Internet Standard STD 37.
ARP ... | Wikipedia/Address_resolution_protocol |
In circuit design, the Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit... | Wikipedia/Star-triangle_transform |
In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function
W
:
[
0
,
1
]
2
→
[
0
,
1
]
... | Wikipedia/Graphon |
A digitally controlled oscillator or DCO is used in synthesizers, microcontrollers, and software-defined radios. The name is analogous with "voltage-controlled oscillator". DCOs were designed to overcome the tuning stability limitations of early VCO designs.
== Confusion over terminology ==
The term "digitally contro... | Wikipedia/Digitally_controlled_oscillator |
Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum.
Leeson's expression for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per hertz) and augmented for flicker noise:
L
(
f
... | Wikipedia/Leeson's_equation |
A numerically controlled oscillator (NCO) is a digital signal generator which creates a synchronous (i.e., clocked), discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digital-to-analog converter (DAC) at the output to create a direct digital synth... | Wikipedia/Numerically-controlled_oscillator |
In statistics, the Fisher transformation (or Fisher z-transformation) of a Pearson correlation coefficient is its inverse hyperbolic tangent (artanh).
When the sample correlation coefficient r is near 1 or -1, its distribution is highly skewed, which makes it difficult to estimate confidence intervals and apply tests... | Wikipedia/Fisher_z-transformation |
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
There are various types of generati... | Wikipedia/Generating_functions |
In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. The advanced z-transform is widely applied, for example, to accurately model processing delays in digital control. It is also known as the modified ... | Wikipedia/Advanced_Z-transform |
The chirp Z-transform (CZT) is a generalization of the discrete Fourier transform (DFT). While the DFT samples the Z plane at uniformly-spaced points along the unit circle, the chirp Z-transform samples along spiral arcs in the Z-plane, corresponding to straight lines in the S plane. The DFT, real DFT, and zoom DFT c... | Wikipedia/Bluestein's_FFT_algorithm |
In applied mathematics, the starred transform, or star transform, is a discrete-time variation of the Laplace transform, so-named because of the asterisk or "star" in the customary notation of the sampled signals.
The transform is an operator of a continuous-time function
x
(
t
... | Wikipedia/Star_transform |
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform ... | Wikipedia/Continuous-time_Fourier_transform |
In mathematics a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral formulas applied to a sequence generating function (see integral transformations) ... | Wikipedia/Generating_function_transformation |
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tan... | Wikipedia/Differentiation_(calculus) |
In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid systems. It has applications in any field that requires simultane... | Wikipedia/Time-scale_calculus |
The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis.
The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, and it is of importance in quantum mechanics in phase space (see, by way of... | Wikipedia/Wigner_distribution_function |
In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewe... | Wikipedia/Fresnel_transform |
For digital image processing, the Focus recovery from a defocused image is an ill-posed problem since it loses the component of high frequency. Most of the methods for focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects... | Wikipedia/Focus_recovery_based_on_the_linear_canonical_transform |
In evolutionary biology, mimicry in vertebrates is mimicry by a vertebrate of some model (an animal, not necessarily a vertebrate), deceiving some other animal, the dupe. Mimicry differs from camouflage as it is meant to be seen, while animals use camouflage to remain hidden. Visual, olfactory, auditory, biochemical, a... | Wikipedia/Mimicry_in_vertebrates |
A computed tomography scan (CT scan), formerly called computed axial tomography scan (CAT scan), is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists.
CT scanners use a rotating X-ray tube and a row o... | Wikipedia/X-ray_Tomography |
The World-Wide Standardized Seismograph Network (WWSSN) – originally the World-Wide Network of Seismograph Stations (WWNSS) – was a global network of about 120 seismograph stations built in the 1960s that generated an unprecedented collection of high quality seismic data. This data enabled seismology to become a quanti... | Wikipedia/World-Wide_Standardized_Seismograph_Network |
The banana doughnut theory - also sometimes known as Born-Fréchet kernel theory, or finite-frequency theory - is a model in seismic tomography that describes the shape of the Fresnel zone along the entire ray path of a body wave. This theory suggests that the area that influences the ray velocity is the surrounding mat... | Wikipedia/Banana_Doughnut_theory |
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.
Filter design characterises filter circuits primarily by their transfer function rather than their topology. Transfer functions may be linea... | Wikipedia/Electronic_filter_topology |
CV/gate (an abbreviation of control voltage/gate) is an analog method of controlling synthesizers, drum machines, and similar equipment with external sequencers. The control voltage typically controls pitch and the gate signal controls note on-off.
This method was widely used in the epoch of analog modular synthesizer... | Wikipedia/Control_voltage |
Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of ele... | Wikipedia/information_theory |
Welch's method, named after Peter D. Welch, is an approach for spectral density estimation.
It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.
The method is based on the concept of using periodogram spectrum estimates, which are the result of conv... | Wikipedia/Welch's_method |
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