The above equations for the quasispecies then become for the discrete version:

* Proportional / Sum / Derivative, a version of the common discrete controller Proportional / Integral / Derivative

The IEEE 802. 3an standard defines the wire-level modulation for 10GBASE-T as a Tomlinson-Harashima Precoded ( THP ) version of pulse-amplitude modulation with 16 discrete levels ( PAM-16 ), encoded in a two-dimensional checkerboard pattern known as DSQ128.

CTC decided to re-implement the new version of the terminal using discrete TTL instead of waiting for a single chip CPU.

Dolby Digital is the common version containing up to six discrete channels of sound.

In the quantum version of the theory, the Faraday lines of these fields become the loops of LQG, and carry discrete quanta of geometry.

There was also a release of the quadraphonic version in the UK in fully discrete 4-channel form on the " Quad-8 " format, a 4-channel variant of the stereo 8-track tape cartridge.

An early example was Gun Fight, Midway's 1975 reprogrammed version of Taito's arcade game Western Gun, with the main difference being the use of a microprocessor in the reprogrammed version, which allowed improved graphics and smoother animation than the discrete logic of the original.

This version is called the L < sup > 2 </ sup > index theorem, and was used by to rederive properties of the discrete series representations of semisimple Lie groups.

* Discrete Fourier Series, the discrete version of Fourier series

In one dimension, Sperner's Lemma can be regarded as a discrete version of the Intermediate Value Theorem.

The discrete version of the transform, the Discrete Hartley transform, was introduced by R. N. Bracewell in 1983.

After the discrete Shepard scale Risset created a version of the scale where the steps between each tone are continuous, and it is appropriately called the continuous Risset scale or Shepard-Risset glissando.

In application, populations are generally finite, making the discrete version more realistic.

The original TI-30, a cost-reduced but functionally equivalent version of TI's unit, utilized an LED display, was powered by a ubiquitous 9 volt battery, and contained nearly all of its functionality in one chip, where previous calculators used many discrete components.

Theorem ( discrete time version ).

Applying reduction of order in case of a multiple root m < sub > 1 </ sub > will yield expressions involving a discrete version of ln,

It is not clear how this version of applying the analogy might be used to the check the rates of discrete events.

It also received a standardized 500GB 7200rpm hard drive as well as the standard-for-M11x-line dual-GPU setup combining NVIDIA's discrete GeForce GT 540M for higher-end gaming and Intel's integrated HD Graphics 3000 for older gaming and application use, by the end of 2011 a second revision of the motherboard design used on the R3 series was made available on a limited amount of laptops, this second version used the more powerful Nvidia GF108 chipset, the GTX 550M with 1GB video memory.

This method is, in fact, a simple version of the discrete Fourier transform ( DFT ).

# The VDC was programmed by writing commands to and reading status messages from a single control register and transferring data between system RAM and the chip's dedicated video RAM ( 16 or 64KB, depending on C128 version ) via a single data register, following a relatively complex protocol — a laborious and slow procedure compared with the straightforward use of the several discrete, memory mapped control / status registers the shared system / video memory setup of the VIC-II.

Its simplest combinatorial version is due to Zuk: let be a discrete group generated by a finite subset S, closed under taking inverses and not containing the identity, and define a finite graph with vertices S and an edge between g and h whenever g < sup >− 1 </ sup > h lies in S. If this graph is connected and the smallest non-zero eigenvalue of its Laplacian is greater than ½, then has property ( T ).

A more general geometric version, due to Zuk and, states that if a discrete group acts properly discontinuously and cocompactly on a contractible 2-dimensional simplicial complex with the same graph theoretic conditions placed on the link at each vertex, then has property ( T ).

A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum.

In mathematics, the discrete Fourier transform ( DFT ) is a specific kind of discrete transform, used in Fourier analysis.

Relationship between the ( continuous ) Fourier transform and the discrete Fourier transform.

Fourier transform ( bottom ) is zero except at discrete points.

* It completely describes the discrete-time Fourier transform ( DTFT ) of an N-periodic sequence, which comprises only discrete frequency components.

* It is the discrete analogy of the formula for the coefficients of a Fourier series:

The discrete Fourier transform is an invertible, linear transformation

A fast Fourier transform ( FFT ) is an efficient algorithm to compute the discrete Fourier transform ( DFT ) and its inverse.

This operation is useful in many fields ( see discrete Fourier transform for properties and applications of the transform ) but computing it directly from the definition is often too slow to be practical.

For example, JPEG compression uses a variant of the Fourier transformation ( discrete cosine transform ) of small square pieces of a digital image.

The coefficients in the upper and lower figures are respectively computed by the Fourier series integral and the discrete Fourier transform | DFT summation.

Thus we have the important result that when a discrete data sequence, s, is proportional to samples of an underlying continuous function, s ( t ), one can deduce something about the continuous Fourier transform, S ( ƒ ).

For periodic functions, both the Fourier transform and the DTFT comprise only a discrete set of frequency components ( Fourier series ), and the transforms diverge at those frequencies.

# compute the instantaneous frequency / amplitude relationship of the signal using the STFT, which is the discrete Fourier transform of a short, overlapping and smoothly windowed block of samples ;

By making measurements of the signal at many discrete positions of the moving mirror, the spectrum can be reconstructed using a Fourier transform of the temporal coherence of the light.

Formally stated, the FFT is a method for computing the discrete Fourier transform of a sampled signal.

The equivalent to Laplace transform in the discrete domain is the z-transform.

The continuous Laplace transform is in Cartesian coordinates where the axis is the real axis and the discrete Z-transform is in circular coordinates where the axis is the real axis.

In order to determine what information in an audio signal is perceptually irrelevant, most lossy compression algorithms use transforms such as the modified discrete cosine transform ( MDCT ) to convert time domain sampled waveforms into a transform domain.

Today, nearly all commonly used video compression methods ( e. g., those in standards approved by the ITU-T or ISO ) apply a discrete cosine transform ( DCT ) for spatial redundancy reduction.

The DCT that is widely used in this regard was introduced by N. Ahmed, T. Natarajan and K. R. Rao in 1974 ; see Reference 1 in discrete cosine transform.

Other methods, such as fractal compression, matching pursuit and the use of a discrete wavelet transform ( DWT ) have been the subject of some research, but are typically not used in practical products ( except for the use of wavelet coding as still-image coders without motion compensation ).

An example of the 2D discrete wavelet transform that is used in JPEG2000.

In numerical analysis and functional analysis, a discrete wavelet transform ( DWT ) is any wavelet transform for which the wavelets are discretely sampled.

For real inputs, the real part of is none other than the discrete Hartley transform, which is also involutary.

Clenshaw – Curtis quadrature is essentially a change of variables to cast an arbitrary integral in terms of integrals of periodic functions where the Euler – Maclaurin approach is very accurate ( in that particular case the Euler – Maclaurin formula takes the form of a discrete cosine transform ).