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According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.

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## Some Related Sentences

According and theorem

__According__

**to**Cauchy's functional equation

__theorem__

**,**

**the**logarithm is

**the**only continuous transformation

**that**transforms real multiplication

**to**addition

**.**

__According__

**to**

**the**

__theorem__

**,**it is possible

**to**expand

**the**power ( x + y )< sup > n </ sup > into a sum involving terms of

**the**form ax < sup > b </ sup > y < sup > c </ sup >, where

**the**exponents b and c are nonnegative integers with

**,**and

**the**coefficient a of each term is a specific positive integer depending on n and b

**.**When an exponent is zero

**,**

**the**corresponding power is usually omitted from

**the**term

**.**

__According__

**to**Noether's

__theorem__

**,**

**the**conservation of energy is a consequence of

**the**fact

**that**

**the**laws of physics do not change over time

**.**

__According__

**to**

**the**

__theorem__

**,**within every sufficiently powerful logical system ( such as Principia ), there exists a statement G

**that**essentially reads

**,**" The statement G cannot be proved

**.**

*

__According__**to**a__theorem__of Nikolay Nikolov and Dan Segal**,**in any topologically finitely-generated profinite group (**that**is**,**a profinite group**that**has a dense finitely-generated subgroup )**the**subgroups of finite index are open**.**__According__

**to**

**the**spin-statistics

__theorem__

**,**particles with integer spin occupy symmetric quantum states

**,**and particles with half-integer spin occupy antisymmetric states ; furthermore

**,**only integer

**or**half-integer values of spin are allowed by

**the**principles of quantum mechanics

**.**

__According__

**to**Rice's

__theorem__

**,**if there is

**at**least one computable function in a particular class C of computable functions and another computable function not in C then

**the**problem of deciding whether a particular program computes a function in C is undecidable

**.**

__According__

**to**

**the**Rouché – Capelli

__theorem__

**,**

**the**system is inconsistent if

**the**rank of

**the**augmented matrix is greater than

**the**rank of

**the**coefficient matrix

**.**

__According__

**to**

**the**optical Raychaudhuri's

__theorem__

**,**

**this**requires a violation of

**the**averaged null energy condition

**.**

__According__

**to**

**the**Nyquist

__theorem__

**,**error-free detection of

**the**line code requires a channel bandwidth of

**at**least

**the**Nyquist rate

**,**which is half

**the**line code pulse rate

**.**

__According__

**to**Shannon's source coding

__theorem__

**,**

**the**optimal code length for a symbol is − log < sub > b </ sub > P

**,**where b is

**the**number of symbols used

**to**make output codes and P is

**the**probability of

**the**input symbol

**.**

__According__

**to**

**the**CPT

__theorem__of particle physics

**,**antihydrogen atoms should have many of

**the**characteristics regular hydrogen atoms have ; i

**.**e., they should have

**the**same mass

**,**magnetic moment

**,**and transition

**frequencies**( see atomic spectroscopy ) between their atomic quantum states

**.**

__According__

**to**Liouville's

__theorem__

**,**any bounded complex analytic function defined on

**the**whole complex plane is constant

**.**

__According__

**to**Allen Weiss

**,**in Mirrors of Infinity

**,**

**this**optical effect is a result of

**the**use of

**the**tenth

__theorem__of Euclid ’ s Optics which asserts

**that**“

**the**most distant parts of planes situated below

**the**eye appear

**to**be

**the**most elevated .” In Fouquet ’ s time

**,**interested parties could cross

**the**canal in a boat

**,**but walking around

**the**canal provides a view of

**the**woods

**that**mark what is

**no**longer

**the**garden and shows

**the**distortion of

**the**grottos previously seen as sculptural

**.**

__According__

**to**

**the**virial

__theorem__

**,**

**the**gravitational binding energy of a star is about two times its internal thermal energy

**.**

__According__

**to**

**the**correspondence principle and Ehrenfest's

__theorem__as a system becomes larger

**or**more massive ( action >> Planck's constant )

**the**classical dynamics tends

**to**emerge

**,**with some exceptions

**,**such as superfluidity

**.**

__According__

**to**

**the**Kutta – Joukowski

__theorem__

**,**lift is

**the**product of circulation

**,**airspeed

**,**and air density

**.**

__According__

**to**

**the**Shannon – Hartley

__theorem__

**,**

**the**channel capacity of a properly-encoded

**signal**is proportional

**to**

**the**bandwidth of

**the**channel and

**the**logarithm of

**the**signal-to-noise ratio ( SNR ) ( assuming

**the**noise is additive white Gaussian noise ).

__According__

**to**

**the**inverse function

__theorem__

**,**

**the**matrix inverse of

**the**Jacobian matrix of an invertible function is

**the**Jacobian matrix of

**the**inverse function

**.**

__According__

**to**one leading historian of statistics

**,**he may have been

**the**earliest discoverer of Bayes

__theorem__

**.**

According and reconstructed

__According__

**to**him

**,**while

**the**first two visions (

**the**alter-globalism and

**the**anti-globalism ) represent

**the**

__reconstructed__forms of old and new left ideologies

**,**respectively

**,**in

**the**context of current globalization

**,**only

**the**third one has shown

**the**capacity

**to**respond more effectively

**to**

**the**intellectual requirements of today ’ s global complexities

**.**

__According__

**to**a

__reconstructed__inscription found on

**the**site

**,**"

**the**emperor Vespasian ordered

**this**new amphitheatre

**to**be erected from his general's share of

**the**booty

**.**

__According__

**to**

**this**theory

**,**fairies are personified aspects of nature and deified abstract concepts such as ‘ love ’ and ‘ victory ’ in

**the**pantheon of

**the**particular form of animistic nature worship

__reconstructed__as

**the**religion of Ancient Western Europe .< ref >

__According__

**to**Breuer

**,**

**the**slow and laborious progress of her “ remembering work ” in which she recalled individual symptoms after they had occurred

**,**thus “ dissolving ” them

**,**came

**to**a conclusion on 7 June 1882 after she had

__reconstructed__

**the**first night of hallucinations in Ischl

**.**

"

__According__**to**Islamic tradition**,****the**Kaaba was built by Adam as a place of worship**,**and then later__reconstructed__by Abraham and Ishmael**.**

According and signal

* Compressible:

__According__**to**Miller**,**" Uncompressed digital data is very large**,**and in its raw form would actually produce a larger__signal__( therefore be more difficult**to**transfer ) than analog data**.**__According__

**to**one definition of digital

__signal__

**,**

**the**modulated

__signal__is a digital

__signal__

**,**and according

**to**another definition

**,**

**the**modulation is a form of digital-to-analog conversion

**.**

__According__

**to**Alan V

**.**Oppenheim and Ronald W

**.**Schafer

**,**

**the**principles of

__signal__processing can be found in

**the**classical numerical analysis techniques of

**the**17th century

**.**

__According__

**to**

**the**most common definition of digital

__signal__

**,**both baseband and passband signals representing bit-streams are considered as digital transmission

**,**while an alternative definition only considers

**the**baseband

__signal__as digital

**,**and passband transmission of digital data as a form of digital-to-analog conversion

**.**

__According__

**to**signaling theory

**,**education does not lead

**to**increased human capital

**,**but rather acts as a mechanism by which workers with superior innate abilities can

__signal__those abilities

**to**prospective employers and so gain

**above**average wages

**.**

__According__

**to**Dick Hebdige

**,**members of a subculture often

__signal__their membership through a distinctive and symbolic use of style

**,**which includes fashions

**,**mannerisms

**,**and argot

**.**

__According__

**to**Julian Symons

**,**" Ellery ... occasionally lost his father

**,**as his exploits took place more frequently in

**the**small town of Wrightsville ... where his arrival as a house guest was likely

**to**be

**the**

__signal__for

**the**commission of one

**or**more murders

**.**

__According__

**to**a critical analysis in The Independent

**,**

**the**genre rose

**to**prominence in

**the**1990s not as a continuance of

**the**celebration of " sex and shopping reflected

**the**materialism of

**the**1980s ", but as a

__signal__of " disillusionment with those values ".

__According__

**to**Thackery ( in a 2011 exchange on Facebook ), " A smart tech guy fixed us up with

__signal__boosting cords

**to**prevent a loss of

__signal__due

**to**

**the**extraordinarily long guitar cables

**.**

__According__

**to**Stevens ' definition

**,**a loudness of 1 sone is equivalent

**to**

**the**loudness of a

__signal__

**at**40 phons

**,**

**the**loudness level of a 1 kHz tone

**at**40 dB SPL

**.**

__According__

**to**him

**,**our ancestors

**,**like many other social animals

**,**used contact calls

**to**maintain constant contact with

**the**members of

**the**group

**,**and a

__signal__of danger was communicated through becoming silent and freezing

**.**

__According__

**to**

**the**jurisprudence of

**the**Boards of Appeal of

**the**EPO

**,**a technical effect

**provided**by a computer program can be

**,**for example

**,**a reduced memory access time

**,**a better control of a robotic arm

**or**an improved reception and /

**or**decoding of a radio

__signal__

**.**

__According__

**to**another telling of

**this**story

**,**Étaín

**,**deciding

**that**she still loved Eochaid

**,**gave him a

__signal__so he would choose correctly

**.**

__According__

**to**Article 5

**,**George explains

**that**Domon is not allowed

**to**fight more than one fighter

**,**however Domon claims he received

**the**

__signal__

**to**fight before Neo Cuba's Gundam Fighter had arrived

**.**

__According__

**to**

**the**sampling

**theorem**

**,**any

__signal__with bandwidth B can be perfectly described by more than 2B samples per second

**.**

__According__

**to**local legend

**,**

**this**is

**the**site where Robert

**the**Bruce mistook farmers ' fires on

**the**mainland as

**the**

__signal__

**to**launch his campaign

**.**

__According__

**to**nepahdtv

**.**com

**,**

**this**move was met with some dismay from viewers in areas where reception of signals from Penobscot Knob is difficult if not impossible

**,**leaving many people in rural areas without their

__signal__

**.**

1.963 seconds.