2024年3月20日发(作者：呼延冷雪)

4Fouriertransformationanddata

processing

数据处理

Inthepreviouschapterwehaveseenhowtheprecessingmagnetizationcan

bedetectedtogiveasignalwhichoscillatesattheLarmorfrequency–the

commentedthatthissignalwilleventually

decayawayduetotheactionofrelaxation;thesignalisthereforeoftencalled

stionishowdoweturnthissignal,

whichdependsontime,intotheaspectrum,inwhichthehorizontalaxisis

frequency.

ThisconversionismadeusingamathematicalprocessknownasFourier

ocesstakesthetimedomainfunction(theFID)and

convertsitintoafrequencydomainfunction(thespectrum);thisisshownin

chapterwewillstartoutbyexploringsomefeaturesofthe

spectrum,suchasphaseandlineshapes,whicharecloselyassociatedwith

theFouriertransformandthengoontoexploresomeusefulmanipulationsof

NMRdatasuchassensitivityandresolutionenhancement.

4.1TheFID

time

Fourier

transformation

Insection3.6wesawthatthexandycomponentsofthefreeinductionsig-

nalcouldbecomputedbythinkingabouttheevolutionofthemagnetization

discussionweassumedthatthemagneti-

zationstartedoutalongthe−yaxisasthisiswhereitwouldberotatedtoby

a90

◦

purposesofthischapterwearegoingtoassumethatthe

magnetizationstartsoutalongx;wewillseelaterthatthischoiceofstarting

positionisessentiallyarbitrary.

y

x

frequency

Fig.4.1Fouriertransformation

isthemathematicalprocess

whichtakesusfromafunction

oftime(thetimedomain)–such

asaFID–toafunctionof

frequency–thespectrum.

M

x

M

y

time

Fig.4.2Evolutionofthemagnetizationovertime;theoffsetisassumedtobepositiveandthemagnetization

startsoutalongthe

x

axis.

c

JamesKeeler,2002Chapter4“Fouriertransformationanddataprocessing”

2024年3月20日发(作者：呼延冷雪)

4Fouriertransformationanddata

processing

数据处理

Inthepreviouschapterwehaveseenhowtheprecessingmagnetizationcan

bedetectedtogiveasignalwhichoscillatesattheLarmorfrequency–the

commentedthatthissignalwilleventually

decayawayduetotheactionofrelaxation;thesignalisthereforeoftencalled

stionishowdoweturnthissignal,

whichdependsontime,intotheaspectrum,inwhichthehorizontalaxisis

frequency.

ThisconversionismadeusingamathematicalprocessknownasFourier

ocesstakesthetimedomainfunction(theFID)and

convertsitintoafrequencydomainfunction(thespectrum);thisisshownin

chapterwewillstartoutbyexploringsomefeaturesofthe

spectrum,suchasphaseandlineshapes,whicharecloselyassociatedwith

theFouriertransformandthengoontoexploresomeusefulmanipulationsof

NMRdatasuchassensitivityandresolutionenhancement.

4.1TheFID

time

Fourier

transformation

Insection3.6wesawthatthexandycomponentsofthefreeinductionsig-

nalcouldbecomputedbythinkingabouttheevolutionofthemagnetization

discussionweassumedthatthemagneti-

zationstartedoutalongthe−yaxisasthisiswhereitwouldberotatedtoby

a90

◦

purposesofthischapterwearegoingtoassumethatthe

magnetizationstartsoutalongx;wewillseelaterthatthischoiceofstarting

positionisessentiallyarbitrary.

y

x

frequency

Fig.4.1Fouriertransformation

isthemathematicalprocess

whichtakesusfromafunction

oftime(thetimedomain)–such

asaFID–toafunctionof

frequency–thespectrum.

M

x

M

y

time

Fig.4.2Evolutionofthemagnetizationovertime;theoffsetisassumedtobepositiveandthemagnetization

startsoutalongthe

x

axis.

c

JamesKeeler,2002Chapter4“Fouriertransformationanddataprocessing”