Fourier Transform and applications - University of Central Florida傅立叶变换及应用-中佛罗里达大学.ppt

该【Fourier Transform and applications - University of Central Florida傅立叶变换及应用-中佛罗里达大学 】是由【小落意心冢】上传分享，文档一共【22】页，该文档可以免费在线阅读，需要了解更多关于【Fourier Transform and applications - University of Central Florida傅立叶变换及应用-中佛罗里达大学 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。FourierTransformandapplications-UniversityofCentralFlorida傅立叶变换及应用-中佛罗里达大学
【通用模板】【教育说课】【述职报告】【工作汇报】
Overview
Transforms
MathematicalIntroduction
FourierTransform
Time-SpaceDomainandFrequencyDomain
DiscretFourierTransform
FastFourierTransform
Applications
Summary
References
Transforms
Transform:
Inmathematics,afunctionthatresultswhenagivenfunctionismultipliedbyaso-calledkernelfunction,andtheproductisintegratedbetweensuitablelimits.(Britannica)
Canbethoughtofasasubstitution
Transforms
Exampleofasubstitution:
Originalequation:x+4x²–8=0
Familiarform:ax²+bx+c=0
Let:y=x²
Solvefory
x=±√y
4
Transforms
Transformsareusedinmathematicstosolvedifferentialequations:
Originalequation:
ApplyLaplaceTransform:
TakeinverseTransform:y=Lˉ¹(y)
FourierTransform
Propertyoftransforms:
Theyconvertafunctionfromonedomaintoanotherwithnolossofinformation
FourierTransform:
convertsafunctionfromthetime(orspatial)domaintothefrequencydomain
TimeDomainandFrequencyDomain
TimeDomain:
Tellsushowproperties(airpressureinasoundfunction,forexample)changeovertime:
Amplitude=100
Frequency=numberofcyclesinonesecond=200Hz
TimeDomainandFrequencyDomain
Frequencydomain:
Tellsushowproperties(amplitudes)changeoverfrequencies:
TimeDomainandFrequencyDomain
Example:
Humanearsdonothearwave-likeoscilations,butconstanttone
Oftenitiseasiertoworkinthefrequencydomain
Applications
Inimageprocessing:
Insteadoftimedomain:spatialdomain(normalimagespace)
frequencydomain:spaceinwhicheachimagevalueatimagepositionFrepresentstheamountthattheintensityvaluesinimageIvaryoveraspecificdistancerelatedtoF