Fourier Transform Theorems Presentation

8
حمد عرساڻين احسا ا

description

good presentation on fourier series

Transcript of Fourier Transform Theorems Presentation

  • )()( fXtx If

    And

    Then

    )()( fYty

    )()()()( fbYfaXtbytax

  • If

    Then

    )()( fXtx

    )/(1

    )( afXa

    atx

  • If

    Then

    )()( fXtx

    )()( fXtx

  • If

    Then

    )()( fXtx

    )(*)(* fXtx

  • If

    Then

    )()( fXtx

    )()( fxtX

  • Given that and

    Find using duality theorem

    Let , hence

    It can be said that and

    tj

    ty23

    1

    fuefxfY f 3

    fY

    fj

    tue t

    23

    13

    fj

    fX23

    1

    tuetx t3

    tj

    tX23

    1

    fuefx f3

  • tx fX tX fx fx

    ty fY

    t fc sin tc sin

    f

    f

    tue at fja 21

    tja 2

    1

    fueaf fueaf

    tae

    22 22

    fa

    a

    22 22

    ta

    a

    fa

    e0a

    0a 0a

    0a fae

    22tae2

    a

    f

    ea

    2

    a

    t

    ea

    22 fae

    22 fae

    t fc 2sin tc 2sin

    f

    f