From Fourier Series towards Fourier Transform
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1 From Fourir Sris owards Fourir rasform D D d D, d wh lim Dparm of Elcrical ad Compur Eiri
2 D, d wh lim L s Cosidr a fucio G d W ca xprss D i rms of Gw D G Dparm of Elcrical ad Compur Eiri
3 D G G 3 Dparm of Elcrical ad Compur Eiri
4 x G D 3 Dparm of Elcrical ad Compur Eiri
5 xx G D 3 Dparm of Elcrical ad Compur Eiri
6 x D G Fourir rasform 3 Dparm of Elcrical ad Compur Eiri
7 Fourir rasform of a Sial G F[ ] G d Plas o ha his dos o apply oly o apriodic sials, i ca apply o ay sial, priodic or apriodic Now L s alk abou h Ivrs Fourir rasform F [ G ] Dparm of Elcrical ad Compur Eiri
8 D G lim G G Dparm of Elcrical ad Compur Eiri
9 Dparm of Elcrical ad Compur Eiri G G G d G ] [ G F Ivrs Fourir rasform
10 Fourir rasform of a Sial G F[ ] G d Ivrs Fourir rasform F [ G ] G d Dparm of Elcrical ad Compur Eiri
11 Summary Chars Ahad Dparm of Elcrical ad Compur Eiri
12 Dparm of Elcrical ad Compur Eiri cx x d x E c d x ad x ar orhooal if x c * E m d x x if m if m= * d x or if x is complx If a s of fucios x xiss h * d x E c
13 Dparm of Elcrical ad Compur Eiri si cos, cos d a si d b d a si cos b a a x c * E m d x x if m if m= If a s of fucios x xiss h * d x E c
14 Dparm of Elcrical ad Compur Eiri si cos, b a C a C cos C C a b a x c * E m d x x if m if m= If a s of fucios x xiss h * d x E c
15 Dparm of Elcrical ad Compur Eiri D x c * m d x x If a s of fucios x xiss h * d x E c if m if m= d D C D D
16 Fourir rasform of a Sial D d G d Ivrs Fourir rasform D G d G Dparm of Elcrical ad Compur Eiri
17 Som Exampls of Fourir rasform. A impuls fucio. A cosa fucio via ivrs rasform 3. Complx xpoial fucio via ivrs rasform 4. Siosoidal Fucio Dparm of Elcrical ad Compur Eiri
18 Fourir rasform of Impuls Fucio Dfiiio: Fourir rasform of a Sial G G d d G Dparm of Elcrical ad Compur Eiri
19 Fourir rasform of a Cosa Fucio Fourir rasform of a Sial G d d L s ry idircly l s fid h Ivrs Fourir rasform of F F [ G ] G [ ] d d F [ ] F[ ] Dparm of Elcrical ad Compur Eiri
20 Dparm of Elcrical ad Compur Eiri Fourir rasform of a Complx Expoial L s fid h Ivrs Fourir rasform of d G G F ] [ d F ] [ ] [ F ] [ F
21 Dparm of Elcrical ad Compur Eiri Fourir rasform of a Siusoidal Sial cos ] [ ] [cos F F x si ] [ ] [si F F ] [ ] [
22 Dparm of Elcrical ad Compur Eiri Fourir rasform of a Rcaular Fucio / / rc d G F ] [ / / ] [ d rc F / / / / / / / /
23 F[ rc ] / / [ / / si / si / / si c / ] or Dfiiio si si c si si c Dparm of Elcrical ad Compur Eiri
24 Dparm of Elcrical ad Compur Eiri Symmry G G Som Propris of Fourir rasform Scali G a G a a Liariy G k k G k k
25 Som Propris of Fourir rasform --- co. im Shifi liar phas shif G Frqucy Shifi - modulaio G Dparm of Elcrical ad Compur Eiri
26 Som Propris of Fourir rasform --- co. Covoluio - dfiiio * w w d If G w W ad im Covoluio * w G W Frqucy Covoluio w G * W Dparm of Elcrical ad Compur Eiri
27 Som Propris of Fourir rasform --- co. im Diffriaio ad Iraio Diffriaio Iraio G d d G G d G No: Equival o covolvi wih a ui sp fucio Dparm of Elcrical ad Compur Eiri
28 Sial rasmissio hrouh a Liar Chal h y h - Impuls Rspos of a Liar im Ivaria Sysm y * h Y G H h H Dparm of Elcrical ad Compur Eiri
29 Idal Disoriolss rasmissio y k d Y kg d w kow Y G H H k d Dparm of Elcrical ad Compur Eiri
30 H k d Ampliud Rspos k H Phas Rspos H d Dparm of Elcrical ad Compur Eiri
31 Idal vs. No Idal Filrs Idal Filr H d maiud phas No Idal Filr H rc B d maiud B phas B Dparm of Elcrical ad Compur Eiri
32 No Idal Filr H rc B d k maiud B phas B Impuls Rspos h? h F rc B d B si c[ B d Dparm of Elcrical ad Compur Eiri
33 No Idal Filr H rc B d maiud B phas B Impuls Rspos B h si c[ B d ] Is his pracical? h d Dparm of Elcrical ad Compur Eiri
34 No Idal Filr H rc B d Pracical Filr B B B B B h si c[ B d ] h h d d Dparm of Elcrical ad Compur Eiri
35 A Exampl of Pracical Filr H / B H Dparm of Elcrical ad Compur Eiri
36 A Exampl wih =4 Dparm of Elcrical ad Compur Eiri
37 Dparm of Elcrical ad Compur Eiri Ery of a Sial ad Parsval s horm d E * d d G E * d d G E * d G G E * d G E
38 Ery Spcral Dsiy E G G f df d G f ry pr ui badwidh Hz G Dparm of Elcrical ad Compur Eiri
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