Lecture (1) Chapter One: Fourier Transform. Reference: Advanced Engineering Mathematics (By Erwin Kreyszig)

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1 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss Lcur Chpr O: Fourir rsorm Rrc: Advcd Egirig Mhmics By Erwi Kryszig. Priodic ucios: A ucio is sid o priodic i i is did or r d i hr is som posiiv umr such h his umr is cd priod o si Uivrsiy o choogy Dp. O Ecric & Ecroic Eg. Egirig Aysis Lcur os hird yr Lc. Dr. As H. Iss

2 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss. Ev d Odd Fucios: i y = is sid o v i - = or d ii d d I g is odd ucio h g-= -g d g d Emp: si r odd ucios 6 r v ucios Emp: sih o h ucio is odd <<<>>> rigoomric sris: Homwor sc.. Rrc Our prom i h irs w scios o his chpr wi rprsio o vrious ucios o priod =π i rms o h simp ucios si si si h sris h wi ris i his cocio wi o h orm si si Whr r r s such sris is cd rigoomric sris d d r cd coicis o h sris. Usig h summio sig si ] Uivrsiy o choogy Dp. O Ecric & Ecroic Eg. Egirig Aysis Lcur os hird yr Lc. Dr. As H. Iss

3 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss. Fourir ris: Eur ormus s ssum h is priodic ucio o priod π. h c rprsd y rigoomric sris: d d d si... whr ] si Emp: Fid h Fourir sris o h ucio i h igur. ouio: Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lc. Dr. As H. Iss Homwor sc.. Rrcs d wh ] si si si si si si si } { si si 6 d d d d d d d

4 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss. Dirich s codiio: ] si is good vry poi o coiuiy. A poi o discoiuiy h sid o q. is rpcd y i.. h m vu h discoiuiy Emp: Giv <<<>>> Fucios hvig rirry priod: Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lc. Dr. As H. Iss Emp: Fid Fourir sris o h ucio i igur wi q d h. priod hs h uppos ] si si... whr d d d ] d d d d si d

5 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss. wh = v =. wh = odd = 9 = π = 7 = -π si d Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lc. Dr. As H. Iss wh d Homwor sc.. Rrc. Fourir ris o Ev d Odd Fucios h Fourir sris o v ucio o priod is Fourir i sris whr d d h Fourir sris o odd ucio o priod is Fourir si sris si whr si d Homwor sc.. Rrc

6 Uivrsiy o choogy Egirig Aysis Lcur os Dp. O Ecric & Ecroic Eg. hird yr Lcur Lc. Dr. As H. Iss.6 H Rg Epsios: uppos is did o irv d o his irv w w o rprs y Fourir sris. W my corrspod o h is w s = or = usig h Fourir i sris w ruc h v priodic sio o o priod = d whr d d... Usig h Fourir si sris w ruc h v priodic sio o o priod = d si si d whr... h wo sios r cd H-rg psios o h giv ucio. Homwor sc.. Rrc Uivrsiy o choogy Dp. O Ecric & Ecroic Eg. 6 Egirig Aysis Lcur os hird yr Lc. Dr. As H. Iss

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