Lecture 7 Introduction to Fourier Transforms

Lecture 7 ELE 301: Signals and SystemsProf. Paul CuffPrinceton UniversityFall 2011-12 Cuff ( Lecture 7)ELE 301: Signals and SystemsFall 2011-121 / 22 Introduction to Fourier TransformsFourier transform as a limit of the Fourier seriesInverse Fourier transform: The Fourier integral theoremExample: the rect and sinc functionsCosine and Sine TransformsSymmetry propertiesPeriodic signals and functionsCuff ( Lecture 7)ELE 301: Signals and SystemsFall 2011-122 / 22 Fourier SeriesSupposex(t) is not periodic. We can compute the Fourier series as ifxwas periodic with periodTby using the values ofx(t) on the intervalt [ T/2,T/2).ak=1T T/2 T/2x(t)e j2 kf0tdt,xT(t) = k= akej2 kf0t,wheref0= 1 two signalsxandxTwill match on the interval [ T/2,T/2) but x(t) will be happens if we letTincrease?]]

Lecture 7 ELE 301: Signals and Systems Prof. Paul Cu Princeton University Fall 2011-12 Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 1 / 22 Introduction to Fourier Transforms Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine ...

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