Please answer the following questions below:

(a) In the figure above match the Fourier pairs. Report your answers as order pairs of the corresponding letters labelling the plots (ex. (X,Y)).
(b) Identify the ordered pairs of Fourier pairs you determined in (a) by their name: Box function, Gaussian, Lorentzian, or Superposition.
(c) Of the Fourier pairs identified in (b), which is its own inverse?

Transcribed Image Text:

Re[f(t)] JA, -a<t <a else A f(t) B Re[f(t)] f(t) = e-at² F(w) F(w) E W 1 a F(w) = = √27 ( 1² + 1² ) F(w) = [cn 8(w-n) w²² 11 A Fourier pair refers to a Fourier transform, 1 f(t) = (11) 2π and its corresponding inverse, 1 F(w) VZπ L dtf (1) pitw (12) Fourier pairs express the same function in two different domains or representation. In some applications, one representation is more convenient than another hence their utility. F Re[f(t)] [e-at, -t> 0 0, else F(w) G nh. F(w) = 2Aa sin(aw) να παω C f(t) Re[f(t)] Jabataba www. t f(t) = [cn Cn e-int √√27T F(w) Lo dwF(w)e-itw H Л F(w) = 1e-w²/4a √2a W Re[f(t)] JA, -a<t <a else A f(t) B Re[f(t)] f(t) = e-at² F(w) F(w) E W 1 a F(w) = = √27 ( 1² + 1² ) F(w) = [cn 8(w-n) w²² 11 A Fourier pair refers to a Fourier transform, 1 f(t) = (11) 2π and its corresponding inverse, 1 F(w) VZπ L dtf (1) pitw (12) Fourier pairs express the same function in two different domains or representation. In some applications, one representation is more convenient than another hence their utility. F Re[f(t)] [e-at, -t> 0 0, else F(w) G nh. F(w) = 2Aa sin(aw) να παω C f(t) Re[f(t)] Jabataba www. t f(t) = [cn Cn e-int √√27T F(w) Lo dwF(w)e-itw H Л F(w) = 1e-w²/4a √2a W

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Ans A ft A a G Box function Gaushan Gauthan fimation Fourier Transform ft Si... View the full answer